Please cite this article as: Nakashima, N.A., Halali, E. & Halevy, N., Third parties promote cooperative norms in repeated interactions, Journal of Experimental Social Psychology (2016), doi: 10.1016/j.jesp.2016.06.007
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Third Parties Promote Cooperation
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Third Parties Promote Cooperative Norms in Repeated Interactions
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Nathaniel A. Nakashima, Eliran Halali, & Nir Halevy
Author note: We thank Christine Hart for assistance with programming the experiment in Ztree, Lauren Agnew and Michele Peretz for assistance with carrying out the experiment, and participants at the seminars at Harvard, MIT, Brown, Northwestern, and the University of Virginia for discussion and comments.
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Abstract How likely are third parties to intervene in repeated conflicts between adversaries? Can third party
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intervention redirect competitive interactions toward collectively beneficial cooperation? Does
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mutual cooperation persist when the third party can no longer intervene in the conflict? To address these theoretically and practically important questions, we introduce the Repeated Peacemaker
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Game. Adversaries and third parties interacted for 60 game rounds in our incentivized experiment,
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producing a rich dataset of 7,200 decisions. Participants made decisions under one of two conditions: In the Early Intervention condition, third party intervention was initially possible and
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then became impossible. In the Late Intervention condition, third party intervention was initially impossible and then became possible. Third parties in the Early Intervention condition intervened at
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high rates and established cooperative norms that outlasted the intervention period, resulting in sustainable cooperation even after intervention was no longer possible. By comparison, third parties
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in the Late Intervention condition intervened at relatively lower rates, but still effectively promoted cooperation, despite the initial history of competition between adversaries. We find strong evidence for ‘conditional cooperation’, whereby adversaries and third parties reciprocate each other’s choices in preceding rounds: Adversaries were more likely to cooperate when third parties intervened in the preceding round; third parties, in turn, were more likely to intervene when one or both adversaries cooperated in the preceding round than if both adversaries competed in the preceding round. These findings help explain when, why, and how third parties promote cooperation in groups.
Keywords: Competition and cooperation, conflict, third party intervention, repeated game, norms.
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Human conflict is seldom a private matter. Adversaries are typically surrounded by third parties who observe the conflict directly (Bernhard, Fischbacher, & Fehr, 2006; De Wit, Greer,
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& Jehn, 2012; Fehr & Fischbacher, 2004) or learn about it indirectly (Feinberg, Willer, &
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Schultz, 2014; Wu, Balliet, & Van Lange, 2016). Third parties’ awareness of others’ conflicts puts them in a position to choose whether or not they wish to intervene in it. The possibility of
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third party intervention, in turn, is likely to influence adversaries’ decisions to cooperate or
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compete. Although third parties have played a pivotal role in promoting cooperation since the dawn of history (Boehm, 2012; Rubin, 1980), surprisingly little is known about the processes
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that propel individuals to intervene in others’ conflicts, and allow them to effectively promote sustainable cooperation.
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Decisions to cooperate or compete typically take place within relational contexts that involve repeated interactions (e.g., between siblings, coworkers, or political rivals). Repeated
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interactions, in turn, enable the use of contingent strategies (e.g., tit-for-tat; Axelrod, 1984), facilitate learning (Erev & Roth, 2014), and allow the development of social norms (Ostrom, 1999; Peysakhovich & Rand, 2015). Considering these two fundamental characteristics of social conflicts in tandem – the possibility of intervention by a third party and the existence of repeated interactions – raises theoretically and practically important questions: How likely are third parties to intervene in repeated conflicts between adversaries? Can third party intervention redirect competitive interactions towards collectively beneficial cooperation? To what extent does mutual cooperation persist when the third party can no longer intervene in the conflict? The current research addresses these three fundamental questions. To model the interdependence between adversaries and third parties in repeated conflict, we use an iterated version of the Peacemaker Game, an experimental paradigm specifically
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designed to investigate the behavior of adversaries and third parties in conflict (Halevy & Halali, 2015). In the Peacemaker game, two participants are assigned to the roles of adversaries and a
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third participant is assigned to the role of a third-party. The two adversaries choose to cooperate
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or compete1; the third-party chooses whether or not to intervene in the conflict. The two adversaries and the third party make their choices simultaneously.
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If the third-party chooses not to intervene, adversaries’ payoffs are based on their
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respective choices in a two-person Prisoner’s Dilemma game and the third party receives a fixed payoff irrespective of adversaries’ choices. In the current research we operationalized the
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Peacemaker Game such that, if the third party chose not to intervene in a given round of the game, the third-party received 25cents, and adversaries received 10, 20, 30, or 40 cents
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depending on their respective choices in the Prisoner’s Dilemma Game (see Figure 1, Table 1a for the complete payoff structure).
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If the third-party chooses to intervene, adversaries’ payoffs are based on their respective choices in a two-person Maximizing Difference game, which is a much more cooperative situation, and the third party receives a variable payoff that depends on adversaries’ choices. In the current research we operationalized the Peacemaker Game such that, if the third party chose to intervene in a given round of the game, the third-party received 10 cents if both adversaries competed; 25 cents if one of them competed while the other cooperated; and 40 cents if both adversaries cooperated. Adversaries received 10, 20, 30, or 40 cents depending on their respective choices in the Maximizing Difference Game (see Figure 1, Tables 1b and 1c). Third party intervention in the Peacemaker Game introduces side-payments that effectively change the nature of the situation adversaries are facing from a highly competitive situation to a highly cooperative situation. A close examination of Tables 1a and 1b will reveal
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that third-party intervention in the Peacemaker Game simultaneously rewards cooperation by 10 cents and punishes competition by 10 cents. This simple transformation rule changes the game
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adversaries are playing from Prisoner’s Dilemma (Table 1a, where competition is the dominant
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strategy, and in which unilateral competition results in the best possible outcome for a player) to a Maximizing Difference game (Table 1b, where cooperation is the dominant strategy, and in
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which mutual cooperation results in the best possible outcome to a player; Halevy & Katz,
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2013). By opting to intervene in the conflict the third-party also becomes vulnerable to adversaries’ choices: If both adversaries cooperate, the third-party gains from intervening
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whereas if both adversaries compete, the third-party loses from intervening. Thus, third-party intervention simultaneously modifies the situation for adversaries and exposes the third-party to
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risk.
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Our perspective on third party intervention in conflict challenges and complements existing models of third party behavior, which assume third parties unilaterally influence other parties’ outcomes and can never benefit from intervening in other parties’ conflicts (Balliet, Mulder, & Van Lange, 2011; Bernhard, Fischbacher, & Fehr, 2006; Charness, Cobo-Reyes, & Jimenez, 2008; Fehr & Fischbacher, 2004; Fehr, Fischbacher, & Gachter, 2002; Molenmaker, de Kwaadsteniet, & van Dijk, 2014). We propose that, whereas withholding intervention is a riskaverse strategy that allows third parties to keep their resources to themselves, choosing to intervene can result in gains or losses, depending on the conflict’s outcome. Successfully promoting cooperation provides third parties with a positive return on their investment. This aspect of our model captures tangible and intangible benefits that accrue to third parties who
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promote cooperation (e.g., exchange opportunities and status conferral). In contrast, interventions that fail to promote cooperation result in a loss relative to not intervening (e.g., of
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the resources invested in intervening; diminished reputation).
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Recent research using the Peacemaker Game demonstrated that the possibility of third party intervention is sufficient to significantly increase cooperation among adversaries in a single
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interaction, and that cost-benefit calculations underlie third parties’ intervention decisions.
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Specifically, intervention rates were under 8% when third parties could only lose from intervening; at 35% when third parties could neither gain nor lose from intervening; and
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exceeded 80% when third parties could only gain from intervening (Halevy & Halali, 2015). However, many conflicts involve repeated interactions rather than just a single, fleeting
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interaction. The existence of repeated interactions can fundamentally change interactive behavior as it allows the use of contingent strategies, and enables learning and norm development
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(Axelrod & Hamilton, 1981; Erev & Roth, 2014; Kramer, 1999; Peysakhovich & Rand, 2015). Acknowledging the recurring nature of many conflicts, the current research investigates the choices of adversaries and third parties in repeated interactions. Shadow of the Past: Third Parties as Game Changers
Research on learning in repeated interactions suggests decision makers tend to choose options that resulted in favorable outcomes in similar situations in the past (Erev & Roth, 2014). Thus, adversaries are likely to learn to cooperate over time, if cooperation serves their interests well. By incentivizing cooperation relative to competition, third parties can facilitate such learning by the adversaries. However, compared to third parties who are not aware of any competitive history among adversaries, third parties who observe a history of competition among adversaries may perceive the repeated conflict as impervious to intervention. They may doubt
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that adversaries can learn to cooperate late in their repeated interaction and therefore be unwilling to risk resources to intervene. Hence, a history of conflict may undermine third parties’
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willingness to intervene, even though this is exactly when external intervention is most needed to turn around the interaction. Including both an early intervention and a late intervention condition
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in our experiment allowed us to test our ‘bad blood hypothesis’, which stipulates:
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hinder third parties’ willingness to intervene.
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Hypothesis 1: Observing a history of competition between adversaries will
An additional, interrelated question concerns the effectiveness of third party intervention
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following a history of conflict. To explore the extent to which introducing the possibility of third party intervention following a history of conflict can redirect repeated interactions toward
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collectively beneficial cooperation, we compare cooperation rates before the possibility of third party intervention is introduced to cooperation rates after the possibility of third party
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intervention is introduced in the late intervention condition. Thus, a second goal of our experiment was to test the ‘transformation hypothesis’, which postulates: Hypothesis 2: Third party intervention will increase cooperation among adversaries even following a history of conflict, thereby transforming the course of their repeated interaction.
It is important to note that we do not expect third party intervention following a history of conflict to increase cooperation levels such that they would be comparable to those observed in situations in which there was no prior history of conflict. Instead, our focus is on whether the possibility of third party intervention increases cooperation among adversaries following a history of conflict. The Emergence of Cooperative Norms
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There is considerable consensus among researchers that the mere possibility of third party intervention is sufficient to significantly promote cooperation (Balliet, Mulder, & Van Lange,
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2011; Charness, Cobo-Reyes, & Jimenez, 2008; Lergetporer et al., 2014). However, it is a
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pertinent open question whether continuous monitoring and sanctioning is required to enforce compliance with cooperative norms, or whether early repeated experiences of mutually
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beneficial cooperation in the presence of a third party will result in persistent cooperative norms
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that outlast the intervention period, thereby allowing adversaries to maintain mutual cooperation even after the third party can no longer intervene in the interaction.
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Third parties who incentivize cooperation early in the interaction help adversaries experience the benefits of mutual cooperation, thereby facilitating their learning of cooperative
reinforces adversaries’ cooperative choices, which in turn, increases the likelihood of future
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cooperative choices (Erev & Roth, 2014). Once such learning takes place and the norm of cooperation is internalized, it is likely to be sustained even when the third party can no longer intervene. Our experiment was designed to test the ‘norm development hypothesis’, which postulates:
Hypothesis 3: Early third party intervention will facilitate the development of sustainable cooperative norms in repeated interactions that will persist even after the third party can no longer intervene. Our experiment tested this hypothesis by comparing cooperation rates before the possibility of third party intervention is removed to cooperation rates after the possibility of third party intervention is removed in the early intervention condition.
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In sum, our experiment was designed to test three hypotheses: The bad blood hypothesis, according to which observing a history of conflict diminishes third parties’ willingness to
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intervene; the transformation hypothesis, according to which late third party intervention can
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effectively promote cooperation, thereby redirecting the course of competitive repeated interactions; and the norm development hypothesis, according to which early third party
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intervention helps adversaries develop sustainable norms of cooperation that outlast the
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intervention period. We test the first hypothesis by comparing third parties’ intervention rates in the early and late intervention conditions. We test the second hypothesis by comparing
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cooperation rates before and after the possibility of third party intervention is introduced in the late intervention condition. We test the third hypothesis by comparing cooperation rates before
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and after the possibility of third party intervention is removed in the early intervention condition. Finally, our repeated game paradigm also allows us to explore whether third parties are
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‘conditional cooperators’, whose willingness to intervene in others’ conflict is contingent on adversaries’ cooperative behavior (cf. Fischbacher, Gächter, & Fehr, 2001; Frey & Meier, 2004). Recall that third party intervention in the Peacemaker Game is costly to the third party when both adversaries compete; beneficial to the third party when both adversaries cooperate; and neither costs nor benefits the third party when one adversary cooperates while the other competes. Hence, finding that third parties condition their intervention on the cooperation of one or both adversaries will provide evidence that third parties are risk averse and motivated, at least in part, by the desire to maximize their own outcomes (Halevy & Halali, 2015). In the current paper we test the extent to which third parties are conditional cooperators with a series of lagged analyses that use decisions in earlier rounds of the repeated game to predict third party intervention in subsequent rounds of the repeated game.
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 10 The Experiment Method
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Participants. We recruited 144 Stanford University students and staff (56% female; age:
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M = 22.82, SD = 6.31; 80.56% US citizens; ethnicity 25.00% Caucasian, 39.58% Asian, 5.56% African–American, 12.50% Hispanic, and 17.36% other) to participate in a laboratory study
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involving an “interactive decision making” task. Sessions lasted between 30 and 60 minutes. We
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had set an a priori target of 144 participants in advance (i.e., 24 three-person groups in each condition). Previous research suggested that our target sample size was more than sufficient to
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detect effects using a similar experimental design (e.g., Halevy, Weisel, & Bornstein, 2012). The fact that participants would be making decisions across multiple rounds ensured that we would
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collect a rich data set of 7,200 total decisions (96 adversaries x 60 rounds + 48 third parties x 30 rounds). The number of participants per session ranged from 6 to 21, depending on the
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availability of participants. We paid participants $10 for their time in addition to their earnings from the decisions they made in the experiment. Procedure. We provided participants with written instructions explaining that we will randomly assign them to three-person anonymous groups and that the decision of each person in the group will influence his or her own outcome as well as the outcomes of the other two individuals in the group. The terms adversary, third party, conflict, peacemaking, cooperation, and competition, or any equivalent terms, were never mentioned in the instructions. Instead, colors and letters were used to denote participants’ roles and choice alternatives, respectively. We randomly assigned participants to one of three roles: “red,” “blue,” or “green.” Red and blue were the adversaries, who could choose either “Q” or “S.” Because red and blue were perfectly symmetric roles, we collapsed the data in our experiment across the different colors
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 11 used to denote the adversaries’ roles. Green was the third party, who could choose either “M” or “R.” As Figure 1a shows, the payoff structure conformed to the Prisoner’s Dilemma Game; all of
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the participants learned that, in each round, if both red and blue choose “Q” (i.e., mutual cooperation), they will each get $0.30; if both red and blue choose “S” (i.e., mutual competition),
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they will each get $0.20; and if one of them chooses “Q” and the other chooses “S” (i.e.,
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unilateral cooperation/competition), the person choosing “Q” will get $0.10 and the person
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choosing “S” will get $0.40.
Experimental sessions were randomly assigned to one of two conditions: Early
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Intervention or Late Intervention. Participants knew that the experiment involved multiple decision rounds, but did not know how many rounds. In rounds 31-60 of the Early Intervention
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condition and rounds 1-30 of the Late Intervention condition, the participant assigned to the role of green (i.e., the third party) could not intervene in the conflict; instead individuals in the role of
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green could only observe red’s and blue’s decisions and outcomes on their own screens. In rounds 1-30 of the Early Intervention condition and rounds 31-60 of the Late Intervention condition, participants assigned to the role of green could choose either “M” (i.e., not intervene) or “R” (i.e., intervene).
Participants learned that, in each round when intervention was possible, if green were to choose “M”, then green would receive $0.25 no matter what blue and red choose, and red’s and blue’s payoffs would be influenced only by their own choices (in a Prisoner’s Dilemma game, as in all the rounds in which green could not intervene). However, if green were to choose “R”, then green would receive an amount of $0.10, $0.25, or $0.40, depending on the choices of blue and red. Thus, choosing to intervene introduced outcome interdependence between the third party and the adversaries. As Figure 1b shows, choosing “R” changed the payoff structure to a
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 12 Maximizing Difference Game: If red and blue were to choose “Q” (i.e., mutual cooperation), they would each get $0.40, and green would also get $0.40. If red and blue were to choose “S”
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(i.e., mutual competition), they would each get $0.10 and green would also get $0.10. If one of the adversaries were to choose “Q” while the other chose “S” (i.e., unilateral
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cooperation/competition), then the player who chose “Q” would get $0.20 and the player who
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chose “S” would get $0.30, and green would get $0.25 (i.e., green neither gains nor loses relative
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to not intervening). This payoff structure was designed such that the main difference between intervening and not intervening from the perspective of green was that the former option resulted
to green (i.e., it is a higher risk option).
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in fixed payoffs (i.e., no variance) to green, whereas the latter option resulted in variable payoffs
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Participants interacted anonymously via computers. Participants’ assignment to 3-person groups, and to roles within groups, was fixed throughout the sixty rounds of the repeated game.
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Each computer station was visually partitioned from all others using large white cardboards. Ztree software was used for conducting the study (Fischbacher, 2007). At the beginning of each round, players were prompted to make their decision. Third-parties only made decisions in rounds in which they could intervene, otherwise they were observing the other players’ decisions and outcomes on their screens. The round number appeared in the top left-hand corner of the screen. Players’ total profit in points (accumulated across all rounds) was displayed at the center of the screen. Below that information were the options that players could select. After they indicated their choice, players clicked the “OK” button at the right-hand border of the screen and were asked to wait for other players in the session to make their decisions (Appendix A). Only after all the players in the session made their choices in a given round did they receive feedback about the choices and profits of the players in their group including their own. Once they were
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 13 finished looking at this feedback, they clicked the “continue” button to advance to the next round (Appendix A). After all 60 rounds ended, participants responded to a post-experimental
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questionnaire in which they indicated their motivations during the game and demographic
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information. At the end of each session participants were dismissed and paid one by one, in private.
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Overall, this experimental design resulted in a rich dataset of 7,200 decisions made by
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adversaries and third parties. The total payoff for each red and blue player was calculated by adding the amount of cents they earned across all rounds rounded to the nearest hundred. Since
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green players made exactly half the number of decisions red and blue players made, we doubled their total earnings and rounded them to the nearest hundred. This procedure ensured that,
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overall, participants assigned to different roles earn equivalent amounts. Red and blue players earned on average $29.15 and green players earned on average $32.33 in the experiment.
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Post-experimental questionnaire. After participants made all of their decisions, they indicated how much each of four considerations influenced their decisions in the game. The four considerations were the desires to maximize: (a) personal profits; (b) the joint profits of the two adversaries and the third party; (c) the relative difference between one’s personal profits and others’ profits; and (d) equality in profits. Participants rated their motivations on 5-point scales ranging from 1=”Not at all” to 5=”Very much”. In addition to these items, participants responded to two open-ended questions in which they could explain their choices in the game and share any comments about the study. Finally, participants reported their demographic information. In this section, we have reported all measures and manipulations that were part of the experiment, and no participants were excluded. Results
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 14 Early versus late third party intervention. Figure 2 depicts the intervention rates of third parties across the 60 rounds of the game in the Early Intervention and Late Intervention
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conditions. Our data on third party intervention behavior from the Repeated Peacemaker Game
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(N = 1440 decisions2) consists of repeated binary decisions of participants in fixed groups. In order to account for this nested structure, we perform a set of repeated measures logistic
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regressions estimated using Generalized Estimating Equations (GEE), with fixed effects for
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condition and the possibility of intervention and random effects for participants nested in groups. We used the GENMOD procedure of the SAS software to conduct the GEE analysis. Our
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analysis assumes an autoregressive, AR(1), correlation structure clustered by participant. Our dependent variable, intervening, obtains a value of 1 if the third party decided to intervene and 0
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otherwise. We use a dummy variable to indicate the condition that a participant was randomly assigned to, where 1 indicates that the participant was in the Early Intervention condition and 0
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indicates that the participant was in the Late Intervention condition. In Table 1, we provide the coefficient estimates of the GEE. In Model 1, we find no effect of round on the decision to intervene. In Model 2, we find that third parties in the Early Intervention condition were significantly more likely to intervene compared to third parties in the Late Intervention condition. As shown in Figure 2, third parties in the Early Intervention condition intervened at an average rate of 99% while third parties in the Late Intervention condition intervened at an average rate of 85% (GEE, p < .0001). This finding indicates that, consistent with the bad blood hypothesis (Hypothesis 1), third parties are more likely to intervene in repeated conflicts if they have not been exposed to adversaries’ conflict history. Observing a history of repeated conflict plausibly highlights the risk inherent in the choice to intervene (i.e., the potential costs to the third party if the adversaries continue to compete),
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 15 thereby leading a significant portion of third parties to withhold intervention. In Model 3, the effect of condition remains significant when controlling for round. In Model 4, we include the
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interaction between round and condition, which is non-significant. Conditional third party intervention. We further explored the possibility that third
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parties’ decisions to intervene were contingent on adversaries’ behavior by examining how
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behavior in a given round (k) influenced behavior in the following round (k+1). Given the costs
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and benefits associated with intervening, the manner in which third parties condition their intervention decisions on adversaries’ past behavior can reveal the motivations underlying their
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behavior. For instance, intervening primarily following rounds in which both adversaries defected constitutes a more prosocial strategy because it entails high risk to the third party (who
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will pay a cost if both adversaries continue to compete) and can produce the greatest benefit for adversaries in the long run by helping transform the nature of their interaction. In contrast,
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intervening primarily following rounds in which both adversaries cooperated is less prosocial, because the third party gains from doing so (if both adversaries continue to cooperate) and intervention under such circumstances produces a smaller benefit for adversaries, who were able to establish mutual cooperation without the third party’s help. In the following analyses, we examine which of these strategies characterized third parties’ behavior. We conducted a GEE analysis to determine whether third parties’ decisions to intervene were conditional on adversaries’ decisions to cooperate in previous rounds. This analysis consists of only the 30 rounds during which third party intervention was possible, and uses decisions to intervene and cooperate in each round as predictors of the decision to intervene in the subsequent round (N = 1392 decisions3). Our dependent variable, intervening, obtains a value of 1 if the third party decided to intervene and 0 otherwise. We used a dummy variable to
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 16 indicate the condition that a participant was randomly assigned to, where 1 indicates that the participant was in the Early Intervention condition and 0 indicates that the participant was in the
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Late Intervention condition. We included a dummy variable to indicate whether each third party
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intervened in the previous round, where 1 indicates that the third party intervened and 0 otherwise. We also included dummy variables to indicate whether neither, only one, or both
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adversaries cooperated in the previous round.
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In Table 2, we provide the coefficient estimates of the GEE. Similar to our previous findings, we find that third parties in the Early Intervention condition were significantly more
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likely to intervene compared to third parties in the Late Intervention condition. In addition, we find that third parties were more likely to intervene if they had intervened in the previous round
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and when either one or both adversaries cooperated (rather than mutually defected) in the previous round. These results indicate that third parties’ decisions to intervene are sensitive to
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adversaries’ level of cooperation in the previous round. More specifically, they suggest that third parties are reluctant to intervene when doing so might be costly to them (i.e., when they expect both adversaries to compete), even though conflicts characterized by ongoing mutual competition are those in which third party intervention is most required to turn around the interaction. Thus, the conditional strategies third parties employed did not seem to be prosocially oriented. It is important to note that condition remained a significant predictor of intervention even when we controlled for adversaries’ and third parties’ behavior in the previous round. Put differently, whether the possibility of third party intervention was introduced early or late in the repeated game explains variance in intervention rates above and beyond adversaries' and third parties' behaviors in the previous round.
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 17 We subsequently conducted the same analysis noted above with third parties in the Late Intervention condition only. The purpose of this analysis was to determine whether and how
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adversaries’ average cooperation rates in rounds 1-30 (N = 720 decisions4) influenced third
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parties’ choices to intervene or not to intervene in rounds 31-60. Table 3 provides the coefficient estimates of the GEE. Model 1 shows that third parties were significantly more likely to
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intervene when they observed higher cooperation rates between adversaries in rounds 1-30.
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These results lend additional support to our “bad blood hypothesis”, which postulated that observing a history of conflict between adversaries diminishes third parties’ willingness to
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intervene. In Model 2, we added third parties’ decisions to intervene and adversaries’ decisions to cooperate in the previous round as predictors. Similar to our previous GEE analysis (presented
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in Table 2), we find that third parties were significantly more likely to intervene when they themselves intervened in the previous round, and when one or both adversaries cooperated in the
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previous round as compared to when both adversaries had defected. That is, third parties were more likely to intervene when their risk (and the long-term benefit to adversaries) was lower rather than higher. We note that adversaries’ average cooperation rates in rounds 1-30 are no longer a significant predictor of third party intervention when considered jointly with behavior in the previous round. Thus, although we find support for our “bad blood hypothesis”, these results indicate that third parties’ willingness to intervene is more sensitive to behaviors that occurred in the immediate past compared to the relatively distant past. The motivations underlying third party intervention. In the previous section we drew inferences about the motivations underlying third party intervention from the contingent strategies third parties employed. Here we aim to explicitly address this question using the motivations participants reported at the end of the study. In the post-experimental questionnaire,
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 18 participants rated the extent to which their decisions were motivated by the desire to maximize personal profits (i.e., an individualistic orientation; M = 4.88, SD = .44); the desire to maximize
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the relative differences between their own and others’ outcomes (i.e., a competitive orientation;
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M = 1.29, SD = .62); the desire to maximize everyone’s joint profits (M = 4.02, SD = 1.02); and the desire to maximize equality in outcomes (M = 2.75, SD = 1.49). Because the latter two items
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(i.e., the desires to maximize joint profits and equality in outcomes) fit together theoretically
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(Van Lange, 1999) and were positively correlated among third parties in our data (r (48) = .41, p = 0.004), we averaged them to form a prosociality index (M = 3.39, SD = 1.06). Third parties’
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individualistic orientation did not correlate with either their competitive (r (48) = -.17, p = .235) or prosocial orientation (r (48) = -.01, p = .955). Their competitive and prosocial orientations
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were also uncorrelated (r (48) = .10, p = .496). This pattern may reflect that fact that, in the Peacemaker Game, intervention allows third parties to simultaneously maximize both individual
> .05).
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and collective gains. Third parties’ self-reported social motives did not differ by condition (all ps
We conducted a GEE analysis to explore the role that these three self-reported motivations played in shaping third parties’ intervention decisions. Similar to our previous GEE analyses of third party intervention, intervening was our dependent variable and obtained a value of 1 if the third party decided to intervene and 0 otherwise. We used a dummy variable to indicate the condition that a participant was randomly assigned to, where 1 indicates that the participant was in the Early Intervention condition and 0 indicates that the participant was in the Late Intervention condition. Finally, we mean-centered each self-reported motivation and used it to predict third party intervention. Table 4 provides the coefficient estimates of the GEE analysis. In Models 1, 2, and 3, we show how each self-reported motivation separately predicts
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 19 intervention decisions, controlling for condition and round. In Models 4, 5 and 6, we added the condition by motivation interactions. In Model 7, we included all three social motives together.
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Finally, in Model 8 we included all three social motives and each of their interactions with the experimental condition.
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When each motivation was entered separately to predict third parties’ intervention
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behavior, only the individualistic motivation emerged as a significant predictor (Model 1). This
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finding is consistent with our inferences from the conditional strategies identified in the previous GEE analyses, and suggests that decisions to intervene reflected primarily third parties’
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motivation to maximize their own outcomes. Importantly, the findings summarized in Table 4 reveal that none of the self-reported motivations significantly moderated the effect of condition
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on third parties’ decisions to intervene (Models 4-6), even when including all of the motivations as predictors (Models 7 and 8). Across all of the models, our experimental manipulation of the
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timing at which third parties could intervene (early vs. late) remained a significant predictor of third party intervention. These findings suggest that the effect of early versus late intervention was robust to individual differences in social motivations. Adversaries’ cooperation rates. Figure 2 depicts adversaries’ cooperation rates across the 60 rounds of the game in the Early Intervention and Late Intervention conditions. Our data on cooperative behavior from the Peacemaker Game (N = 5760 decisions5) consists of repeated binary decisions of participants in fixed groups. In order to account for this nested structure, we performed a set of repeated measures logistic regressions estimated using Generalized Estimating Equations (GEE), with fixed effects for condition and the possibility of intervention and random effects for participants nested in groups. We used the GENMOD procedure of the SAS software to conduct the GEE analysis. Our analysis assumes an autoregressive, AR(1),
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 20 correlation structure. We account for the fact that each participant was associated with multiple choices in our dataset by including a random participant effect in the analysis; results were
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identical when adding a unique group ID to account for the nested structure of the data. Our
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dependent variable, cooperation, obtains a value of 1 if the cooperative choice is selected and 0 otherwise. We use a dummy variable to indicate the condition a participant was randomly
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assigned to, where 1 indicates that the participant was in the Early Intervention condition and 0
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indicates that the participant was in the Late Intervention condition. In addition, we use a dummy variable to indicate whether the third party could intervene, where 1 indicates that third party
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intervention was possible and 0 indicates that it was not possible. Finally, we treat round as a continuous variable with values ranging from 1-30 in each of the two halves of the repeated
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game.
In Table 5, we provide the coefficient estimates of the GEE. In Model 1, we find a
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significant negative effect of round on cooperation. In Model 2, we find that participants in the Early Intervention condition were significantly more likely to cooperate compared to participants in the Late Intervention condition. In Model 3, we show that participants were significantly more likely to cooperate when third party intervention was possible compared to when it was not possible. Model 4 shows that round, condition, and the possibility of intervention, were all significant when entered simultaneously to predict cooperation rates. Models 5 and 6 show that the interaction between condition and the possibility of third party intervention is significant (Model 5), and remains significant after controlling for the 2-way interactions between round and condition, and round and the possibility of third party intervention, as well as their 3-way interaction, which did not reach accepted levels of significance (Model 6).
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 21 In Table 6, we decompose the interaction between condition and the possibility of third party intervention. Consistent with the transformation hypothesis (Hypothesis 2), our analysis
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revealed a significant increase in cooperation rates after the possibility of third party intervention
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was introduced in the Late Intervention condition. As Figure 2 shows, in the Late Intervention condition, adversaries cooperated 47% of the time in rounds 1-30 and 79% of the time in rounds
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31-60 (GEE, p < .0001). This finding suggests that introducing the possibility of third party
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intervention can transform a history of repeated competition into cooperation. Table 6 also shows that cooperation rates were comparable in the Early and Late Intervention conditions for rounds
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in which third party intervention was possible (GEE, p = .1553). In addition to finding evidence consistent with our transformation hypothesis, our
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findings also lend support to the norm development hypothesis (Hypothesis 3). Specifically, our analysis revealed no significant decrease in cooperation rates after the possibility of third party
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intervention was removed. In the Early Intervention condition, adversaries cooperated 92% of the time in rounds 1-30 and 85% of the time in rounds 31-60 (GEE, p = .2575; Table 6). Thus, early third party intervention allowed adversaries to sustain mutually beneficial cooperation even when the third party could no longer intervene in their repeated interaction. In particular, these results are notable because when adversaries played the Prisoner’s Dilemma game (in rounds in which third parties could not intervene), cooperation rates were significantly higher in the Early Intervention condition as compared with the Late Intervention condition (GEE, p < .0001). Finally, we found that cooperation rates were comparable in rounds 31-60 in the Early Intervention and Late Intervention conditions (GEE, p = .5402), despite the fact that participants in the former condition played a more competitive game in these rounds (i.e., they played a Prisoner’s Dilemma game 100% of the time in these rounds) than participants in the latter
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 22 condition (who played a Maximizing Difference game 85% of the time in these rounds). These findings are testament to the strength and endurance of the cooperative norm that emerged in the
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Early Intervention condition. Conditional cooperation. We conducted additional GEE analyses to examine the extent
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to which adversaries’ decisions to cooperate were conditional on third parties’ decisions to
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intervene, as well as their own and their counterparty’s decisions to cooperate, in previous
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rounds. This analysis consists of only the 30 rounds for which third party intervention was possible, and uses decisions to intervene and cooperate in each round as predictors of
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adversaries’ decision to cooperate in the subsequent round (N = 2784 decisions6). Our dependent variable, cooperation, obtains a value of 1 if an adversary chose to cooperate and 0 otherwise.
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We used a dummy variable to indicate the treatment that a participant was randomly assigned to, where 1 indicates that the participant was in the Early Intervention condition and 0 indicates that
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the participant was in the Late Intervention condition. We included a dummy variable to indicate whether each third party intervened in the previous round, where 1 indicates that the third party intervened and 0 otherwise. We also included dummy variables to indicate whether each adversary cooperated in the previous round and whether their counterpart cooperated in the previous round, where 1 indicates the cooperative choice and 0 otherwise. In Table 7, we provide the coefficient estimates of the GEE analysis. Model 1 shows that we did not find a significant effect of condition on the decision to cooperate. Note that we did not expect to find a significant effect of condition, as there was no significant difference in adversaries’ cooperation rates for rounds in which third party intervention was possible (see Table 6). However, we find that adversaries were significantly more likely to cooperate when the third party intervened in the previous round. This finding provides additional evidence for the
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 23 effectiveness of third party intervention in promoting cooperation. In addition, adversaries were significantly more likely to cooperate when they cooperated in the previous round and when their
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counterpart cooperated in the previous round. Model 2 shows a significant interaction between
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adversaries’ decisions to cooperate. Probing this interaction, we find that adversaries were more likely to cooperate when both of them cooperated in the previous round (all ps < .0001 for all
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comparisons with mutual cooperation). These findings replicate and extend previous research
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findings concerning the effectiveness of reciprocal strategies in repeated interactions in the Prisoner’s Dilemma game (Axelrod, 1984; Axelrod & Hamilton, 1981).
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We subsequently repeated the same analysis4 within the Early Intervention condition, to determine whether adversaries’ decisions to cooperate in rounds 31-60 were influenced by
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intervention and cooperation rates in rounds 1-30 (N = 1440 decisions7). Table 8 provides the coefficient estimates of the GEE. Model 1 shows that, the higher third party intervention rate was
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in rounds 1-30, the more likely the adversaries were to cooperate. Model 2 shows that adversaries were significantly more likely to cooperate when their cooperation rate in rounds 130 was higher. Finally, in Models 3 and 4 we added adversaries’ decisions to cooperate in the previous round as predictors. We find that adversaries were significantly more likely to cooperate when either one or both of them cooperated in the previous round (all ps < .0001 for all comparisons with mutual cooperation). We note that third parties’ average intervention rates and adversaries’ average cooperation rates in rounds 1-30 are no longer significant predictors of adversaries’ cooperation in rounds 31-60 when considered together with behavior in the previous round. These results suggest that, similar to third parties' decisions to intervene, adversaries’ decisions to cooperate may be more responsive to the immediate past (i.e., the previous round) compared to the distant past (rounds 1-30).
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 24 The motivations underlying cooperation. Similar to third parties, adversaries rated how much their decisions were motivated by the desire to maximize personal profits (i.e., an
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individualistic orientation: M = 4.36, SD = .91); the relative difference in outcomes
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(competitiveness; M = 1.99, SD = 1.34); everyone’s joint profits (M = 3.96, SD = 1.14); and equality in outcomes (M = 3.13, SD = 1.34). Because the latter two items (i.e., the desires to
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maximize joint profits and equality in outcomes) fit together theoretically and were positively
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correlated among adversaries in our data (r (96)=.62, p < 0.0001), we averaged them to form a prosociality index (M = 3.45, SD = 1.16). Adversaries’ individualistic orientation did not
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correlate with their competitive orientation (r (96) = .08, p = .439), but was negatively correlated with prosocial orientation (r (96) = -.28, p = .005). Their competitive and prosocial orientations
condition (all ps > .05).
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were negatively correlated (r (96) = -.20, p = .053). Adversaries’ social motives did not differ by
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We conducted a GEE analysis to explore the role that these self-reported motivations played in shaping adversaries’ decisions to cooperate. Similar to our previous GEE analyses of adversaries’ cooperation decisions, cooperating was our dependent variable and obtains a value of 1 if an adversary decided to cooperate and 0 otherwise. We used a dummy variable to indicate the condition that a participant was randomly assigned to, where 1 indicates that the participant was in the Early Intervention condition and 0 indicates that the participant was in the Late Intervention condition. In addition, we use a dummy variable to indicate whether the third party could intervene, where 1 indicates that third party intervention was possible and 0 indicates that it was not possible. Finally, we mean-centered each self-reported motivation and used them to predict adversaries’ decisions to cooperate. Table 9 provides the coefficient estimates of the GEE analysis. In Models 1, 2, and 3, we show how each self-reported motivation separately predicts
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 25 decisions to cooperate, controlling for round, condition, the possibility of third party intervention, and the condition by intervention possibility interaction. In Models 4, 5 and 6, we
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added the interactions between condition and motivation and the possibility of intervention and
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motivation. In Model 7, we included all three social motives together. Finally, in Model 8 we included all three social motives and each of their interactions with condition and the possibility
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of intervention.
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Of the self-reported motivations that were entered as separate predictors of cooperation (Models 1-3), prosociality and competitiveness emerged as significant predictors of cooperation
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(Model 1 and Model 2). However, none of the self-reported motivations significantly moderated the effects of the possibility of intervention or the timing of intervention (Models 4-6), even
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when we included all of the motivations as predictors together (Models 7 and 8). Across all of the models, the interaction between the possibility of intervention and the timing of intervention
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(early vs. late) remained a significant predictor of cooperation. These findings suggest that our situational effects were robust to individual differences in social motivation. General Discussion
The current research provides clear answers to theoretically and practically important questions about repeated human conflicts, and explains when, why, and how third parties promote cooperation in groups. Challenging and complementing existing models of third party intervention that assume humans influence others’ conflicts unilaterally and altruistically (Balliet, Mulder, & Van Lange, 2011; Bernhard, Fischbacher, & Fehr, 2006; Charness, CoboReyes, & Jimenez, 2008; Fehr & Fischbacher, 2004; Fehr, Fischbacher, & Gachter, 2002; Molenmaker, de Kwaadsteniet, & van Dijk, 2014), the present findings suggest that self-interest underlies third parties’ choices to become interdependent with adversaries by intervening in their
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 26 conflict. Converging evidence from analyses of third parties’ contingent strategies, as well as from the effects of their own self-reported motives on their behavioral choices, indicate that the
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individualistic motivation to maximize one’s own outcomes shapes third parties’ intervention
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decisions. Accordingly, we found that information about adversaries’ history of repeated conflict discouraged third party intervention.
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Theoretical Contributions
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The current paper extends previous research on the conditions that contribute to the emergence of cooperation in groups by highlighting third parties’ role in promoting sustainable
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human cooperation. Specifically, we demonstrate that third parties are often willing to act as game changers who effectively transform harmful repeated conflicts into collectively beneficial,
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cooperative interactions. These findings make four contributions to multiple streams of research in social, cognitive, evolutionary, and organizational psychology. First, we extend social
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psychological research on competition and cooperation, which typically focuses on the isolated dyad (e.g., Halevy, Chou, & Murnighan, 2012; Kelley & Thibaut, 1978; Simunovic, Mifune, & Yamagishi, 2013), by demonstrating how the presence of third parties who can intervene in the conflict influences the process and outcomes of conflict. Second, we contribute to research in cognitive psychology by showing that utilitarian thinking (Wang, Zhong, & Murnighan, 2014) can promote collectively beneficial cooperation: By incentivizing cooperation, third parties enable self-interested adversaries to simultaneously maximize both personal and collective gains (Halevy & Halali, 2015). Third, we advance knowledge on the emergence of cooperative norms in groups via repeated social interactions (Fehr & Fischbacher, 2004; Peysakhovich & Rand, 2015). We find that environments that incentivize cooperation can have enduring effects on subsequent social interactions. Specifically, we demonstrate that early third party intervention
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 27 can help parties coordinate their choices to achieve mutually beneficial outcomes even after the third party can no longer incentivize cooperation. Finally, we contribute to research in
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organizational psychology on monitoring and sanctioning systems (Malhotra & Murnighan,
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2002; Tenbrunsel & Messick, 1999) by showing that mutually beneficial cooperation can outlast the institutional arrangements that instigated it.
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Practical Implications
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Our findings also have four important implications for practice. First, our findings suggest that effective third party intervention does not require holding a formal third party role
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(such as that of an arbitrator or a mediator: Brett, Goldberg, & Ury, 1990; Conlon, Moon, & Ng, 2002). Rather, individuals who can consistently reward cooperative behavior and punish
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competitive behavior have the power to transform repeated interactions from suboptimal competition to collectively optimal cooperation. Second, our results highlight a fruitful avenue
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for leaders who wish to take on an active role in managing conflicts among subordinates. Specifically, our findings suggest that leaders can use their control over valuable resources to introduce side-payments that effectively change the situation that adversaries face. By creating an environment in which mutual cooperation provides everyone with their best possible outcome (like the Maximizing Difference Game), leaders can instill in followers enduring norms of cooperation. Third, our findings highlight the importance of the timing of third party intervention. Given the effectiveness of third party intervention in promoting cooperation, and the negative effect of a history of conflict on third parties’ willingness to intervene, third party conflict managers would do well to intervene early, rather than late, in the course of a repeated interaction between adversaries. Finally, our finding that third party interveners are risk averse and motivated primarily by the desire to maximize their own outcomes suggests that adversaries
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 28 who wish to draw a third party to intervene in their conflict would do well to minimize the risk for the third party from intervening and highlight the benefits that can accrue to the third party
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from intervening. Our findings suggest that adversaries who demonstrate their cooperativeness
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are more likely to be able to draw third party interveners to their interaction. Limitations and Future Directions
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Like any research, the current investigation is constrained by our methodological choices.
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Future research should enrich our repeated game paradigm with elements designed to capture additional important aspects of real-world conflicts, including social identities (Roccas, Klar, &
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Liviatan, 2006) and communication (Balliet, 2010; Halevy, Bornstein, & Sagiv, 2008). Similar to other game paradigms, the Repeated Peacemaker Game is amenable to many systematic
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variations. Future research may alter the payoffs associated with cooperation versus competition as well as those that are associated with intervening in the conflict; introduce the possibility of
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asymmetric third party intervention (e.g., that only targets one of the two adversaries); or include multiple observers who can compete over opportunities to act as third party interveners in others’ conflicts.
In addition to changing the structure of the Repeated Peacemaker Game to extend the current findings, future research should also examine the role that social motives play in third parties’ decisions to intervene. Although our findings were robust to individual differences in social motives, our measure of social motives may not have been sophisticated enough to adequately capture such individual differences. Previous research using validated measures of social preferences (e.g., Social Value Orientation) has highlighted how individual differences in goals can affect interdependent decision-making (e.g., Messick & McClintock, 1968; Murphy & Ackermann, 2014). Therefore, future research should use such measures to understand how
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 29 individual differences in social motives may shape interactions between adversaries and third parties.
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We hope that the current paper will stimulate research on informal third party
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intervention also outside the lab, in various field settings. For instance, future research may investigate whether, when, and how managers use the resources they control to transform the
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games their subordinates are playing; how the characteristics of third parties and adversaries
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influence third parties’ propensity to intervene, as well as the effectiveness of different situational transformations in promoting cooperation in organizational settings.
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Conclusion
Conflict is ubiquitous and extremely costly. Every year, millions of working days are
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spent on managing conflicts at work (CPP Global Human Capital Report, 2008) in addition to the suffering and harm caused by repeated conflicts in many other life domains (Cohen & Insko,
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2008). A constant concern with interventions aimed at reducing conflict is whether they produce lasting changes in patterns of social interaction (Schroeder & Risen, 2014). We find that early third party intervention can have enduring effects on subsequent social interactions. Our research also shows that individuals can act as third parties and positively influence the course and outcomes of conflicts without having formal conflict management roles: Observing other people in conflict puts all of us in a position to act as game changers.
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 30
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ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 33 Murphy, R. O., & Ackermann, K. A. (2014). Social value orientation: Theoretical and measurement issues in the study of social preferences. Personality and Social Psychology
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ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 35 Notes 1. The term “competition” is used here to denote the non-cooperative strategy in the game, i.e.,
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the choice that maximizes one’s payoff relative to one’s counterparty.
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2. The analysis included the 48 participants who had been randomly assigned to the role of third party and the decisions they made across the 30 rounds in which intervention was possible.
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3. The analysis included the 48 participants who had been randomly assigned to the role of third
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party; only 29 of the 30 rounds in which intervention was possible could be included in this analysis because decisions in round 1 could not be based on previous behavior.
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4. The analysis included the 24 participants who had been randomly assigned to the role of third party in the Late Intervention condition. Model 1 includes the 30 rounds in which third party
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intervention was possible. Model 2 includes only 29 of the 30 rounds in which intervention was possible so that round 1 could be included as a predictor of behavior.
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5. The analysis included the 96 participants who had been randomly assigned to the role of adversary and the decisions they made across 60 rounds. 6. The analysis included the 96 participants who had been randomly assigned to the role of adversary; only 29 of the 30 rounds in which intervention was possible could be included in this analysis because decisions in round 1 could not be based on previous behavior. 7. The analysis included the 48 participants who had been randomly assigned to the role of adversary and the Early Intervention condition. Both Models 1 and 2 include the 30 rounds in which intervention was possible. Since all third parties in the Early Intervention condition intervened in the round just prior to when intervention was removed (i.e., round 30), we did not include an indicator to capture third party intervention in this round.
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 36 Table 1. Logistic regressions of intervention decisions as a function of condition and round
Table 2. Logistic regression of intervention decisions as a function of behaviors in previous rounds
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QIC Note: Standard errors in parentheses. **** p < .0001, *** p < .001, ** p < .01, * p < .05, † p < .10. ^ Reference group is mutual defection in previous round.
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 38 Table 3. Logistic regressions of intervention decisions in rounds 31-60 of the Late Intervention condition as a function of behaviors in previous rounds
Intercept
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5.1145** (1.7687)
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Unilateral cooperation in Previous Round^
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Intervened in Previous Round Mutual cooperation in Previous Round^
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Round Cooperation rate in Rounds 1-30
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QIC 504.0219 Note: Standard errors in parentheses. **** p < .0001, *** p < .001, ** p < .01, * p < .05, † p < .10. ^ Reference group is mutual defection in previous round.
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 39 Table 4. Logistic regressions of intervention decisions as a function of self-reported social motives
Early Intervention x Individualistic Early Intervention x Prosocial Early Intervention x Competitive QIC 720.2166 761.2199 761.2199 Note: Standard errors in parentheses. **** p < .0001, *** p < .001, ** p < .01, * p < .05, † p < .10
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 40 Table 5. Logistic regressions of adversaries’ cooperation as a function of condition and possibility of third-party intervention
Early Intervention x Intervention Possible Round x Early Intervention Round x Intervention Possible Round x Early Intervention x Intervention Possible QIC 6495.4549 5907.5380 6129.1332 Note: Standard errors in parentheses. **** p < .0001, *** p < .001, ** p < .01, * p < .05, † p < .10
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 41 Table 6. Decomposing the interactive effects of condition and intervention possibility on adversaries’ cooperation rates.
Not Possible
vs
Condition Early Intervention
Not Possible
vs
Late Intervention
Early Intervention
Possible
vs
Late Intervention
Late Intervention
Not Possible
vs
Late Intervention
Possible
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Note: Standard errors in parentheses. **** p < .0001, *** p < .001, ** p < .01, * p < .05, † p < .10
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Not Possible
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Early Intervention
Intervention
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Intervention
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Condition Early Intervention
Estimate -0.4478 (0.03955) 2.0692**** (0.3920)
Possible
0.7303 (0.5140)
Possible
-1.7867**** (0.2972)
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 42 Table 7. Logistic regression of cooperation as a function of behaviors in previous rounds (1) -3.6727**** (0.4709) 0.0077 (0.0109) 0.2585 (0.4173) 1.5550**** (0.3719) 4.2409**** (0.4824) 1.6550**** (0.3414)
Table 8. Logistic regressions of cooperation decisions in rounds 31-60 of the Early Intervention condition as a function of behaviors in previous rounds
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Intercept
23.6335** (8.0188)
9.1391 (10.1173) 3.8799* (1.7943)
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Intervention Rate in Rounds 1-30
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Round
Cooperation Rate in Rounds 1-30
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Self Cooperated in Previous Round Counterpart Cooperated in Previous Round
CE
Self x Counterpart Cooperation in Previous Round
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QIC 1154.6449 Note: Standard errors in parentheses. **** p < .0001, *** p < .001, ** p < .01, * p < .05, † p < .10
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 44 Table 9. Logistic regressions of cooperation decisions as a function of self-reported social motives
Intervention Possible
MA
Early Intervention x Intervention Possible Individualistic Prosocial
Early Intervention x Individualistic Early Intervention x Prosocial Early Intervention x Competitive Intervention Possible x Individualistic Intervention Possible x Prosocial Intervention Possible x Competitive QIC 5649.7548 5150.8548 5292.6148 Note: Standard errors in parentheses. **** p < .0001, *** p < .001, ** p < .01, * p < .05, † p < .10
-0.5305 (0.5766)
-0.1102 (0.3407)
5716.5341
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 45 Table 9 continued
Early Intervention x Intervention Possible Individualistic Prosocial
0.6440*** (0.3542)
-0.3927* (0.1642)
D
Competitive
TE
PT
Early Intervention x Individualistic Early Intervention x 0.0757 Prosocial (0.3542) Early Intervention x -0.0874 Competitive (0.2528) Intervention Possible x Individualistic Intervention Possible x -0.0381 Prosocial (0.2098) Intervention Possible x -0.0420 Competitive (0.1638) QIC 5230.6057 5327.6913 4926.8059 Note: Standard errors in parentheses. **** p < .0001, *** p < .001, ** p < .01, * p < .05, † p < .10
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 46 Figure 1. The Payoff Structure of the Peacemaker Game 1a.
The Prisoner’s Dilemma Game
1b.
The Maximizing Difference Game
Compete
Compete
30c, 30c
10c, 40c
Red
40c, 40c
20c, 30c
40c, 10c
20c, 20c
Player Compete
30c, 20c
10c, 10c
Cooperate
NU
Player Compete
Cooperate
RI
Cooperate
Cooperate
SC
Red
Blue Player
PT
Blue Player
MA
1c. Third parties’ Payoffs as a Function of Intervention and Adversaries’ Choices
Interaction Partners’ Choices
Withhold Intervention
Intervene 40c
Cooperate: Compete
25c
25c
Compete: Cooperate
25c
25c
Compete: Compete
25c
10c
D
25c
AC CE P
TE
Cooperate: Cooperate
Third-Party’s Choice
Note. The choices of the Red and Blue players determine their respective payoff. “c” represents U.S. cents. The values in the difference cells represent the actual incentives used in each of the rounds in our 60-round repeated game experiment.
ACCEPTED MANUSCRIPT Third Parties Promote Cooperation 47 Figure 2. Cooperation and Intervention Rates in the Repeated Peacemaker Game.
RI
PT
1
SC
0.9
NU MA
0.7
PT ED
0.6 0.5
CE
0.4 0.3
AC
Cooperation and Intervention Rates
0.8
0.2 0.1
Third-party - Early Intervention Third-party - Late Intervention Adversaries - Early Intervention Adversaries - Late Intervention
