The equal division kernel: An equity approach to coalition formation and payoff distribution in N-person games

Most existing models of coalition formation and payoff distribution in groups rest upon normative considerations and are ambiguous in their predictions insofar as they do not determine which of several coalitions will most probably result. The paper sketches the basic features of a model derived from social psychological exchange-and equity-theory which predicts coalitions and payoff distributions for a variety of situations. The evaluation of the model by the results of several experiments indicates that it provides a reasonable starting point for further theoretical developments that are based empirical studies.     

The excluded player in coalition formation

Coalition research generally assumes that people strive to maximize their share of the coalition payoff and that they exclude others from joining a coalition if these others are not needed to obtain the coalition payoff. In two experiments, the authors show that this view is too narrow and that willingness to include such others is dependent on the extent to which people feel that exclusion affects the payoff of the excluded player. This finding was moderated by social value orientations. Proselfs were not affected by the consequences for the excluded players. Prosocials were less willing to exclude others the more harmful were the consequences of exclusion. Results are related to research on social exclusion, the do-no-harm principle, and social value orientations.     

Motivational determinants of coalition formation

Coalition preferences of 300 male and female subjects were ascertained under varying motivational conditions. Two of the experimental conditions repeated the typical three-person coalition paradigm, with a monetary reward (extrinsic motivation) offered for the winning of a luck-determined game. In a third condition, skill rather than luck influenced the outcome and no monetary reward was given for winning (intrinsic motivation). Two additional conditions examined coalition preferences in a mixed-motive situation, with either a small or a large monetary reward offered for winning a skill-related game. In the extrinsic motivation condition, the low and the medium resource persons typically desired to coalesce, contrary to the wishes of the excluded, high resource player. In contrast, the coalition between the low and the medium resource persons also was preferred by the high resource player in the intrinsic motivation condition. Coalition conflict was intermediate in the mixed-motive conditions. In sum, it was demonstrated that coalition formation and interpersonal conflict are dependent upon the motivational determinants of group activity.     

Computer controlled research on bargaining and coalition formation

Described in this paper is a research paradigm, written as a set of computer programs, to conduct on-line bargaining and coalition formation experiments within the characteristic function game framework. The structure of the paradigm is outlined, an example is presented and discussed, and further extensions of the program are briefly discussed.     

The role of sex and personality in the prenegotiation stage of coalition formation

Research in the area of sex differences in coalitional behavior has produced inconsistent results that may be partially resolved through an examination of personality and attitudinal differences between males and females. The responses of males and females to the Shure and Meeker Personality/Attitude Schedule were analyzed and the sexes differed in their elevation on six major factors. A subsample of each sex participated in a coalition game situation. Four of the six personality and attitude factors were related to prenegotiation stage indices of coalition formation. It was suggested that the role of sex differences in coalitional behavior may be mediated by sex role socialization differences.     

Do-no-harm in coalition formation: Why losses inhibit exclusion and promote fairness cognitions

Previous research on coalition formation has established that people will not hesitate to exclude others in order to maximize their payoff. The authors propose that this view is too narrow and that the decision to exclude depends on the valence of the payoff. Consistent with a “do-no-harm” hypothesis, Experiment 1 showed that participants were more reluctant to exclude in order to minimize their losses than to maximize their gains. Experiment 2 replicated this effect and showed that participants were most affected by payoff valence when they were disposed to consider the viewpoint of others. Additional analyses revealed that participants were more motivated by fairness (Experiment 1) and that fairness was more cognitively accessible (Experiment 2) when payoffs were negative rather than positive.     

Common knowledge of payoff uncertainty in games

Using epistemic logic, we provide a non-probabilistic way to formalise payoff uncertainty, that is, statements such as ‘player i has approximate knowledge about the utility functions of player j.’ We show that on the basis of this formalisation common knowledge of payoff uncertainty and rationality (in the sense of excluding weakly dominated strategies, due to Dekel and Fudenberg (1990)) characterises a new solution concept we have called ‘mixed iterated strict weak dominance.’     

Bargaining ability,the utility of playing a game,and models of coalition formation

A utility function for playing a given position in a game is developed as a natural extension of the utility function which defines the rewards available in the game. This function is determined by a player's opinion of his bargaining ability. A characterization of such utilities is obtained which generalizes previous results that the Shapley value and Banzhaf-Coleman index are both cardinal utility functions which reflect different bargaining abilities. The approach taken here is related to models of coalition formation.     

Effects of alternatives in coalition bargaining

A critical factor in bargaining and coalition formation is the alternative outcomes of the bargainers if an agreement cannot be reached. In some situations bargainers have individual alternatives while in other situations their alternatives must be negotiated with others. The purpose of this study was to contrast the effects of one-person and two-person alternatives on coalition outcomes. The second purpose of the study was to contrast the predictions of four theories of coalition formation: bargaining theory, equal excess model, Shapley value, and a special case of equity theory. The results indicate that one-person alternatives enhance the bargaining strength of the stronger players more than two-person alternatives. The predictions of the equal excess model and the Shapley value were more accurate than the predictions of bargaining theory and equity theory. However, the greater accuracy of the equal excess model and the Shapley value may be restricted to situations in which the bargainers have one-person rather than two-person alternatives.     

The interaction of payoff structure and regulatory focus in classification

This report brings together research on motivation and learning by exploring how fit of regulatory focus affects people's ability to acquire new categories. Perceptual categories were learned by people with a promotion focus (a situationally determined sensitivity to gains) or a prevention focus (a sensitivity to losses). Classification performance was closest to optimal (as determined by models fit to individual subjects' data) when the regulatory focus matched the structure of the payoffs for the categories. Promotion-focus subjects performed best when the payoffs consisted of all gains. Prevention-focus subjects performed best when the payoffs consisted of all losses.     

Category discriminability, base-rate, and payoff effects in perceptual categorization

The optimality of perceptual categorization performance under manipulations of category discriminability (i.e., d' level), base rates, and payoffs was examined. Base-rate and payoff manipulations across two category discriminabilities allowed a test of the hypothesis that the steepness of the objective reward function affects performance (i.e., the flat-maxima hypothesis), as well as the hypothesis that observers combine base-rate and payoff information independently. Performance was (1) closer to optimal for the steeper objective reward function, in line with the flat-maxima hypothesis, (2) closer to optimal in base-rate conditions than in payoff conditions, and (3) in partial support of the hypothesis that base-rate and payoff knowledge is combined independently. Implications for current theories of base-rate and payoff learning are discussed.     

Differential payoff and locus of selectivity in a visual memory task

Two experiments were run to investigate the locus of selectivity in a visual memory task involving differential payoff for letters correctly recalled: Major variables consisted of value instructions given before or after the exposure of a display, the ratio of high to low value, and exposure duration. The results showed that Ss make more correct reports of higher value than of lesser value, whether value instructions are given before or after the display. Furthermore, overall performance and extent of selectivity increase with increasing exposure time, but more for the before than the after conditions of instruction. These results suggest that selectivity occurs both during perception and retention and during recall.     

On coalition formation in simple games: A mathematical analysis of Caplow's and Gamson's theories

In this paper, we propose a theory of coalition formation in simple games. The process of coalition formation is modeled as an abstract game. Two solutions of abstract games, the core and the dynamic solution, are used as the predictions of our model. Two classical theories of coalitions in sociology due to Caplow and Gamson are reformulated in a more general and mathematical setting. These theories are then analyzed using the techniques of our theory.     

The faultline activation process and the effects of activated faultlines on coalition formation,conflict, and group outcomes

This research examines the effects of group faultline activation on coalition formation, conflict, and group outcomes. We distinguish between dormant faultlines (potential faultlines based on demographic characteristics) and activated group faultlines (members actually perceive subgroups based on the demographic characteristics) and hypothesize that while dormant faultlines do not automatically turn into active group divisions, a group’s entitlement configuration can activate divisions among group members. Study 1 was a construct validity study to verify the psychometric properties of the activated group faultline measure and explain its connection to other process variables. In Studies 2 and 3, we tested our hypotheses and found that groups with activated faultlines were more likely to form coalitions, have high levels of group conflict, and lower levels of satisfaction and group performance than dormant faultline groups. Furthermore, team identification moderated the effects of activated faultlines on group processes such that a strong workgroup identity decreased the likelihood that activated faultlines led to coalition formation and conflict.