Coalition behavior: Effects of earned versus unearned resources

ORGANIZATIONALBEHAVIOR

Coalition

ANDHUMANDECISIONPROCESSES

38, 257-277(1986)

Behavior: Effects of Earned versus Unearned Resources

CHARLES E. MILLERANDJANEWONG

Previous studies of coalition games involving differences in both individual resources and coalition payoffs have found negligible effects for resources. Instead, coalition behavior in such games is primarily a function of bargaining strength (the payoffs available to players in alternative coalitions). The present study tested the possibility that the lack of resource effects in previous studies was due to resources being randomly assigned to the players, rather than being earned by them. The study also tested three theories of coalition formation: minimum resource theory, bargaining theory, and the equal excess model. It was found that the tendency for coalition members with larger resources to be offered, and actually to receive, more of the payoff than coalition members with smaller resources was stronger when resources were earned than when they were unearned. Players were also more likley to think that payoff divisions favoring the coalition member with larger resources were fairest when resources were earned rather than unearned. Bargaining strength also affected coalition behavior, however. The asymptotic predictions of bargaining theory, which are based partly on resources and partly on bargaining strength, provided the most accurate estimates of payoff divisions, although none of the theories was very accurate. 0 1986 Academic Press, Inc.

Examples of coalition formation are quite common: Some of the stockholders of a corporation join together to elect a new chairperson of the board; several small manufacturing firms form a consortium to obtain a contract from a large buyer; a number of brokerage houses enter into an agreement to underwrite a new issue of stock. Because coalition formation is such an important aspect of life in groups and organizations, it has been a topic of considerable interest to social scientists. The first laboratory study of coalition behavior was conducted nearly 30 years ago (Vinacke & Arkoff, 1957), and since then a large body of experimental data has been gathered (for reviews see Kahan & Rapoport, 1984; Komorita, 1984; Komorita & Kravitz, 1983; Miller & Crandall, 1980; Murnighan, 1978). Formally, a coalition may be defined as two or more individuals who This research was supported by a grant from Northern reprints should be sent to Charles E. Miller, Department University, DeKalb, IL 60115.

Illinois University. Requests for of Psychology, Northern Illinois

257 0749-5978/86 $3.00 Copyright W 1986 hy Academtc Pre\r. lnc All rights of reproduction in any form reserved

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make joint use of their resources to obtain a mutually desired outcome (cf. Gamson, 1964; Thibaut & Kelley, 1959). The resources that the individuals possess may include money, special skills, raw materials, shares of stock, and so on. For experimental purposes, however, resources are ordinarily operationalized as votes in a weighted-majority voting game. Each player in such a game possesses a certain number of votes, and some critical quantity of the votes (e.g., a majority) is needed in order to win a payoff (points, money). When no one player has enough votes to win, some of the players must form a coalition and add their votes together. The members of a coalition are required to agree on how to divide the payoff for winning. Research and theory on coalition behavior are concerned with two basic questions: (a) Which of the possible winning coalitions will form? (b) How will members of the coalition divide the payoff? Early coalition research showed that in simple games, in which the payoff for any winning coalition is the same, both coalition formation and payoff divisions are affected by the resources that players possess. Accordingly, several early theories of coalition behavior were based on resources. Further research, however, showed that the effects of resources tend to decrease as players become more experienced and familiar with coalition games (e.g., Kelley & Arrowood, 1960). In addition, still more recent research has shown that in multivalued games (Komorita & Kravitz, 1983), in which the payoffs for different winning coalitions vary, resources have little or no effect on coalition behavior. Instead, coalition behavior is determined more by bargaining strength, i.e., the payoffs available to players in alternative coalitions (cf. the concept of the comparison level for alternatives, CLd,, Thibaut 8z Kelley, 1959). As a result, interest in resources as a determinant of coalition behavior has declined, and theories based primarily on resources are now largely regarded as inadequate (Komorita & Kravitz, 1983). The present study had two purposes: The first purpose was to examine the possibility that the lack of resource effects in multivalued games is due to the unrealistic way in which resources are typically operationalized. Most laboratory studies operationalize resources by assigning them to players at random (Stryker, 1972). In many real-world situations, however, the resources that individuals possess have been earned by them, through an expenditure of effort or the exercise of skill. The present study compared the effects of earned and unearned (randomly assigned) resources on coalition behavior in two multivalued games. The second purpose of the study was to test three major theories of coalition behavior, which differ in the degree to which they are based on either resources or bargaining strength. The theories tested were minimum resource theory (Gamson, 1961a, 1964), which is based entirely on

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259

resources; bargaining theory (Komorita & Chertkoff, 1973), which is based partly on resources and partly on bargaining strength; and the equal exce.w model (Komorita, 1979), which is based entirely on bargaining strength. Before presenting the design and predictions of the study, it is necessary to review the relevant findings of previous research in more detail, and to give a brief description of each of the theories. BACKGROUND:

FINDINGS AND THEORIES

Early Findings

Early coalition studies involving simple games established two important findings. First, it was found that individuals “weak” in resources are more likely to enter into coalitions than individuals “strong” in resources. A classic example of this “weakness-is-strength” effect is in a frequently studied three-person game in which one of the persons has 4 votes, another has 3 votes, the other has 2 votes, and a majority (5 votes) is needed to win. In this game, denoted 5(4-3-2), the coalition between 3 and 2-the two “weaker” players-is the one most likely to form. Second, it was found that resources also affect the way in which the members of a coalition divide the payoff. The greater the resources of a coalition member, in comparison to the resources of other members, the larger the share of the payoff the member receives. For example, in the 5(4-3-2) game, if 3 and 2 form a coalition, 3 will usually receive a larger share of the payoff than will 2. Minimum

Resource Theory

To explain these two findings, Gamson (l%la, 1964) proposed one of the first major theories of coalition formation, the minimum resource theory. This theory holds that the behavior of individuals involved in a coalition situation will be in keeping with a norm of equity (cf. Adams, 1965; Homans, 1961). According to this norm, the perceived fairness of any social exchange depends on the inputs that the participants contribute, and the outcomes that they receive. The norm of equity prescribes that outcomes should be proportional to inputs. In a coalition, each member should receive a share of the payoff proportional to the resources that he or she contributes. Each player is assumed to want to maximize his or her own payoff. Because a player’s resources remain the same no matter which coalition he or she joins, the smaller the total resources of the coalition, the larger will be the player’s share of the payoff. The theory therefore predicts that when the payoff for any winning coalition is the same, the coalition that

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will form is the one with the minimum amount of combined resources necessary to win. As an example of the predictions of the theory, consider the 5(4-3-2) game and suppose that the payoff for winning is 100 (units, points). According to the equity norm, if the 4-3 coalition were to form, 4 would get 57.1 (4/7)and 3 would get 42.9 (%). Similarly, if the 4-2 coalition were to form, 4 would get 66.7 and 2 would get 33.3; and if the 3-2 coalition were to form, 3 would get 60 and 2 would get 40. The 3-2 coalition is therefore predicted to form because 3 would get more in it than in the 4-3 coalition, and 2 would get more in it than in the 4-2 coalition. Further Findings As experimental research on coalition formation accumulated, two further findings emerged, neither of which could be accounted for by minimum resource theory. The first finding was that the division of the coalition payoff is usually less extreme than predicted by the norm of equity. For example, in the 5(4-3-2) game, the coalition between 3 and 2 is predicted to divide the payoff so that 3 gets 60 and 2 gets 40. The actual payoff division, however, is usually more equal than this (Komorita & Chertkoff, 1973). The second finding was that the effects of resources tend to decline as a consequence of experience or familiarity with coalition games. Kelley and Arrowood (1960) argued that in the 5(4-3-2) game there is no logical or strategic reason for the 3-2 coalition to form more frequently than the 4-2 or 4-3 coalition, or for the coalition member with the greater resources to receive a larger share of the payoff. Any of the two-person coalitions can win, and each partner in a coalition needs the other. Strategically speaking, the player with 2 votes has just as much bargaining strength as the player with 3 votes or the player with 4 votes. Kelley and Arrowood (1960) showed that when subjects play the 5(4-3-2) game repeatedly, there is some tendency for them to behave more in accord with their bargaining strength, with the frequencies of the coalitions and divisions of the payoffs becoming more nearly equal. Bargaining Theory Partly in an attempt to account for these two additional findings, Komorita and Chertkoff (1973) proposed the bargaining theory of coalition formation. Unlike most other theories, bargaining theory predicts that players’ payoffs, and sometimes even the coalitions that form, may change over time. For initial instances of coalition formation, the theory assumes that the division of the payoff will be a compromise between two conflicting norms. A coalition member who is strong in resources will advocate a division of the payoff according to the norm of equity, i.e., in

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proportion to resources. A coalition member who is weak in resources will argue that the payoff ought to be divided according to a norm of equality, i.e., equally among the members. The theory assumes that coalition members will adopt a split-the-difference principle regarding the norms, so that each member’s share of the payoff will lie halfway between equity and equality. A coalition is predicted to form if it maximizes the payoffs to all its members when the payoff is divided in this manner. As an example of the initial predictions of bargaining theory, consider again the 5(4-3-2) game. In the 3-2 coalition, 3’s predicted payoff is 55, halfway between 60 (equity) and 50 (equality), and 2’s predicted payoff is 45, also halfway between equity and equality. Likewise, the predicted payoff division in the 4-3 coalition is 53.6 for 4 and 46.4 for 3, and the predicted payoff division in the 4-2 coalition is 58.3 for 4 and 41.7 for 2. The theory thus predicts that the 3-2 coalition is most likely to form, because 3’s predicted payoff is higher in this coalition than in the 4-3 coalition, and 2’s predicted payoff is higher in this coalition than in the 4-2 coalition. With respect to asymptotic predictions-for the formation of coalitions after an indefinite amount of interaction-bargaining theory assumes that players who have been excluded from the winning coalition will try to tempt one or more members of the winning coalition to defect, by making concessions to them. These concessions are assumed to be such as to make a player’s asymptotic payoff in a coalition depend on his or her maximum payoffs in possible alternative coalitions. It is assumed, in effect, that a player estimates the maximum payoff attainable in each alternative coalition of which he or she might be a member. This estimation is based on applying to each alternative coalition either the equity or the equality norm, whichever would result in the player getting a larger payoff. Given these estimates, the asymptotic payoffs within a coalition are predicted to be proportional to each member’s best maximum expected payoff in alternative coalitions. In the 4-2 coalition, for example, 4’s best maximum expected payoff in an alternative coalition is 57.1 (based on equity in the 4-3 coalition), and 2’s best maximum expected payoff in an alternative coalition is 50 (based on equality in the 3-2 coalition). The predicted asymptotic payoff division in the 4-2 coalition is proportional to these best alternatives, or 53.3 for 4 and 46.7 for 2. Recent Findings A limitation of almost all early coalition research is that it focused on simple games (Miller & Crandall, 1980). In the real word, however, the payoffs for different winning coalitions often vary, i.e., real-world situations are often multivalued. For example, the economic advantages of an

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international alliance such as the Common Market are likely to depend on the particular nations that join the alliance. Although both the minimum resource and bargaining theories are applicable to multivalued games, they were only tested in such games relatively recently. Komorita and Tttmonis (1980) and Miller (1980a, 1980b, 1980~)tested the theories in games in which there were differences in both the resources of the players and the payoffs for the winning coalitions. They found that neither theory received much support. The problem with the theories is that in multivalued games the resources that individuals possess exert much less influence on coalition behavior than is predicted. Individuals evidently disregard the resources of partners in the potential coalitions and pay attention instead to the payoffs for the coalitions. For example, Miller (1980a, 1980~) found that the divisions of coalition payoffs were nearer to equality than predicted by either theory, and that the coalition that occurred most frequently was the one with the largest payoff per member, even when this coalition was not predicted by either of the theories. Miller (1980~) also found better support for the equal excess model of coalition formation, which ignores resources altogether, than for either bargaining theory or minimum resource theory. Equhl Excess Model Predictions of the equal excess model (Komorita, 1979) are based on the payoffs for the coalitions that players have available to them, i.e., on the bargaining strength of the players. The model assumes that members of a potential coalition are most likely to agree on a division of the coalition payoff based on sharing equally the excess of what can be gained by the coalition, relative to the respective payoffs each member could get in his or her best alternative coalition. Like bargaining theory, the model predicts that coalition behavior often changes with experience. The model assumes that in the prenegotiation phase of bargaining, players prefer and attempt to form the coalition that maximizes expectations, given by Eis” =

V(S)/S

7

(1)

where Eiso denotes the expectation of player i in coalition S, v(S) denotes the payoff for coalition S, and s denotes the number of members in coalition S. In other words, it is assumed that during the initial exchange of offers, players prefer the coalition with the largest payoff per member. With regard to the division of the payoff in a particular coalition, it is assumed that the expectation of players will change over successive rounds of bargaining, as follows:

EARNED

Eis’

= !J$+EiTrel

263

RESOURCES

+ (ll~)[v(S)

-

Cmax EjT'-'I,

(2)

where Eis' denotes the expectation of player i in coalition S on round r, max EiT'- * denotes player i’s maximum expectation in alternative coalitions (S # T) on round r - 1, and the summation is over all members of coalitionSO’= 1,2,. . . , s). Equation (2) specifies that members should each receive their best alternative (max EiT), and the excess, v(S) Zmax EiTt should be divided equally by them. Expectations for Round 1 are derived by substituting expectations on Round 0 into Eq. (1). For example, consider a three-person game in which the AB coalition is worth 100 points, the AC coalition 80, the BC coalition 60, and all other coalitions are worth zero. For the AB coalition, the initial expectations (Eo) in alternative coalitions are 40 and 30 for A and B, respectively. Substituting these values into Eq. (1) yields Round 1 expectations of 55 for A and 45 for B. Predicted payoff divisions for succeeding rounds are based on iterations of Eq. (2). For many games of interest, an equilibrium state is predicted at the asymptote (E”), in which the expected payoffs of a given player are the same for each of that player’s alternative coalitions (see Komorita, 1979). For example, in the game just described, A’s asymptotic expectation is 60 in both the AB and the AC coalitions; B’s expectation is 40 in both the AB and BC coalitions; and C’s expectation is 20 in both the AC and BC coalitions. THE PRESENT STUDY: DESIGN AND PREDICTIONS

With the exception of the studies by Komorita and Tumonis (1980) and Miller (1980a, 1980b, 198Oc), most coalition research dealing with multivalued games has not concerned itself with individual resources. It seems possible, however, that the lack of interest in resource effects is not entirely warranted. Most coalition studies have operationalized resources by assigning them to the players at random (Stryker, 1972). Since the Komorita and Tumonis and the Miller studies were concerned with whether resource effects in multivalued games would be comparable to the effects previously found in simple games, they operationalized resources in the same manner as had most previous studies. The problem with such an operationalization is that players have little basis for considering the resources as meaningful contributions or inputs to potential coalitions. Thus, there is not much reason to expect resources to have normative connotations, i.e., to be used as a basis for deciding what constitutes fair payoff divisions. If resources were operationalized in such a way as to cause players to regard them as relevant inputs to coalitions, then resources might have a

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greater effect on coalition behavior, even in multivalued games. Such a finding would have at least three important implications: First, it would suggest that the lack of resource effects in laboratory studies on multivalued games is probably not generalizable to many real-world coalition situations, in which resources are likely to be earned or to represent investments, and hence to represent relevant inputs. Second, it would suggest that the lack of interest in resources in multivalued games is unwarranted and that future research on multivalued games should examine possible resource effects. Third, it would suggest the possible need to reconsider explanations of coalition behavior such as minimum resource theory, which are based on individual resources, and which are now largely discounted. One means of having players regard their resources as relevant inputs or contributions is to have them earn the resources, rather than have the resources randomly assigned to them (Messt, Vallacher, & Phillips, 1975). Earned resources, in addition to being more realistic, should be more likely to serve as a basis for dividing coalition payoffs (Stryker, 1972). The present study tested the minimum resource, bargaining, and equal excess theories against each other in two separate multivalued games, under two different resource conditions: earned resources and unearned (randomly assigned) resources. The study involved the two 3-person games shown in Table 1. In each game, the distribution of resources was 7(6-5-2). In Game 1, the 6-5 coaliTABLE 1 PREDICTIONSOFTHEORIESFORTwo COALITIONGAMES Game 1: Coalition Theory

6-5(1,000)

6-2(980)

5-2(870)

Predicted coalition

Minimum resource Bargaining (initial) Bargaining (asymptotic) Equal excess (EL) Equal excess (Z?)

545-454 523-477 542-458 527-472 555-445

735-245 612-367 545-435 522-457 555-425

621-249 528-342 439-431 440-430 445-425

5-2 6-2 6-2 6-5 6-5

Game 2: Coalition

Minimum resource Bargaining (initial) Bargaining (asymptotic) Equal excess (I??‘) Equal excess (IF“)

5-2(1,ooo)

6-2(980)

6-5(870)

714-286 607-393 470-530 472-527 445-555

735-245 612-367 477-503 457-522 425-555

474-395 456-415 441-429 430-440 425-445

Note. Numbers in parentheses are the payoffs for the coalitions.

5-2 5-2 5-2 5-2 5-2

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RESOURCES

265

tion was worth 1000 points, the 6-2 coalition 980, and the 5-2 coalition 870. These resources and payoffs were deliberately selected so that the minimum resource, bargaining, and equal excess theories could be contrasted in terms of their predictions regarding coalition formation. As Table 1 shows, each theory predicts the formation of a diffeerent coalition. In Game 2, the payoffs for the coalitions were reversed, with the 6-5 coalition being worth 870 points, the 6-2 coalition 980, and the 5-2 coalition 1000. In this game, all the theories predict the formation of the same coalition, the one with the largest payoff per member. The inclusion of this game in the experimental design is important, however, because the payoff divisions in it should provide a very strong test of the possible effects of resources. In Game 1, the resources of the players are consistent with their bargaining strength: The greater the resources of a player, the better the player’s payoffs in his or her possible coalitions. Player 6’s possible coalitions are worth more than 5’s, and 5’s are worth more than 2’s. If the player with the greater resources were to receive a larger share of the payoff in the various coalitions, it would be difficult to know whether this was due to the resources of the player or to the player’s advantage in bargaining strength. In Game 2, the resources of the players are in opposition to their bargaining strength: The best payoffs in possible coalitions belong to Player 2, and the worst belong to Player 6. If the player with the greater resources were to get a larger share of coalition payoffs in this game, it could not be attributed to the player’s superior bargaining strength. Three-person groups each played either Game 1 or Game 2, after having “earned” their resources or having had the resources randomly assigned to them. In addition, each group played four trials of the game. This was done in order to see whether resource effects would decrease as a function of experience, as Kelley and Arrowood (I 960) found for simple games. The full design of the study was thus a 2(game: Game 1 vs Game 2) x 2(resource condition: earned vs unearned) x 4(trials) factorial, in which trials was a repeated-measures factor. METHOD

Subjects Subjects were 120 male volunteers from introductory psychology classes. The subjects took part in the study three at a time, with each three-person group being randomly assigned to one of the cells of the 2 x 2 (game x resource condition) design. Procedure Subjects were told that they were participating in a study of business

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understanding and skills. In the first part of the study, subjects were given a “test of business knowledge,” consisting of a number,of items similar to those on the Graduate Management Admissions Test. Performance on the test purportedly served as the basis on which subjects in the earned resources condition were assigned their resources in the second part of the study. The second part of the study was presented as an investigation of coalition formation in a “business negotiations” game. Each subject was asked to play the role of president of a small business firm. Each of the presidents had either 6, 5, or 2 “investment units” to use in order to try to obtain profits for his firm. In the unearned resources condition, the investment units were assigned to the players by means of a random drawing. In the earned resources condition, subjects were told that the assignment of investment units was based on how well they had performed on the test of business knowledge administered in the first part of the study. In actuality, the subjects were given false feedback regarding their performances, and the investment units were assigned at random. The object of the game was for two of the firms to form a coalition that possessed a majority of the investment units. Any such coalition obtained a profit, but the amount of profit depended on which coalition formed. The profit for each’of the possible coalitions was indicated on payoff tables that were given to the subjects (see Table 1 again for payoffs in the games). Each trial of the game consisted of one or more rounds of bargaining. On each round, subjects made offers to one another using written offer slips. On these slips, subjects indicated with whom they wished to form a coalition and how they proposed to divide the payoff for the coalition. Each subject was permitted to make an offer for only one coalition on a given round. Offers were posted on a blackboard for all the subjects to see. Each subject then had a chance to accept one of the offers, if he wanted to, by filling out a response slip. Only if both members of a proposed coalition (including the player who made the proposal) accepted the proposal, was the coalition considered to have formed. (Thus, two coalitions could not form at once.) Otherwise, subjects went on to the next round. Rounds continued until some coalition formed, thus ending that trial of the game. Each subject was told to try to win as many points for himself as he possibly could, but also to try to be fair and reasonable in making, and in accepting or rejecting, offers. These latter instructions were intended to make normative considerations more salient than is typically the case in coalition games. Of all the subjects who participated in each experimental condition, the one who won the most points in each position (i.e., with resources of 6, 5, or 2) was awarded a $10 prize.

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EARNED RESOURCES

To assist subjects in understanding the bargaining procedure, several examples were provided of how the offer and response slips might be filled out. Any questions the subjects had concerning the procedure were also answered. At the end of the second part of the study, a questionnaire was administered to the subjects. The questionnaire asked subjects to consider each of the possible coalitions (6-5, 6-2, 5-2) in the game they had just played and to indicate (1) what would be the fairest way of dividing the payoff for that coalition; (2) why this would be the fairest way of dividing the payoff, (3) whether the fairest way of dividing the payoff would also be the most likely way of actually dividing the payoff, and (4) if not, what would be the most likely way of actually dividing the payoff. Once the study had been completed, subjects were informed of the purpose of the study, the nature of the false feedback involved (in the earned resources condition), and the reasons for the false feedback. Finally, those subjects who had won a monetary prize were paid. RESULTS

Outcomes Coalition frequencies. Table 2 shows the frequency of occurrence and mean payoff division for each of the coalitions, under each resource condition, in each of the games. Coalition frequencies were analyzed using Sutcliffe’s (1957) procedure for the partitioning of x2 in multiple classification contingency tables. A 2(game: 1 vs 2) x 2(resource condition: earned vs unearned) x 3(coalition: payoff of 1000 vs 980 vs 870) x TABLE 2 COALITIONOUTCOMESBYRESOURCECONDITIONANDGAME Game 1: Coalition 6-5(1,000)

6-2(980)

5-2(870)

Resource condition

Division

f

Division

.f

Division

.f

Earned Unearned

548-452

10 12

570-410

16

556-424

13

473-397 481-389

14 15

517-483

Game 2: Coalition 5-2(l,ooo) Earned Unearned

553-447

515-485

6-2(980) 20 20

520-460 515-465

6-5(870) 17

11

Note. Numbers in parentheses are the payoffs for the coalitions;fis rence of coalition.

442-428 429-441

3 9

frequency of occur-

MILLER AND WONG

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TABLE 3 MEAN PL - Ps SCORESBY RESOURCECONDITION AND GAME

Game Resource condition

1

2

M

Earned Unearned M

114.40 87.50 100.95

80.40 25.40 52.90

97.40 56.45

Note. PL - Ps denotes the payoff to the coalition member with the larger resources, in a given coalition, minus the payoff to the coalition member with the smaller resources.

4(trials) contingency table analysis yielded a significant effect only for the interaction of game and coalition, x*(2) = 9.57, p < .Ol.l In Game 1, in which each theory predicted a different coalition, the various coalitions were about equally frequent. In Game 2, in which all three theories predicted the coalition with the largest payoff, that coalition was the most frequent, and the coalition with the smallest payoff was the least frequent . Payoff&visions. Divisions of the coalition payoffs were analyzed using the index P, - P,, where P, is the payoff received by the coalition member with the larger resources, and Ps is the payoff received by the member with the smaller resources. This index was calculated for each coalition that formed. The index is positive if the coalition member with the larger resources gets more of the payoff, negative if that member gets less of the payoff, and zero if the payoff is split equally. Table 3 shows the mean P, - Ps score for each resource condition and each game (collapsed over trials). P, - Ps scores were analyzed by a 2(game) x 2(resource condition) x 4(trials) analysis of variance (ANOVA).* As expected, there was a significant main effect for resource condition: Scores were higher when resources were earned than when they were unearned, F( 1,36) = 4.16, p < .05. There was also a significant main effect for games: Scores were higher for Game 1, in which resources were consistent with bargaining strength, than for Game 2, in which resources were in opposition to bargaining strength, F(1,36) = 5.73, p < .05. Finally, there was some teni This analysis violates the assumption of independence of observations, since trials involved repeated measures. However, additional analyses, performed for each trial separately, also yielded a significant effect only for game by coalition. * The PL - Ps index does not take into account the differing payoffs in the coalitions. Therefore, an ANOVA was also performed using the index (PL - P&P, + P,), which adjusts for differing payoffs. This analysis yielded virtually the same results as those obtained using the simpler PL - Ps index. Hence, only the results of the latter are presented here.

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269

dency for scores to decline over trials, although this effect did not reach conventional levels of significance, F(3,108) = 2.68, p < .lO. It is interesting that mean P, - P, scores were positive even in Game 2, in which resources and bargaining strength were in opposition to each other. Tests of the mean scores in each of the four (game x resource condition) cells showed that they differed significantly from zero (p < .Ol) in all except the Game 2-unearned resources cell (p < .20). Thus, as long as resources were earned, coalition members with larger resources received larger shares of the payoffs, even when the members’ resources were in opposition to their bargaining strength. Initial Offers The initial offers of coalitions and payoff divisions made by Players 6, 5, and 2 on each trial of the game were analyzed by separate 2 x 2 x 4 (game x resource condition x trials) ANOVA. These analyses yielded effects that were parallel to those for the eventual coalition outcomes. For the sake of brevity, full presentation of these results is omitted here.3 There was, however, one interesting exception to the parallelism between initial offers and final outcomes that deserves comment: Resource condition had no significant effect on the payoff divisions initially proposed by Player 6. That is, Player 6 did not demand any larger share of the coalition payoff from 5 or 2 when resources were earned than when they were unearned. However, resource condition did have the expected significant effects on the payoff divisions initially proposed by Players 5 and 2: Player 5 initially offered a larger share of the payoff to 6 and demanded a larger share from 2 when resources were earned than when they were unearned. Likewise, Player 2 initially offered a larger share of the payoff to 6 and to 5 when resources were earned rather than unearned. The fact that the initial offers of Player 6 were not significantly affected by resource condition may have been due to a kind of “ceiling” effect. Players did not often demand or offer payoff divisions that were more extreme than equity splits, regardless of the resources they possessed. There was a strong tendency for Player 6 to demand equity or near-equity splits in the unearned resource condition, and not to be any more demanding than this in the earned resource condition. Accuracy of Theoretical Predictions The relative accuracy of the theoretical predictions regarding payoff divisions was assessed using the discrepancy index P, - P,, where P, denotes the payoff obtained by the member with the larger resources in a given coalition, and P, denotes the payoff predicted for that member. For 3 A summary of the analyses of initial offers can be obtained by writing to the first author.

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MILLER AND WONG TABLE 4 MEAN PL - Pp SCORESBYTHEORETKALPREDICTIONANDG~E

Game Theoretical prediction

1

2

Minimum resource Bargaining (initial) Bargaining (asymptotic) Equal excess (El) Equal excess (E”)

- 118.14 - 33.79 17.54 29.64 8.16

- 172.15 -73.69 45.10 52.75 78.20

M

- 145.14 - 53.74 31.32 41.19 43.18

Note. PL - Pp denotes the payoff obtained by the coalition member with the larger resources, minus the payoff predicted for that member.

each coalition that occurred, this index was calculated for the minimum resource theory, the initial and asymptotic predictions of bargaining theory, and the Round 1 and asymptotic predictions of the equal excess model. The index is positive if the coalition member with the larger resources gets more of the payoff than predicted, negative if that member gets less than predicted, and zero if the payoff split is exactly as predicted. A 2(game) x 2(resource condition) x 4(trials) x S(theoretica1 predictions) ANOVA was performed on the discrepancy scores4 The only significant effects involving predictions were the predictions main effect, F(1.05,37.62) = 807.49, p < .OOOl,and the predictions x game interaction, F(1.05,37.62) = 78.66, p < .OOOl.Mean scores on the discrepancy index, broken down by theoretical prediction and game, are shown in Table 4. Regarding the main effect for predictions: The last column of Table 4 gives the mean discrepancy scores for the five theoretical predictions. Individual comparisons (Winer, 1962) of the means, disregarding sign of discrepancy, showed that the asymptotic predictions of bargaining theory were significantly more accurate than the Z? and E” predictions of the equal excess model (which did not differ significantly), and the El and E” predictions were significantly more accurate than the initial predictions of bargaining theory. The least accurate predictions were the predictions 4 A problem with using scores for the five theoretical predictions in a single ANOVA is that degrees of freedom will be spuriously inflated. Moreover, it would be possible to use any number of additional theoretical models in the analysis, thereby increasing degrees of freedom for error indefinitely. Studies have typically dealt with this problem by using the Greenhouse and Geisser (1959) correction. Although it does not entirely solve the problem, the correction is conservative in that it appreciably reduces the degrees of freedom for theoretical predictions and error mean squares. The present analysis used this correction. The degrees of freedom shown for the analysis are the adjusted degrees of freedom.

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of minimum resource theory. The asymptotic predictions of bargaining theory and the Round 1 and asymptotic predictions of the equal excess model somewhat underestimated the payoff share received by the coalition member with larger resources. The initial predictions of bargaining theory, and especially the predictions of minimum resource theory, overestimated the share received by the member with larger resources. Regarding the interaction effect: The first two columns of Table 4 give the prediction x game cell means. Individual comparisons revealed that each of the theoretical predictions was more accurate (discrepancy scores closer to zero) for Game 1, in which individual resources and bargaining strength were consistent with each other, than for Game 2, in which individual resources and bargaining strength were in opposition. That is, for the asymptotic predictions of bargaining theory and the E’ and E” predictions of the equal excess model, the discrepancy scores were less positive for Game 1 than Game 2, whereas for minimum resource theory and the initial predictions of bargaining theory, the discrepancy scores were less negative for Game 1 than Game 2. The most accurate predictions for Game 1 were the asymptotic predictions of bargaining theory and the equal excess model (which did not differ significantly). The most accurate predictions for Game 2 were the asymptotic predictions of bargaining theory and the Round 1 predictions of the equal excess model (which did not differ significantly). The absolute, rather than the relative, accuracy of the theoretical predictions was also assessed. This was done by testing to see whether each mean discrepancy score (average signed error) for the predictions differed significantly from zero. All five theoretical predictions (last column of Table 4) were found to be significantly in error (p < .Ol in each case). In spite of the fact that all the predictions were in error, it is important to note that the mean payoff divisions in the various coalitions tended to fall between the initial and asymptotic predictions of the bargaining theory (see Tables 1 and 2). In this sense, the payoff divisions are not inconsistent with bargaining theory. Questionnaire Responses In the questionnaire administered after the second part of the study, subjects were asked to indicate what they thought would be the fairest way of dividing the payoff in each of the three coalitions (6-5, 6-2, and 5-2) in the game that they had just played. They were also asked to explain why they believed this would be the fairest division of each payoff. Responses to these questions were examined to see, for each possible coalition, whether subjects thought that the fairest division of the payoff was one that favored the member with larger resources. Each subject was given a score representing the number of coalitions (0 to 3) for which he

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thought such a payoff split would be fairest. Mean scores, broken down by game, resource condition, and player (6, 5, and 2) are shown in Table 5. These scores were analyzed in a 2(game) x 2(resource condition) X 3(player) ANOVA. As expected, there was a significant main effect for resource condition: Subjects more frequently believed that the fairest division of the coalition payoff was one favoring the member with larger resources, when the resources were earned than when the resources were unearned, F(1,36) = 8.49, p < .Ol. There was also a significant main effect for game: Subjects more frequently thought that splits favoring the member with larger resources were the fairest in Game 1, in which resources were consistent with bargaining strength, than in Game 2, in which resources were in opposition to bargaining strength, F(1,36) = 10.82, p < .005. Finally, there was a significant main effect for player: Subjects who played as Player 6 were the most likely to think that the fairest payoff splits were those that favored the member with larger resources, and subjects who played as Player 2 were the least likely to think that such splits were fairest, F(2,72) = 7.00, p < .005. This effect may be interpreted as a self-serving bias, since the player with the most resources was the most likely to think payoffs should be divided in accord with resources, and the player with the least resources was the least likely to think payoff divisions should be based on resources. The questionnaire also asked subjects whether the fairest payoff division would be the most likely actual division, and, if not, what would be the most likely division, and why. In most instances (54% of all responses), subjects thought that the fairest way of dividing the payoff would also be the most likely way of actually dividing it. When subjects thought that there would be a difference between the fairest division and TABLE 5 MEAN FREQUENCY OF “FAIREST” PAYOFF SPLITS FAVORING THE COALITION MEMBER WITH LARGER RESOURCES

Game 1: Resources

Game 2: Resources

Player

Earned

Unearned

Earned

Unearned

M

6 5 2

2.80 2.90 2.20 2.63

2.60 2.20 1.90 2.23

2.60 2.20 1.70 2.17

2.20 1.20 1.20 1.53

2.55 2.12 1.75

M

Note. Each player indicated what he considered the fairest payoff split to be in each of the coalitions (6-5, 6-2, and 5-2). Frequencies with which players considered splits favoring the coalition member with larger resources the fairest could thus range from 0 to 3.

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the most likely division, it was typically because they thought that the most likely division would be nearer to equality than the fairest division. There were, however, a few instances (6% of all responses) in which subjects thought that the fairest payoff division would be an equal split, but that the most likely payoff division would be a split favoring the coalition member with the larger resources. Most of these instances occurred with subjects who had played as Player 2, and may be interpreted as another example of self-serving bias. DISCUSSION

As expected, the tendency for coalition members with more resources to be offered, and to receive, a larger share of the payoff was stronger in the earned resources condition than in the unearned resources condition. Moreover, when resources were earned, they had a stronger effect on payoff divisions than did bargaining strength: Offers and payoff divisions favored the coalition member with more resources, even when that member had less bargaining strength. These results suggest that previous findings regarding the negligible effects of resources in multivalued games may not generalize to situations in which resources are earned, as they are likely to be in many real-world organizational settings. In general, resources appear to have had a stronger effect in the present study, even when they were unearned, than in previous studies involving multivalued games (e.g., Komorita & TLtmonis, 1980; Miller, 1980a, 1980b, 1980~). Two possible explanations of this difference in findings seem most plausible: One possibility lies in a difference between the instructions used in previous studies and those used in the present study. In the previous studies, subjects were given what might be termed individualistic instructions (Deutsch, 1960), in which they each were told to maximize their own outcomes, without any regard to the outcomes of others. Subjects in the present study were instructed to maximize their own outcomes, too, but they were also told to be reasonable andfair in making offers to others, and in accepting or rejecting offers. These latter instructions represented an attempt to make normative considerations more salient to the subjects, although without suggesting exactly what they ought to regard as “fair” or “reasonable.” It is possible that when subjects are made more sensitive to normative issues, they attend more to resources and use them more as a basis for determining payoff splits, even when the resources are randomly assigned. Another possibility is that most previous studies have presented coalition games in a somewhat different context than the “business” context used in the present study. For example, many studies have used the “poIiticaI convention” paradigm originally employed by Gamson (1961b). It

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AND WONG

may be that asking subjects to represent “business firms” and referring to resources as “investment units” heightened the salience of the equity norm. Equity (proportionality) appears to be regarded as an appropriate standard for judging the fairness of many business transactions (Leventhal, 1976). The fact that subjects were asked to act as though they represented businesses also raises a point concerning the possible generalizability of the results: It could be argued that while the results may be generalizable to between-organization coalitions, they are not necessarily generalizable to within-organization coalitions. It should be remembered, however, that each subject was playing for a chance to win a $10 prize for himself, and no one else. In this respect, the subjects can be regarded as self-interested individuals as much as they can be considered the representatives of organizations. One of the main implications of the study-that relevant inputs such as earned resources may have a stronger effect on coalition outcomes than does bargaining power-seems to hold for many real-world instances of within-organization coalitions. For example, the rewards of collaborative research, in the form of priority of authorship on articles and papers, is based on the relevant professional contributions of the researchers rather than on their bargaining power (CL&. It is considered inappropriate for a full professor, say, to take first authorship over even a lowly graduate student, if the graduate student contributed greater inputs of a relevant nature than did the professor. This is in spite of the fact that the professor is likely to have much greater power than the student. This norm is so strong that it is formalized as part of the ethical principles of psychologists (American Psychological Association, 1981). Norms often seem to serve the function of protecting those who are relatively weak from those who are stronger. Although resources had a strong effect on payoff divisions, there was a nonsignificant trend for this effect to decrease over trials. It is therefore possible that the effect of resources would have continued to decrease, and would have become weaker than the effect of bargaining strength, if the players had been given still more bargaining experience. The questionnaire responses provide support for the notion that payoff divisions favored the coalition member with larger resources because of normative considerations, i.e., because such divisions were considered the fairest, especially when the resources were earned. Of course, since the questionnaires were administered after play of the games had been completed, it is also possible that the perceived fairness of payoff divisions favoring members with more resources is merely an example of the “just world” phenomenon (Lerner, 1971), i.e., what is, ought to be. Arguing against this interpretation, however, is the fact that subjects also believed that actual payoff divisions were likely to be more equal than the

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fairest division. In other words, subjects distinguished between what they saw as most likely and what they saw as fairest, with the fairest payoff divisions being based more on resources. The questionnaire responses also offer evidence of what may be regarded as self-serving biases: The larger the resources of a player, the more often the player thought that the fairest payoff divisions were ones favoring the coalition member with larger resources. In addition, the few instances in which the fairest payoff divisions were thought to be more equal than the most likely actual divisions occurred mostly for players who had the least resources. These self-serving biases are consistent with the assumptions of bargaining theory (Komorita 8z Chertkoff, 1973) that coalition members with larger resources will tend to support payoff divisions more in accord with the equity norm, whereas members with smaller resources will tend to support divisions more in accord with the norm of equality. With respect to the theoretical predictions for coalition formation: The results of Game 1, in which the theories made opposing predictions, were inconclusive. None of the coalitions were significantly more frequent than the others. In Game 2, all of the theories made the same prediction, and this prediction was supported. Games such as Game 2, in which the coalition with the largest payoff is composed of players with relatively small resources, should be relatively easy games for which to make accurate predictions about coalition formation. Coalitions with large payoffs as well as small resources are particularly attractive. With respect to the theoretical predictions for payoff divisions: In spite of the fact that resources had an obvious effect on coalition behavior, the least accurate predictions were those of minimum resource theory, which are based entirely on resources. This inaccuracy may be due partly to the fact that minimum resource theory predicted relatively extreme payoff divisions. Actual payoff divisions were nearer equality, and coalition research has generally shown that there is a tendency for payoff divisions to be more equal than predicted by most theories (Crott & Albers, 1981). The inaccuracy is also a function of the fact that even though resources had an effect, so did bargaining strength, as shown by the significant difference in mean P, - P, scores between Games 1 and 2. All of the theoretical predictions were less accurate in Game 2 than in Game 1. Apparently, all of the theories encounter difficulties in games in which the players’ resources are in opposition to their power, or bargaining strength. Such games present the players with conflicting bases for deciding how to divide the coalition payoff. The present results show that when resources are earned, players give greater weight to resources than to bargaining strength, at least initially. This is a serious problem for the equal excess model, as well as for the many game-theoretic models

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that are based on various concepts of bargaining strength (Rapoport, 1970). In general, the most accurate predictions were the asymptotic predictions of bargaining theory, which are based partly on resources and partly on bargaining strength. Conclusion Power or bargaining strength plays an important role in bargaining and coalition formation (cf. Kahan & Rapoport, 1984), but so do norms of justice such as equity and equality. A variety of justice norms may be salient, depending on the nature of the situation and the individuals involved. Any adequate theory of coalition behavior must be able to specify the relative weight given to bargaining strength and to the various possible norms of justice (cf. Komorita & Kravitz, 1983). It appears that bargainers give at least some weight to each of these factors, and that theories based entirely on one factor or the other fare poorly. The present results indicate that when resources are earned, the relative weight accorded to the norm of equity may be greater than that accorded to the strength of bargaining position. There is also the possibility that equity receives more weight in business-related contexts, or when normative considerations such as fairness are made salient. The results also suggest, however, that the weight given to bargaining strength may increase with increasing experience in bargaining. Finally, it seems likely that the equality norm plays a stronger role in coalition behavior than most theories imply. REFERENCES Adams, J. S. (1965). Inequity in social exchange. In L. Berkowitz (Ed.), Advances in experimental social psychology. New York: Academic Press. American Psychological Association. (1981). Ethical principles of psychologists (rev.). American

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