Quota vs positional power in four-person apex games

In coalition formation experiments, which coalitions will form and how players in coalitions will allocate their jointly gained rewards are typically predicted as a function of the players' relative power. In this paper, we isolated two logically independent sources of a player's power: the player's contribution to the rewards obtainable by coalitions of which he may be a member (“quota power”), and the number of distinct coalitions which a player may join (“positional power”). The separation of the two types of power is clearly shown in apex games, where a single player (Apex) attempts to lure any of the other players (Base) from the coalition of all Bases. A series of four-person computer-controlled apex and nonapex characteristic function games, varying with respect to the relationship of quota power to positional power, were played by 15 quartets of male players. Quota power was strongly manifested in all outcome measures, while positional power appeared only as a bias toward equal allocations of reward when coalitions among players of equal positional power formed. Neither of two social psychological theories that are applicable, pivotal power and weighted probability theory, predicted coalition frequencies. In a test of five solution concepts, the competitive bargaining set predicted payoff allocations better than either of the two aforementioned theories, the kernel, or an equal-split model.     

A PDP-11/45 program for playing n-person characteristic function games

NPER II is an on-line PDP-11/45 computer program for studying bargaining and coalition formation processes within the framework of n-person games in characteristic function form. The extensive vocabulary of the program and its mode of operation are presented nontechnically, followed by an examination of a protocol from a sample four-person game. Improvements over a previous version of the program and applications to other experimental paradigms investigating coalition formation and bargaining are discussed in the last two sections of the paper.     

When three is not always two against one: Coalitions in experimental three-person cooperative games

Four models of coalition formation are tested in a computer-controlled experiment in which three players negotiated to form coalitions in order to gain rewards for themselves. Formation of the grand coalition of all three players as well as any of the three possible 2-person coalitions is permitted. The results indicate that the grand coalition is the most likely to form, followed by the coalition between the two strongest players. The individually rational bargaining set model of coalition formation is supported over an egalitarian model, the Shapley value, and the coalitionally rational bargaining set model. Various measures of the progress of negotiations are introduced, examined, and discussed in an effort to provide an increased data base for the establishment of a behavioral theory of bargaining and coalition formation.     

Hard and Soft Preparation Sets in Boolean Games

A fundamental problem in game theory is the possibility of reaching equilibrium outcomes with undesirable properties, e.g., inefficiency. The economics literature abounds with models that attempt to modify games in order to avoid such undesirable properties, for example through the use of subsidies and taxation, or by allowing players to undergo a bargaining phase before their decision. In this paper, we consider the effect of such transformations in Boolean games with costs, where players control propositional variables that they can set to true or false, and are primarily motivated to seek the satisfaction of some goal formula, while secondarily motivated to minimise the costs of their actions. We adopt (pure) preparation sets (prep sets) as our basic solution concept. A preparation set is a set of outcomes that contains for every player at least one best response to every outcome in the set. Prep sets are well-suited to the analysis of Boolean games, because we can naturally represent prep sets as propositional formulas, which in turn allows us to refer to prep formulas. The preference structure of Boolean games with costs makes it possible to distinguish between hard and soft prep sets. The hard prep sets of a game are sets of valuations that would be prep sets in that game no matter what the cost function of the game was. The properties defined by hard prep sets typically relate to goal-seeking behaviour, and as such these properties cannot be eliminated from games by, for example, taxation or subsidies. In contrast, soft prep sets can be eliminated by an appropriate system of incentives. Besides considering what can happen in a game by unrestricted manipulation of players’ cost function, we also investigate several mechanisms that allow groups of players to form coalitions and eliminate undesirable outcomes from the game, even when taxes or subsidies are not a possibility.     

Social motives among Anglo American and Mexican American children: Experimental and projective measures

The measurement approaches to social motives, cooperation-competition games and projective tests, have revealed apparently similar findings: Anglo American children are more competitive and higher in n Achievement compared to Mexican American children, who are more cooperative and higher in n Affiliation. The present experiment tested the extent to which (1) competitiveness is related to n Achievement, (2) cooperativeness is related to n Affiliation, and (3) the cultural differences in cooperation-competition are related to those in n Affiliation and n Achievement. Results indicate that social motives inferred from a cooperation-competition game have a meaningful relation to those inferred from a projective test, but that the cultural differences in cooperation-competition are larger and are not explained by cultural differences in n Affiliation and n Achievement. Social motives inferred from each measurement methodology, while somewhat related, are distinct.     

Coalition formation in characteristic function games: Competitive tests of three theories

Two experiments tested the bargaining, minimum resource, and minimum power theories of coalition formation in situations involving different payoffs for some of the winning coalitions (characteristic function games). In the first experiment, a triadic resource distribution was employed and payoffs for the coalitions were specified in such a way that each of the three theories predicted the formation of a different coalition. The coalition predicted by minimum power theory formed the most frequently, and the mean divisions of the payoffs among coalition members were also closest to the predictions of minimum power theory. However, the most frequent coalition was not only the one predicted by minimum power theory, it was also the one having the largest payoff per member. There-fore, a second experiment was conducted, which employed a tetradic resource distribution and specified the coalition payoffs in such a way that (a) each of the theories predicted the formation of a different coalition and (b) none of the predicted coalitions was the one with the largest payoff per member. Although the mean payoff divisions in the coalitions in this experiment were closest to those predicted by bargaining theory, the coalition that formed most frequently was not one of those predicted by any of the theories. Rather, it was the one having the largest payoff per member. None of the three theories is able to account adequately for the results of both experiments. The difficulties that the theories have in dealing with coalition formation in situations in which there are different payoffs for winning are discussed.     

Factor structure of the Eating Disorder Examination Questionnaire (EDE-Q) in male and female college athletes

The study explored the psychometric properties of the Eating Disorder Examination Questionnaire (EDE-Q) among 1637 university students. Participants were divided into male (n = 432) and female (n = 544) competitive athletes, and male (n = 229) and female (n = 429) comparison groups comprised of individuals who had not engaged in competitive sports for at least one year. All groups were subjected to confirmatory factor analysis (CFA) to test the fit of the published factor structure in this population, and then exploratory FA (EFA). A three-factor solution was the best fit for three out of four groups, with a two-factor solution providing best fit for the male comparison group. The first factor for all groups resembled a combined Shape and Weight Concern subscale. The factor structure among male and female competitive athletes was remarkably similar; however, non-competitive athletic/low activity males appear qualitatively different from other groups.     

Correspondence analysis and optimal structural representations

Many well-known measures for the comparison of distinct partitions of the same set ofn objects are based on the structure of class overlap presented in the form of a contingency table (e.g., Pearson's chi-square statistic, Rand's measure, or Goodman-Kruskal'sτ _b ), but they all can be rephrased through the use of a simple cross-product index defined between the corresponding entries from twon ×n proximity matrices that provide particular a priori (numerical) codings of the within- and between-class relationships for each of the partitions. We consider the task of optimally constructing the proximity matrices characterizing the partitions (under suitable restriction) so as to maximize the cross-product measure, or equivalently, the Pearson correlation between their entries. The major result presented states that within the broad classes of matrices that are either symmetric, skew-symmetric, or completely arbitrary, optimal representations are already derivable from what is given by a simple one-dimensional correspondence analysis solution. Besides severely limiting the type of structures that might be of interest to consider for representing the proximity matrices, this result also implies that correspondence analysis beyond one dimension must always be justified from logical bases other than the optimization of a single correlational relationship between the matrices representing the two partitions.     

Coordination in Market Entry Games with Symmetric Players

We report the results of two experiments designed to study tacit coordination in a class of market entry games with linear payoff functions, binary decisions, and zero entry costs, in which each of n = 20 players must decide on each trial whether or not to enter a market whose capacity is public knowledge. The results show that although the subjects differ considerably from one another in their decision policies, tacit coordination emerges quickly on the aggregate level and is accounted for most successfully by the Nash equilibrium solution for noncooperative n-person games.     

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.     

Resources and alternatives in coalition formation: The effects on payoff,self‐serving behaviour,and bargaining length

A consistent finding in coalition research is that the payoff of coalition members is related to (a) the resources they contribute to the coalition, and to (b) the number of alternative coalitions they can form. These two factors are, however, often intertwined. A greater number of resources tends to go hand in hand with a greater number of alternatives, leaving unanswered how both factors affect coalition behaviour. This paper attempts to clarify the interplay of resources and alternatives by disentangling the two in a newly developed coalition paradigm. Results indicated that participants base their payoff allocation on both resources and alternatives, but suggest that self‐serving behaviour is more related to alternatives. Furthermore, resources and alternatives had a distinct effect on the bargaining process. It was shown that differences in alternatives led to longer bargaining. Copyright © 2004 John Wiley & Sons, Ltd.     

Concurrent random-interval schedules and the matching law

In Experiment I, a group of eight pigeons performed on concurrent random-interval schedules constructed by holding probability equal and varying cycle time to produce ratios of reinforcer densities of 1:1, 3:1, and 5:1 for key pecking. Schedules for a second group of seven were constructed with equal cycle times and unequal probabilities. Both groups deviated from simple matching, but the two forms of the schedules appeared to produce no consistent patterns of deviation. The data were found to be consistent with those obtained in concurrent variable-interval situations. The parameters of the matching equation in the form of Y=k X^a were estimated; the value of k was unity and a was 0.84. In Experiment II, six pigeons were exposed to two conc RI RI schedules in which one component increasingly approximated an FI schedule. The value of k was not 1.0. Concurrent RI RI schedules were shown to represent a continuum from conc FI VI to conc VI VI schedules. The use of the exponential equation in testing “matching laws” suggests that a<1 will continue to be observed, and this will set limits on the form of new laws and the assumed or rational values of the component variables in these laws.     

Get angry, get out: The interpersonal effects of anger communication in multiparty negotiation

Research on multiparty negotiation has investigated how parties form coalitions to secure payoffs but has not addressed how emotions may affect such coalition decisions. Extending research on bilateral negotiations which has generally argued that it is beneficial to communicate anger, we argue that it constitutes a considerable risk when there are more than two people present at the negotiation table. Using a computer-mediated coalition game we show that communicating anger is a risky strategy in multiparty bargaining. The main findings of three studies were that participants: (1) form negative impressions of players who communicate anger and therefore (2) exclude such players from coalitions and from obtaining a payoff share, but (3) make considerable concessions on those rare occasions that they choose to form a coalition with an angry player, or (4) when they had to form a coalition with an angry player. We discuss the implications of these results for theorizing on emotions, negotiations, and coalition formation.     

Motivational bases of choice in three-choice decomposed games

Subjects were presented a series of decomposed games that permitted them to select alternatives that maximize one or more of the following motivational dispositions: (1) own gain (individualism), (2) joint gain (cooperation), (3) relative gain (competition), or (4) minimization of other's gain (aggression). There were two types (cases) of games. Case 1 games permitted the S the same or a greater number of points than the other player across all alternatives; Case 2 games afforded the same or fewer points than the other player across all alternatives. It was found: (1) the motive of minimization of other's gain was negligibly reflected in Ss' choices; (2) the other motives were present and affecting Ss' choices; (3) more competitive and fewer cooperative choices occurred in Case 2 than in Case 1 games; (4) sex of subject affected choice behavior in only one game, where males tended to be more cooperative and females more individualistic; and (5) though information on choice and outcome of others was highly limited, some behavioral imitation occurred within dyads.     

Threats,Promises, and Coalitions: A Study of Compliance and Retaliation in a Simulated Organizational Setting1

This research sought to examine the effects of threats and promises on compliance and the formation of subordinate coalitions in a simulated employeremployee conflict situation. It also sought to determine some of the motives underlying coalition decisions-tangible and intangible-and the conditions under which each of these possible motive types would be salient. Coalition motives were examined by manipulating the consequences for coalition members following their use of coalition power (presence vs. absence of monetary gain). A control condition was present in which no such power was available. Ninety male undergraduate business students were randomly assigned to one of six experimental conditions in a 3 × 2 factorial design. Three Ss engaged in a modified bilateral monopoly bargaining task in which two of them (the “employees”) believed they were exchanging a series of offers and counteroffers with the third (the “employer”) over a hypothetical wage increase for a maximum of eight rounds. Ss were told they would earn a sum of money proportional to the effectiveness of their bargaining. In actuality, all Ss were assigned the employee role and all employer “offers” were pre-programmed. On round six, the Ss were “sent” either a threat or promise message by the employer demanding that they accept his round five offer. Compliance-noncompliance was defined as employee acceptance-rejection of this demand, respectively. In addition to compliance behavior, S s in coalition conditions had the power to form an alliance with the other employee against the employer after the latter used his threat or promise power. Coalitions could confiscate up to 25% of the employer's earnings and, depending on experimental condition, could either keep or not keep any money their coalition acquired. It was hypothesized that threateners would elicit less compliance, and be responded to with more, and more severe subordinate coalitions than would promisers. It was further assumed that there would be less compliance when subordinates had coalition power, and that the effect of monetary reward on the likelihood of coalition formation would be contingent on the type of power (threats vs. promises) the employer used. Specifically, it was assumed that a majority of S s in the Threat condition who had this power would form coalitions against the employer regardless of whether or not they realized any tangible gain for doing so. In the promise condition, however, it was expected that coalition decisions would be based primarily on whether Ss stood to gain monetarily. The hypotheses were supported. These results were discussed in terms of the impact of power acquisition as a variable mediating perception and compliance behavior, and in terms of the role of economic vs. retaliatory motives as factors underlying subordinate coalition decisions. Some of the conditions which influence the relative salience of these two coalition motives were proposed, and the organizational implications of these findings were suggested.     

A counterexample to Fishburn's conjecture on finite linear qualitative probability

Kraft, Pratt and Seidenberg (Ann. Math. Statist. 30 (1959) 408) provided an infinite set of axioms which, when taken together with de Finetti's axiom, gives a necessary and sufficient set of “cancellation” conditions for representability of an ordering relation on subsets of a set by an order-preserving probability measure. Fishburn (1996) defined f(n) to be the smallest positive integer k such that every comparative probability ordering on an n-element set which satisfies the cancellation conditions C₄,…,C_k is representable. By the work of Kraft, Pratt, and Seidenberg (1959) and Fishburn (J. Math. Psychol. 40 (1996) 64; J. Combin. Design 5 (1997) 353), it is known that n-1?f(n)?n+1 for all n?5. Also Fishburn proved that f(5)=4, and conjectured that f(n)=n-1 for all n?5. In this paper we confirm that f(6)=5, but give counter-examples to Fishburn's conjecture for n=7, showing that f(7)?7. We summarise, correct and extend many of the known results on this topic, including the notion of “almost representability”, and offer an amended version of Fishburn's conjecture.     

Game outcome and elite Japanese women’s field hockey player’s experience of emotions and stress

Objectives: To measure the effects of game outcome on pleasant and unpleasant emotions and stress during elite-level competition.Design: Quasi-experimental repeated pre- and post-game measurement in a field setting.Methods: Participants were 16 members of the Japanese women’s field hockey team playing a world cup preliminary qualifying tournament in Trinidad. Players completed the Tension and Effort Stress Inventory (TESI), a measure of emotion and stress, at the seven games of the tournament (five wins, two losses).Results: The pattern of emotions after game 1 (a loss) were in sharp contrast to the results from the other six games (five wins, one loss). When compared to other games, significant increases in anxiety, humiliation and excitement pre- to post-game 1 were found, as were significantly higher scores in sullenness and lower scores in relaxation post-game 1. No significant decreases in external tension stress and somatic tension and effort stress pre- to post-game 1 were found. For the other games, athletes were significantly more relaxed and excited after games, increasing with each game in the tournament. Also, the unpleasant emotion and stress results, associated with game 1, significantly diminished as the team progressed to the tournament final. There was no evidence for a simple win/loss difference on post-game emotions and stress.Conclusions: The relationship between game outcome and emotional response is not straightforward. Other factors, such as cognition, may also play a role.     

Keeping Abreast of Hypersexuality: A Video Game Character Content Analysis

This study examined male and female sexuality in video game characters. The top 20, best selling console (Microsoft Xbox, Sony PlayStation2, and Nintendo GameCube) video games from the U.S. market for fiscal year 2003 were content analyzed. The 60 video games yielded a total of 489 separate characters with an identifiable sex for coding. Chi-square analyses indicated that female characters (n?=?70) were underrepresented in comparison to their male counterparts (n?=?419) as hypothesized. In comparison to male characters, females were significantly more likely to be shown partially nude, featured with an unrealistic body image, and depicted wearing sexually revealing clothing and inappropriate attire as also predicted. Implications for these findings are discussed using social cognitive theory as a theoretical anchor.