The timing effect in public good games

Journal of Experimental Social Psychology 41 (2005) 470–481 www.elsevier.com/locate/jesp

The timing effect in public good gamesq Susanne Abelea,*, Karl-Martin Ehrhartb a b

Rotterdam School of Management, VG2, Erasmus University Rotterdam, The Netherlands Institute for Economic Theory and Operations Research, University of Karlsruhe, Germany Received 1 April 2004; revised 8 September 2004 Available online 2 December 2004

Abstract In public good situations, expectations concerning other persons
moves are important and subtle cues can affect these expectations. In Experiment 1, participants in a public good game who moved simultaneously made high contributions and expected their opponents to make high contributions. However, participants who moved pseudo-sequentially (one after the other, but without knowledge of the other
s decision) expected their opponents to make medium-sized contributions, but made almost no contribution themselves. In Experiment 2, we manipulated expectations experimentally. Participants who moved simultaneously reciprocated what they expected their partners to do. Participants who moved pseudo-sequentially defected, regardless of what they expected from their opponents. Furthermore, we found that simultaneous movers were more likely than pseudo-sequential movers to conceptualize themselves and the other player as a group. This sense of groupness seemed to account partly for their inclination to reciprocate anticipated behavior.
2004 Elsevier Inc. All rights reserved.

Introduction Day in and day out, we find ourselves in situations in which we have to make decisions. Often we cannot determine the outcome of a decision entirely on our own because it may depend also on somebody else
s decision. These other decision makers may remain unknown to us (e.g., ‘‘Shall I take the car or public transport to work to arrive on time?’’), or we may be fully aware of who the other persons are (e.g., ‘‘Shall I propose to her or would it be too risky?’’). Game theory analyzes strategic decision situations by developing solution concepts that describe how rational

q We gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim. We thank an anonymous reviewer for helpful comments on earlier drafts of this paper, and Herbert Bless, and Daan van Knippenberg for valuable comments to the research reported in the article. * Corresponding author. E-mail address: [email protected] (S. Abele).

0022-1031/$ - see front matter
2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jesp.2004.09.004

players,1 who assume that the other players are also rational, arrive at a decision (Von Neumann & Morgenstern, 1947). However, results of experimental gaming often deviate from the solution concepts of classic game theory (Camerer, 2003; Colman, 2003; Cooper & Van Huyck, 2003). For example, people are much more likely to cooperate in a prisoner
s dilemma game than the solution in classic game theory would suggest (Sally, 1995). Moreover, there is evidence that social information processing escorts interdependent decision making (e.g., DeDreu, Yzerbyt, & Leyens, 1995; Parks, Sanna, & Posey, 2003). Furthermore, it has been shown that subtle cues affect our judgment and individual decision making, even when we are not aware of their effect (Nisbett & Wilson, 1977; Schwarz, 1996). One of the subtle cues that interests us here is the timing of unobserved moves. In particular, we want to consider the effect on strategic decision 1 In game theory, a person in a strategic decision situation is referred to as a player or mover.

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making of whether decision makers decide simultaneously or pseudo-sequentially. Imagine, you just took your final exam for your university degree. You are waiting for the exam committee to let you know whether you passed, and what your final grade is. Imagine the situation in which you know the committee has not yet met to make a final decision on your grade. Now compare that with the situation in which you know that the committee is about to decide at the moment. And now compare it to the situation in which you know the committee has made its decision, and you are waiting to hear the outcome. In all these three situations the information set is the same. You do not know the outcome of the decision. However, most people will admit that they would feel slightly differently in these situations. In a similar vein, Miller and Gunasegaram (1990) have shown that people perceive different mutability of events depending on the temporal order (see also Tversky & Shafir, 1992). It has long been known that the timing of events affects our willingness to take risks (Strickland, Lewicki, & Katz, 1966; Langer & Roth, 1975). More recently, it has also been discovered that knowing the timing of an event without knowing its outcome plays a role in interdependent decision making. More specifically, knowing about the timing of another person
s move will affect your decision, even though you do not know what the other
s move is. Timing trumps unobservability in strategic decision making. The invisible opponent—effects of unobserved moves Knowing about the timing of a move, but keeping moves concealed (until the game or round is over) is an important issue. For instance, think of situations in which you bid for a house, decide on the price at which to offer merchandise, or select a romantic partner. For a certain period of time, no other interested buyer reveals her bid price on the house, no supplier of the same merchandise reveals his offer price, and the potential partner does not reveal his or her preference. From an experimental game-theoretic perspective, we can distinguish two game structures in which players know the timing of actions but not their outcomes: (1) players move simultaneously or (2) players move sequentially, but the moves are not known until the game is over and players are aware of order of the moves. The first game structure will be referred to as simultaneous and the second as pseudo-sequential. We consider two types of effects that may emerge when timing of decisions is varied. When players who move pseudo-sequentially make different decisions depending on whether they are the first or second movers, we refer to this as the positional order effect. The positional order effect has been shown in resource dilemma games (Budescu, Suleiman, & Rapoport, 1995; Rapoport, 1997), as well as in coordination games (Coo-

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per, DeJong, Forsythe, & Ross, 1993). Differences in decisions between players who move pseudo-sequentially and players who move simultaneously are referred to as timing effects. We first review research concerning positional order effects in games that embody conflict among players and those that do not. Subsequently we will discuss research on the timing effect. The positional order effect Coordination games do not involve conflict among the players but can be conceptually divided into coordination games with a first-mover advantage and coordination games without a first-mover advantage. In the first case, the first mover has an advantage when a specific equilibrium2 is played, and the second mover has an advantage when a different equilibrium is played. For instance, suppose that you want to meet up with a friend within the next few hours, you prefer to go to a soccer game, but you know that your friend prefers watching hockey matches. Still, both of you want to be together more than you want to watch your preferred sport (but you cannot get connected via your cell-phones). In this situation, if decisions are known when they are made, choosing first has the advantage because the other person will forego his/her preferred activity to be together. However, even if moves are not observable, simply knowing the order of moves can maintain the firstmover advantage in such situations. Cooper et al. (1993) had players play a coordination game with a first-mover advantage. They showed that pseudo-sequential movers chose the option preferred by the first mover more often than players who received no information about the order of moves. This ordering of moves should be inconsequential because the second mover was not informed of the first mover
s choice until after both had made a choice. Budescu et al. (1995) and Budescu, Au, and Chen (1997) found the positional order effect in threshold resource dilemmas that were played in a pseudo-sequential order (see Budescu & Au, 2002; for a formal model about the positional order effect). Players
requests decreased in the first three positions. Hence, it is apparently possible that a mere sequence in time without an alteration of the information structure can trigger behavior patterns that are usually associated with true sequential decision making. The experimental results from Cooper et al. (1993), Budescu et al. (1995), and Budescu et al. (1997) can be summarized as follows: in a coordination game with a first-mover advantage the timing cue is used as a coordination device. Or, put differently, the one who gets to choose first gets more of the cake, even if moves are unobserved. 2

Equilibrium is a concept from game theory. It refers to a state in which no player has an incentive to deviate from his or her current position (strategy).

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The timing effect There is also evidence for a timing effect in coordination games without a first-mover advantage (Abele, 2001; Weber, Camerer, & Knez, 2004). In coordination games without a first-mover advantage you prefer the same thing than the other person, but in case of a mismatch, you would have a greater loss choosing the option that you both prefer, compared to choosing the option that is less attractive for both of you. For example, Abele, Bless, and Ehrhart (2004) had players play an extended version of the stag-hunt coordination game. Players could choose any number between 9 and 19. They received the number they chose as a payoff if the other player chose the same number or a higher number. If the other player chose a smaller number they did not receive any payoff from the game. Note that choosing the number 9 is the Maxmin strategy, as it provides the highest payoff in the worst case. Choosing the number 19 is the Maxmax strategy, as it provides the highest payoff in the best case. Abele et al. (2004) showed that players moving in a pseudo-sequential order are more likely to choose risky strategies (Maxmax), whereas simultaneous movers are more likely to opt for risk-avoiding alternatives (Maxmin). These results showed that using knowledge about timing of unobserved moves is not only done, when it can function as a coordination device. These results suggested that using the timing cue could be the result of very subtle cognitive processes. Abele et al. (2004) offered a schemata activation explanation of the timing effect in coordination games. They argued that pseudo-sequential game structures are more likely than simultaneous game structures to activate schemata of social interactions. The argument hinges on the notion that persons involved in a social interaction act and react sequentially to each other. People might be reminded of a social interaction merely by the sequence cue, even when the outcomes of earlier actions are not known at the time of later actions (see also Baldwin, 1992; Baldwin & Sinclair, 1996). Activating concepts of social interactions might in turn increase individual
s interpersonal trust and decrease risk avoidance in situations of interdependence without conflict of interests (coordination situations). Furthermore, Abele et al. (2004) proposed that the simultaneous game structure in a coordination game is more likely than the pseudo-sequential game structure to activate schemata of games of chance. This argument is based on the notion that actions that take place simultaneously often have nothing to do with each other and do not refer to each other. If these actions match, individuals are more likely to attribute this to chance or good luck: people do not believe they have control over an event that happens simultaneously with their own actions at another place, in the same way that they would

believe in causality between two temporally sequential events at the same place. Therefore, when things happen simultaneously, they are inclined to treat all possible outcomes as equally likely. This makes the possibility of an actual total loss more salient, compared to a situation where they have an implicit hint to move to an attractive option. Consequently, people should be more prone to risk avoiding choices when moving simultaneously. With the research presented here we wanted to look at possible differences between simultaneity and pseudo-sequentiality when a conflict of interests exists such as in a public good game. The issue is whether the schemata activation approach, which was initially formulated for coordination games, can predict decisions under different timing conditions in mixed motive games. It follows from the notion that pseudo-sequential game structures are more likely to activate schemata of social interactions that players who move pseudo-sequentially are more likely to contribute to the common pool than simultaneous movers. However, Abele et al. (2004) have also stated that the context can confer a competitive connotation to the activated social interaction, which leads to different choices. Along these lines, it could also be that a mixed motive game, like the public good game, has the competitive feature inherent in a way that, if concepts of social interactions are activated, they have a competitive connotation. Moreover, there is a different line of reasoning that would also predict higher cooperation rates among simultaneous movers compared to pseudo-sequential movers. This reasoning is outlined in the following section. Temporal order of moves: Implications for feelings of groupness? In a public good game, the collective interests of the involved persons clash with the individual interests of each person. Put differently, an individual maximizes her individual payoff by choosing a strategy different from the one that would maximize the payoff for all decision makers as a collective. As the interests of the collective become more salient or important, the likelihood that the individuals will choose the alternative that yields a higher outcome for the group will increase. One potential way of increasing the salience and importance of the collective interests is to enhance the feelings of groupness (Smith, Jackson, & Sparks, 2003). More specifically, the more strongly each person identifies with the group the better they will feel when the group benefits. This enhanced feeling of groupness will increase the likelihood that individuals will cooperate and choose the strategy that will benefit the collective (see e.g., Brewer & Kramer, 1986; De Cremer & vanVugt, 1999). Think of two students sharing an apartment. They have to work through their daily routines of living to-

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gether and sharing the housework. The more they perceive each other as a social unit, the more likely they will be to take the other person into account when deciding what to do. In other words, the more the two individuals construe themselves in relational terms, the more likely they are to try and reciprocate the actions of the other person (Deutsch, 1975; Gaertner & Insko, 2000). The more they see themselves as the unit, the more likely they will be to do equal shares of the housework without further verbal arrangements. Of course there are other ways, apart from living together, in which two or more individuals can think of themselves as a group. Moreover, there are even very subtle ways in which people may form a sort of group identity. Sharing anything, from a common project to a preference for a painter, fosters people
s sense of belonging together and being part of a group (Tajfel, Billig, Bundy, & Flament, 1971; Turner, Hogg, Oakes, Reicher, & Wetherell, 1987). In a similar way, we suggest that deciding simultaneously will emphasize the public good more than moving pseudo-sequentially when there is a conflict of interests. In other words, when collective and individual interests are in conflict, individuals might be more prone to act in the common interest when they are deciding simultaneously because acting at the same time might subtly foster the notion of belonging together. By contrast, when moving pseudo-sequentially, they might be more prone to decide in their own interest because moving pseudo-sequentially underscores the differences rather than the commonalities between the two players. That is, they might be more prone to think of the other in terms of another person rather than in terms of a member of the same group. This notion is complemented by Morris, Sim, and Girotto (1995, 1998), who investigated the different reasons that first and second movers have for contributing in a Prisoner
s Dilemma Game. They proposed causal illusion for the first movers and felt ethical obligation for the second movers as key determinants for cooperation. This implicitly also suggests a tactical thinking component, which we are proposing for the pseudo-sequential movers, and it is different from cooperation out of concern for the group, which we are proposing for the simultaneous movers. Imagine somebody who feels obliged to reciprocate (potential contributions) and therefore cooperates. That is somewhat different from a contribution to the collective out of a positive attitude to the collective per se. The same is true for causal illusion: somebody who cooperates because he believes he can influence another person by doing so is also not cooperating merely out of concern for the group. Hence, Morris et al. do not look at differences in cooperation rates between pseudo-sequential and simultaneous movers, but make refinements about reasons to contribute for pseudo-

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sequential movers, which can be seen as complementing our hypothesis. To sum up, we will consider two competing hypotheses concerning the timing effect in a public good game. The first hypothesis is based on the schemata activation approach suggested by Abele et al. (2004) to account for timing effects in coordination games. It says that pseudo-sequential game structures are more likely to activate schemata of social interactions whereas simultaneous game structures are more likely to activate concepts of games of chances. People should be more likely to cooperate, when given the alternatives of doing something for the collective or just for themselves, when thinking of a social interaction compared to a game of chance. From this reasoning it would follow that pseudo-sequential movers should cooperate more than simultaneous movers. The second hypothesis is based on the idea that moving simultaneously could, as compared to moving pseudo-sequentially, trigger a feeling of groupness. When the collective is more salient than the individual, people should be more likely to do something for the collective when given the choice between acting in their individual interests or in the collective
s interest. Consequently, simultaneous movers should be more likely to cooperate in a public good game than pseudo-sequential movers. Experiment 1
s main objective was to test the two competing hypothesis concerning the timing effect in a twoperson public good game.

Experiment 1 Method Participants and design Eighty-six (86) male students from the University of Karlsruhe, Germany, participated in the experiment. They volunteered by listing their names on sign-up sheets offering monetary compensation depending on performance. Participants were randomly assigned to a 1 by 3 (simultaneous vs. first mover vs. second mover) between-factorial design. Game Players were told that they had to allocate an endowment of 10 units between a private and a public option. Everything that they assigned to the private option was multiplied by 3, and would be their payoff A. Everything that they allocated to the public option was multiplied by 2, and would be paid to both of them. Outcomes from the public alternative would be their payoff B. Their final payoff consisted of their payoff A plus their payoff B minus 20 units. So players would be best off collectively, if they both contributed all their endowments to the public alternative. That strategy

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would yield each of them a total payoff of 20 units. If they both allocated all of their endowments to the private alternative, they would both get a total payoff of 10 units. If one of them allocated all his/her endowments to the public alternative, while the other one allocated all of her/his endowments to the private alternative, the public allocater would have a total payoff of 0 units while the private allocater would have total payoff of 30 units. One money unit was worth 1 German mark (1 German Mark was approximately US$ 0.55). Note that there is no provision point in this game. The appendix contains a formal description of the game. Procedure Upon arrival, participants were seated in two different computer rooms. They were then given the instructions for the game on a sheet. To ensure that every player understood the game, participants had to answer a set of questions about the game on the computer before the game started. Participants played the game with one other participant in the other room, but they could not identify that person. The different timing of movement was achieved in the following way. In the condition in which players chose pseudo-sequentially, participants in one room were assigned the role of the first mover, while participants in the other room were assigned the role of the second mover. Second movers could only make their choice after all first movers had made their choice. However, all moves were revealed only after the game was over. Hence, second movers knew only that first movers had made their decision, but did not know what it was. All participants were fully aware of this procedure. In the condition in which players chose simultaneously, they also played the game with a participant in the other room. The invitation to make the choice by pressing a certain key was given at exactly the same time. All simultaneous movers were aware of this procedure. After the participants had made their decision and before they were informed about the result of the game, they were asked about their assumption concerning their opponent
s decision. They indicated how many of the possible units (0–10) that they expected the other player to contribute. Subsequent to the experiment, participants went to a third room where they were paid anonymously. Results Data from all 86 participants were included in the analysis. Mean contributions to the public option (level of cooperation) by simultaneous movers, first movers, and second movers are depicted in Table 1. The average

Table 1 Contributions depending on temporal order of unobserved moves in Experiment 1 Average contribution Simultaneous movers First movers Second movers

7.61 (3.36) 3.21 (3.7) 3.55 (4.08)

Table entries are means with standard deviations in parentheses.

contribution of the simultaneous movers is equal to 7.61, which is more than twice as high as the average contributions of the first movers and second movers (3.21 and 3.55). Simultaneous movers, first movers, and second movers show a significant different level of cooperation, F (2, 83) = 12.19, p < .001. A weighted contrast analysis (using weights of 2 for the simultaneous condition and
1 for the two pseudo-sequential conditions) revealed that simultaneous movers are more cooperative than first movers and second movers together, t (83) = 4.93, p < .001. First movers and second movers (using weights of 1 for first movers,
1 for second movers and 0 for simultaneous movers) do not differ in their choices, t < 1. First movers alone are less cooperative than simultaneous movers, t (83) = 4.45, p < .001 (using weights of 1 for simultaneous movers,
1 for first movers, and 0 for second movers); just as second movers alone are less cooperative than simultaneous movers t (83) = 4.1, p < .001 (using weights of 1 for simultaneous movers,
1 for second movers, and 0 for first movers). As described earlier, participants were asked about their assumption concerning their opponent
s decision after they had made their decision and before they were informed about the result of the game. For participants who played the game simultaneously, there is a strong positive correlation between their own level of cooperation and their assumptions about their opponent
s level of cooperation. The Spearman rank correlation coefficient is r = .75 and significantly positive, p < .001. Furthermore, there is no significant difference between the average level of contributions, MC, and the average expectation concerning the contribution of the other player, ME, when participants moved simultaneously: MC = 7.61, ME = 7.57, t (27) = .08, p = .941. However, the rank correlation coefficient between contributions and expectations of other
s contributions is not significant for first movers or second movers, r = .27, p = .077 and r = .25, p = .092, respectively. Moreover, the first movers contributed significantly less than they assumed their fellow player would contribute, MC = 3.21, ME = 5.38, t (28) = 2.17, p = .018. The same is true for the second movers, MC = 3.55, ME = 5.38, t (27) = .2.07, p = .048.

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Discussion Our results showed that people make different contributions to the public good depending on the order of unobserved moves. The mere knowledge that the other person in a two-person public good game moved before, after, or simultaneously affected the choice to either contribute endowments to a collective or keep them to yourself. Participants who decided simultaneously were much more likely to cooperate than players who made their choice sequentially, with moves not revealed until the end of the game. Moreover, our results showed that participants who were moving simultaneously indicated—before they knew the outcome of the game—that they expected their opponent to also make a fairly high contribution, as they indeed did themselves. However, participants who were moving pseudo-sequentially indicated that they expected their fellow player to make a mediumsized contribution, but made a low contribution themselves. Furthermore, there was an association between the indicated expectation and one
s own contribution for simultaneous movers, but that relationship does not exist for first and second movers. These relationships imply that people reciprocated what they expected from the other player when moving simultaneously. When moving pseudo-sequentially, people apparently did not reciprocate what the expected from the other person, but defected. One implication is that information about the timing of the decision to contribute or not elicits different cognitive processes which, in turn, result in different contribution rates. This implication, of course, raises the question of how these cognitive processes might differ: do simultaneous movers see themselves as more of a social unit than pseudo-sequential players? And if so, how does the provision of explicit expectations moderate the effect of timing?

Experiment 2 The goal of Study 2 was to investigate whether people view their fellow player and, more specifically, the expectation they have about the other player
s behavior, differently depending on the order of unobserved moves. In other words, the issue is whether players are more likely to reciprocate what they expect the other person to do when they are moving simultaneously compared to when they make their moves in a pseudo-sequential order. Is it that pseudo-sequential movers, compared to simultaneous movers, do not consider the other person, but just go ahead and play the dominant strategy? Note that the game-theoretic dominant strategy in the public good game is to keep all the endowments for ones self.

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Results of Experiment 1 suggest that this could be the case. However, in Experiment 1 participants indicated the expectation concerning the move of the other player. It could be that pseudo-sequential movers indicated a mediocre contribution from the other person, but really believed something else. Maybe they were reluctant to say that they expected selfish behavior from a person they did not know. Moreover, in Experiment 1, the participants own decision could have affected their reported expectations. To examine more directly the role of expectation, we manipulated expectations experimentally in Experiment 2. Furthermore, we wanted to look at the issue of whether players conceptualize themselves and the other player differently depending on the order of unobserved moves. More specifically, we suggested that simultaneous movers, compared to pseudo-sequential movers, would think of the two players of the game—i.e., themselves and the other person—more as a group. We reasoned that this notion is best captured on an operational level by using the Inclusion of the Other in the Self Scale devised by Aron, Aron, and Smollan (1992). This scale seems particular suitable for the current purpose, as it has been shown to detect differences in the feeling of groupness in a variety of contexts (Batson et al., 1997; Cialdini, Brown, Lewis, Luce, & Neuberg, 1997; Wright, Aron, McLaughlin-Volpe, & Ropp, 1997). We hypothesized that participants who make their choices simultaneously with the other player would be affected by the expectation manipulation. In other words, if we told them that others had contributed little to the common pool, they would also make a smaller contribution compared to the situation in which we told them that others had made a large contribution in previous experiments. We hypothesized further that participants who made their choice in a pseudo-sequential order would not be affected as much by the expectation manipulation. They would make small contributions to the common pool regardless of whether we told them that people on average had contributed little or much to the common option in previous studies. Predictions concerning results on the Inclusion of the Other in the Self Measure are a bit more complicated. We hypothesized that simultaneous movers should indicate that they perceive a closer relationship between themselves and the other player compared to pseudo-sequential movers. However, we also speculated that for simultaneous movers, the feelings of groupness might be slightly influenced by the induced expectation, in the sense that they could see the other as slightly further away from themselves when low expectations are induced. In contrast, pseudo-sequential movers
sense of social inclusion should not be affected by the expectation manipulation.

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Moreover, we expected a high correlation between the Inclusion of the Other in the Self Measure and the contribution rate. Ideally, social inclusion should account for the different levels of cooperative play that we predicted for the different timing conditions. Method Participants, Design, and Game One hundred ninety-two (192) students from the University of Karlsruhe, Germany, participated in the experiment. Again, they volunteered by listing their names on sign-up sheets that offered monetary compensation depending on performance. They were randomly assigned to the conditions of a 2 (simultaneous vs. pseudo-sequential movers) by 2 (induced expectation: high vs. low) between-factorial design. We chose not to differentiate between first and second movers, as there were essentially no differences between first and second movers in the first experiment. But as participants were really playing the game, we had first and second movers. Participants played the same Game as in Experiment 1. One money unit was now worth 0.5 Euros (1 Euro was approximately US$ 1.2). Procedure The procedure resembled that used in the first experiment. High expectations were induced by giving participants the following information after they had read the instructions and answered the comprehension question about the game: ‘‘We have conducted this experiment before. On that occasion, participants assigned, on average, 1.3 tokens to A and 8.7 tokens to B.’’ Note that option B represents the common pool. Low expectations were induced by reversing the allocation of the tokens. After participants had made their choice, they were given the Inclusion of the Other in the Self Measure. It consisted of seven sets of two circles, one labeled self, the other labeled other. The first consists of two circles next to each other. In the following sets, the two circles overlap each other more and more. Participants had to choose the set of two circles that best represented their relationship with the other player. Each set of circles had a letter assigned to it, which participants had to type into the computer. These letters were later transformed into numbers, so that 1 indicates that the participant chose the set of circles that were next to each other whereas 7 indicates that the participant chose the set of circles that were almost overlapping completely. After participants had made their judgment on how close they felt the other player and they were, they were asked about their expectation concerning their opponent
s decision, and then they were told the outcome of the game. Subsequent to the experiment, participants went to a third room where they were paid anonymously.

Results Cooperation rates Data from all 192 participants were included in the analysis.3,4 Mean choices are depicted in Fig. 1. Conducting a 2 (Timing) · 2 (Induced Expectation) ANOVA revealed a main effect of timing, F (1,188) = 4.32, p < .039, a main effect of the induced expectation F (1,188) = 4.98, p < .027, and a marginally significant interaction between timing and induced expectation F (1,188) = 2.51, p < .11. We expected participants who were making their choice simultaneously to be affected by the induced expectation. More specifically, we expected them to make higher contributions in the conditions in which we told them that others had contributed a considerable amount to the common pool, compared to the conditions in which we told them that others had contributed little to the common pool. We expected participants who made their move pseudo-sequentially, however, to make small contributions to the common pool, regardless of what we told them others had done. We assigned contrasts in keeping with this pattern. Conducting a 1 · 4 ANOVA revealed that the means of decisions made under the four different experimental conditions differ significantly, F (8, 188) = 3.94, p < .009. Furthermore, the weighted contrast analysis (using weight 3 for the simultaneous movers with high induced expectations and
1 for the other three conditions) revealed that participants in the four different conditions made different decisions consistent with our predictions, t (188) = 3.41, p < .001. Hence, in Experiment 2 participants who were choosing simultaneously with another player, and had been told that others had contributed a considerable amount to the common pool, made larger contributions (M = 4.8) than simultaneous movers who had been told that others contributed little (M = 2.68), and than pseudo-sequential movers with low (M = 2.41) and high (M = 2.77) induced expectations.

3

The finding of no difference between first and second movers from Experiment 1 was replicated in Experiment 2. First movers contributed on average M = 2.54, and second movers were contributing on average M = 2.64, t < 1. We do not want to propose that there is absolutely no difference between first and second movers in their perception of the situation and the cognitive processes. However, the current research focuses on the difference between simultaneous moving and pseudosequential moving. Since there was no difference between first and second movers in cooperation rates in both experiments, we combined their data for ease of presentation. 4 Participants in the high expectation condition indicated that they had expected on average a contribution of ME = 5.0, whereas participants in the low expectation condition indicated that they expected on average a contribution of M E = 3.5 tokens, F (1,190) = 6.79, p < .01.

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Fig. 1. Contributions to the common pool depending on the temporal order of unobserved moves and induced expectation in Experiment 2. Note, means are on top of the bars with standard deviations in parentheses.

Inclusion of the Other in the Self The cooperation rates, again, seemed to be favoring hypothesis 2, which is derived from a group identity perspective. This hypothesis also suggests that pseudo-sequential movers perceive a looser relationship between themselves and the other player than simultaneous movers. Indeed, pseudo-sequential movers reported more distance between themselves and the other player (M = 2.72) than simultaneous movers did (M = 3.31), t (190) = 1.8, p < .05, one-tailed. For an overview, all mean choices are depicted in Table 2. Recall that 1 indicates that participants saw themselves as two entities whereas 7 indicates that the participants saw the two of them as close together. As predicted, we found a strong association between the perception of closeness and the contribution rate to the common pool. Overall, the correlation between contribution rates and social inclusion judgments was r = .84, p < .0001. Recall that the order of unobserved moves had a significant effect on contribution rates and a marginally significant effect on social inclusion. Moreover, contributions and perceptions of closeness were highly correlated. We therefore wanted to investigate the role of the perception of closeness to the other player more closely. We conducted a 2 (Timing) · 2 (Induced Expectation) ANCOVA with contribution as a dependent variable and with the social inclusion scores as a covariate. The main effect of timing on contribution ceased to be significant, F (1, 187) = 1.04, p < .3, whereas the effect of expectations remained significant, F (1, 187) = 13.61, Table 2 Inclusion of the Other in the Self ratings depending on timing of unobserved moves and induced expectation in Experiment 2

Pseudo-sequential movers Simultaneous movers

High expectation

Low expectation

2.7 3.46

2.75 3.17

p < .0001. Consistent with the correlation analysis, the effect of the covariate was significant, F (1, 187) = 523.8, p < .0001. This pattern of findings supports the conclusion that perceptions of closeness mediate, at least in part, the timing effect on contributions, whereas they do not mediate the effect of the manipulated expectations. Discussion First, our results revealed that people who are entangled in a mixed motive situation are affected by the expectation manipulation differently depending on the information about the other person
s timing of the decision. Hence, simply knowing that the other person already decided or would decide later, as opposed to deciding simultaneously, reduced the inclination to reciprocate what the other person was expected to do. This finding added the insight that different levels of cooperation depending on the timing cue come about not because pseudo-sequential movers are more likely to expect the other person to defect, but because they are not eager to reciprocate what they expect others to contribute to the common pool. Simultaneous movers, by comparison, are more likely to try to reciprocate the anticipated contribution of the other person. It seems that the relatively high cooperation rates among the simultaneous movers that we observed in the first experiment resulted from the fact that simultaneous movers expected a high cooperation rate from their counterparts and wanted to reciprocate. Second, our results showed that the degree of feeling of groupness is affected by knowing decision timing even without knowing what that decision is. More specifically, moving simultaneously with another person fostered a greater degree of social inclusion with that person than moving pseudo-sequentially did. This effect was only marginally significant. However, one should

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note that we were also manipulating expectations in this experiment, which might have worked against obtaining a greater difference in perceived closeness between simultaneous and pseudo-sequential movers. Third, our results showed a strong association between the level of cooperation and the indicated perceived feelings of groupness. The more a person conceptualized him/herself and the other person as a group, the more that person contributed to the common pool. Fourth, our findings supported the conclusion that perceptions of closeness mediate, at least in part, the timing effect on contributions, whereas they do not mediate the effect of the manipulated expectations. Of course, due to the correlational nature of the analysis and the fact that the social inclusion measure was obtained after the decision was made, other interpretations are possible. For instance, contributions to the common pool and social inclusion judgments might be highly correlated because decisions to contribute directly affect judgments of closeness, and not vice versa. An argument against this particular alternative interpretation is that perceptions of closeness were not affected by manipulated expectations, whereas decisions were. Hence, it would appear that the feelings of groupness, caused simply by simultaneous as opposed to pseudo-sequential moving, is so strong that it leads people to contribute more to a public good, although the rational thing for an individual would be to defect, especially as participants knew that they were going to play this game only once.

General discussion The current findings clearly demonstrate that the timing of unobserved moves affects people
s decision in interdependent decision making. However, contrasting the current findings with earlier work suggests that the nature of the effect seems to differ depending on the nature of the interdependency. The riddle of why that is the case is not completely understood but, the current research adds another substantial piece to the puzzle. Earlier research on the difference between pseudo-sequential and simultaneous movers in coordination games suggested that pseudo-sequential movers might contribute more to a common pool than simultaneous movers. However, a public good type of situation has a conflict of interests that is not present in coordination problems where the task is to converge on mutually beneficial equilibriums. Therefore, we reasoned that the timing cue might activate concepts different from those in a coordination situation. More specifically, we reasoned that the different timing of moves could create different feelings of groupness, which would in turn affect the perceived importance of the common pool and common outcome.

We showed that knowing that the timing of decision without the decision being known affects cooperation rates in public good games. The nature of the effect seems qualitatively different from the timing effect observed in other games such as coordination games or ultimatum bargaining (Abele et al., 2004; Weber et al., 2004). Specifically, we demonstrated in Experiment 1 that people who move simultaneously with another person in a public good game contribute more to the public option than do people who move pseudo-sequentially. The global schemata activation approach proposed by Abele et al. (2004) would have suggested that, in the pseudo-sequential conditions, social interactions are activated and as a consequence participants should contribute more to the common than in the simultaneous conditions. Our current experiments did not address directly whether concepts of social interactions were activated in the pseudo-sequential game-structures, which had a competitive connotation, because the game itself embodies a conflict of interest. It could be that these more competitive interactions were activated, and that they also contributed to a lower contribution rate in the pseudo-sequential than simultaneous game-structures. But there is also another way of looking at this: the schemata activation idea suggests that simultaneous decisions make the social nature of the interaction in coordination games less salient. However, our current findings suggest that something quite different is happening when decisions are made simultaneously in a public good game. Simultaneous decision makers were more inclined to view themselves as a social unit than pseudo-sequential decision makers. One possible explanation for this difference is that a game involving conflict of interests, such as a public good game, may inherently trigger the concept of social interaction regardless of the timing of decisions. That is, conflict implies social interdependence. Thus, the function of the timing cue is to vary the balance of concern for common versus individual interests. However, our current experiments did not address directly whether concepts of social interactions were activated because the game itself embodies a conflict of interest. Moreover, it could be that once the idea of more competitive interactions was activated, the pseudo-sequential timing enhanced the competitive overtones of the game and thus contributions were lower in the pseudo-sequential than simultaneous game structures. Subsequent research should test whether competitive social interactions were activated in the pseudo-sequential compared to other conditions. To understand better the locus of the effect, a condition without any information about timing could be a potentially informative comparison. Another possibility is that pseudo-sequential movers are thinking about any game more strategically and realize that they are always better off, in the public good game, by keep-

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ing all the endowments to themselves. This also means that they are focusing on maximizing their individual outcome. We demonstrated that people are differently affected by the information about what other people contributed previously, depending on the order of unobserved moves. Players who played simultaneously in a public good game were more likely to reciprocate what they expected from the other person compared to people who decided pseudo-sequentially. The latter were more likely to defect, regardless of what they expected the other person to do (Experiment 2). In addition, we obtained a link—albeit a weak one—between the timing of unobserved moves and the sense of groupness. Moreover, the different willingness and intention to reciprocate contributions to the common pool seemed to be mediated by the endorsement of the group feeling (Experiment 2). People who decided in a simultaneous order indicated greater social inclusion of the other person than did players who moved in a pseudo-sequential order. This seems to account, at least in part, for the greater willingness to reciprocate cooperative behavior among the simultaneous movers. By demonstrating the timing effect in a public good game, we illustrated how sensitive to situational cues the decision to contribute to a common pool is. It is, of course, possible that other mechanisms also play a role in the timing effect in public good games, mechanisms that were not captured by our experiments. It is possible, for instance, that simultaneous movers figure that they are in exactly the same situation as the other player, and therefore expect the other to act like them and see, as they do, the mutual benefit of cooperation. This could be an alternative explanation to the notion that collective concerns are more salient than individual interests when the sense of the group is stronger. Nonetheless, our experiments illustrated the importance of the timing cue in interdependent decision making and how the timing cue can provide social information. Along this vein, we have added evidence to the claim that the timing cue can trigger certain aspects of our social knowledge (Morris et al., 1995, 1998). Morris et al.
s point was to trace different motives for cooperation in Prisoner
s Dilemma games in first and second movers. We have shown that pseudo-sequential movers have reason to, and in fact do, cooperate less than simultaneous movers, or, put differently, why simultaneous movers cooperate so much. It should be mentioned that we obtained lower contribution rates among simultaneous movers in Experiment 2 in the conditions in which we induced a high expectation, compared to contribution rates among simultaneous movers in Experiment 1. A possible reason could be that the intended high expectation manipulation, which consisted of the information that previous players had contributed 8.7 tokens on average, func-

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tioned as an anchor. The data suggests that this could have been the case. The information might have kept some simultaneous players from contributing all their ten tokens to the common pool, which they might have done without the information. They might have even contributed more, if the information was represented differently, for instance in frequencies, so that they would know how many participants contributed all their tokens. Further research should clarify what the difference could be due to. Concerning our initial competing hypothesis about the timing effect in public good games, the presented experiments suggest that a group identity based perspective can account better for behavior in public good games in different timing conditions than the global schemata activation approach. This suggests that the structure of the game predisposes which concept can possibly be activated. If the game structure is as such that it presents a choice between maximizing the individual outcome and maximizing the joined outcome, feelings of groupness can be activated by a very subtle cue like timing. If however, the game structure presents choices between safer and more risky options, concepts of games of chances can be activated by subtle cues. This also suggests that the structure of the game, and its embedded type of conflict, determines how we perceive the other player, a person we have not met and will remain anonymous to us. On a broader level, the point of the present paper is attuned to how the features of the game change the nature of the social relationship, and how the game itself changes the relationship to the other person. Deciding whether to join a leisure activity that your employer is offering is different from deciding whether to respond to requests for contributions to the local library. Moreover, it has previously been shown that subtle cues, like the timing cue can become informationally loaded in interdependent decision making. The current research demonstrates that, depending on the nature of the game, the timing cue leads to different inferences about the nature of the social relationship between players. These inferences, in turn, are related to the players
decisions. Future research should take a closer look at how the game itself affects perception of the other player and the relationship between the players.

Appendix. Formal description of the public good game from Experiments 1 and 2 We employed an n-person symmetric public good game in normal form. In this game, each of the n players has an endowment w to be allocated between a private and a public option, where xi denotes player i
s spending for the private good, and yi denotes player i
s contribution to the public good, xi + yi 6 w. The total amount of

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the P contribution to the public good is denoted by y = i yi. Player i
s payoff function of this game is defined as follows: H i ðxi ; yÞ ¼ axi þ by þ c: The parameters a and b are crucial for the character of the game, particularly the ratio b/a, which represent the marginal rate of substitution (MRS) between the public and the private good. The game becomes a public good game with a unique Nash equilibrium and a unique symmetric Pareto optimum if a, b > 0 and 1/n < b/ a < 1. Since a > b, a dominant strategy for each player is to spend the whole endowment on the private option. Thus, the game has a unique Nash equilibrium with xi = w for all i and therefore y = 0. Since b/a > 1/n, the solution in dominant strategies does not maximize the sum of payoffs of the players. The symmetric Pareto optimum is achieved if each player contributes the entire endowment to the public alternative, i.e., xi = 0 and yi = w for all i and therefore y = nw. In conducting our experiments, we made the following assumptions concerning the public good game: n = 2, w = 10, a = 3, b = 2, and c =
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