Two results concerning the relation between rationality and equilibrium concepts in normal form games are generalized for the case where players do not satisfy the reduction of compound lotteries axiom. The crucial axiom of expected utility theory is the independence axiom which itself is a combination of two axioms: the compound independence axiom and the reduction of compound lotteries axiom. This paper is an effort to extend game theory to non-expected utility preferences. It generalizes the results of Aumann (1987) and Aumann and Brandenburger (1991) to games with players who do not satisfy the reduction of compound lotteries axiom. We show that the results of the above authors do not depend on the specific definition of rationality applied by them.

The internal problem of collective action that arises when groups, as opposed to individuals, are in conflict cannot be studied in the context of two-person games that treat the competing groups as unitary players. Traditional N-person games are also too restrictive for this purpose, since they ignore the conflict of interests between the groups. Because the intergroup conflict motivates the need for intragroup collective action, and the groups' respective success in mobilizing collective action determines the outcome of the intergroup competition, the intergroup and intragroup levels should be considered simultaneously. This paper: (a) proposes to model intergroup conflicts as team games (Palfrey & Rosenthal, 1983); (b) offers an initial taxonomy for this class of games; and (c) illustrates some applications for strategic analyses of intergroup conflict and political interactions.

Given a (TU or NTU) game in characteristic form an auxiliary two-person zero sum game is presented whose maximin = minimax value is precisely the potential of the game. In the auxiliary game one of the players tries to buy off the members of the original game by choosing the order in which to approach them, while the other player sets the price of those members so as to make the expense incurred as high as possible.

Much of the core's appeal stems from the intuitive and natural story behind it, the story that first motivated F.Y Edgeworth in 1881. Thus the primary motivation for the core is noncooperative in nature. Nonetheless, the core is not a noncooperative solution concept. This is because, in particular, the possibilities for forming coalitions, and making offers and counteroffers, are not explicitly modeled. In this work, we provide a noncooperative implementation of the core. However, we do not merely implement the core. The nature of the game form employed is designed to reflect the motivating story as accurately as possible. The present results thus provide formal content to the usual intuitive justification for the core. In our view, the core would lose much of its appeal were it not possible to provide such a noncooperative foundation.

We associate each bankruptcy problem with a bargaining problem and derive old and new allocation rules for the former by applying well known bargaining solutions to the latter.

We propose a non-cooperative treatment to the problem of collective decision making within committees, by modelling this process as a sequential bargaining game. We show that stationary subgame perfect equilibria of this bargaining game fully implements the core of the corresponding committee problem. We also discuss the inefficiency of non-stationary (subgame perfect) equilibria, and shortly refer to the problem of manipulability. Based on these results we then consider multi-issue committees, and address the problem of constructing agendas. In particular we will argue in favor of agendas where the important issues are discussed first.

In the first part, Rubinstein's two-person, complete information, alternating-offers bargaining model is extended to that of a fairly general contested pie which accommodates non-stationary preferences and physical joint payoffs with non-stationary constraints and outside options. The generalization in discrete-time and its continuous-time limit as bargaining rounds shorten are designed to bring the non-cooperative alternating-offers bargaining model to a form whose predictions can be compared and contrasted with those of the various axiomatic bargaining theories. This is done in the second part, where a bayesian approach is developed, which is used to optimally predict bargaining outcomes in game situations where full information about the bargaining procedure is lacking. This methodology gives rise to bayesian bargaining solution-functions, that generalize axiomatic bargaining solution-functions, thus setting the axiomatic theories on non-cooperative foundations.

We offer a definition of coalition-proof communication equilibria. The use of games of incomplete information is essential to our approach. Deviations of coalition are introduced after their players are informed of the actions they should follow. therefore, improvements by coalition on a given correlated strategy should always be made when their players have private information. Coalition-proof communication equilibria of two-person games are characterized by "information efficiency". Several examples are analyzed, including the Voting Paradox.

A class of non-cooperative games in which the players share a common set of strategies is described. The payoff a player receives for playing a particular strategy depends only on the total number of playing the same strategy and decreases monotonously with that number in a manner which is specific to the particular player. It is shown that each game in this class possesses at least one Nash equilibrium in pure strategies.

We start with giving an axiomatic characterization of the Nash equilibrium (NE) correspondence in terms of consistency, converse consistency, and one-person rationality. Then axiomatizations are given of the strong NE correspondence, the coalition proof NE correspondence and the semi-strong NE. In all these characterizations consistency and suitable variants of converse consistency play a role. Finally, the dominant NE correspondence is characterized. We also indicate how to generalize our results to Bayesian and extensive games.

In this paper we analyze a simple non-cooperative bargaining model for coalition formation and payoff distribution in games with coalition form. We show that under our bargaining regime a cooperative game is core implementable if and only if it possesses the property of increasing returns to scale for cooperation. Namely, the game is convex. This offers a characterization of a purely cooperative notion by means of its non-cooperative foundations.

Whenever one deals with an interactive decision situation of long duration, one has to take into account that priorities of the participants may change during the conflict. In this paper we propose an extensive-form game model to handle such situations and suggest and study a solution concept, called credible equilibrium, which generalizes the concept of Nash equilibrium. We also discuss possible variants to this concept and applications of the model to other types of games.

This is the second of two papers developing the theory of Egalitarian solutions for games in coalitional form with non-transferable utility (NTU) and a large number of players. This paper is devoted to the study of the egalitarian solutions of finite games as the number of players increases. We show that these converge to the egalitarian solution of the limit game with a continuum of players as defined in our previous paper. The same convergence holds for the underlying potential functions.

Aumann and Brandenburger (1991) describe sufficient conditions on the knowledge of the players in a game for a Nash equilibrium to exist. They assumed, among other things, mutual knowledge of rationality. By rationality of a player, they mean that the action chosen by him maximizes his expected utility, given his beliefs. There is, however, no need to restrict the notion of rationality to expected utility maximization. This paper shows that their result can be generalized to the case where the players preferences over uncertain outcomes can be represented by a continuous function, not necessarily linear in the probabilities.

This is a survey of some connections between game theory and theoretical computer science. The main emphasis is on theories of fault-tolerant computing. The paper is largely self-contained.

Formally, a conjunction fallacy and a disjunction fallacy cannot be distinguished. Both consist of a violation of the rule that an event cannot be more probable than another event which includes it. Hitherto, only a special kind of violation of this rule has been demonstrated, namely, that people sometimes judge the probability of A & B to be higher than the probability of A (Tversky & Kahneman, 1983). This study demonstrates a violation of the rule in a context that justifies the label disjunction fallacy. Subjects received brief case descriptions, and ordered seven categories according to one of four criteria for including the case as a member of the category : 1. probability of membership ; 2. willingness to bet on membership ; 3. inclination to predict membership ; 4. suitability for membership. The category list included nested pairs of categories, such as Brazil and South American country, or Physics and A Natural Science. The more inclusive category was a union of basic level sets like the smaller category. From a normative standpoint, the first two criteria are equivalent, and either ranking a category as more probable than its superordinate, or betting on it rather than on its superordinate, is fallacious. On the other hand, inclination to predict may be guided by the desire to be maximize informativeness rather than merely likelihood of being correct, and suitability needs to conform to no formal rule. Hence, with respect to these two criteria, such a ranking pattern is not fallacious. In spite of this crucial difference, subjects in all four groups rendered highly similar judgments, and the ranking of categories higher than their superodinates was not lower when it amounted to a fallacy than when it did not. The results support the representativeness thesis against some alternative interpretations.

The basic rule of distributive justice is the proportionality rule, which states that "Distributive justice involves a relationship between ... two persons, P1 and P2 one of whom can be assessed as higher than, or lower than, the other; and their two shares, or ... rewards, R1 and R2. The condition of distributive justice is satisfied when ... : P1/P2=R1/R2". (Homans, 1961). We studied this rule, in survey style, using cases such as the following: "suppose you have 12 grapefruit which you divide between Jones and Smith in as just a manner as possible. How should this be done ?". in our problems, either one or two goods were to be allocated between two recipients who differed on at most one dimension, either needs (e.g, Smith requires more grapefruit than Jones), beliefs (e.g, Smith believes that grapefruit are less nutritious than Jones believes them to be), or tastes (e.g, Smith enjoys grapefruit more than Jones). the results show that it is very hard to be more specific than the general formulation above without being ad hoc. For example, most people wish to allocate proportionately to need, only a minority wish to allocate proportionately to beliefs, and insofar as people wish to take tastes into consideration, they do so in a non-compensatory fashion. In other words, with regard to needs, less efficient extractors are awarded larger shares, but with regard to pleasure, more efficient extractors are awarded larger shares. Since real world distribution problems don't come neatly labelled as needs, tastes, etc., it is hard to predict or theorize what would be "just" in them.

We describe a non-cooperative bargaining model for games in coalition form without transferable utility. In this model random moves determine the order by which the players take their actions. the specific assignment of probability distributions to these chance moves is called the mechanics of the bargaining. Within this framework we examine the relation between the property of mechanism robustness, and coalition stability of the bargaining outcome, by showing that these two properties boil down to be the same.

This study addresses the momentary rules of foraging behavior on carpet inflorescences. It has long been suggested that patchiness in the distribution of nectar can give an advantage to near-far type of foraging strategies, that is, to foragers which search "near" (in the neighborhood of the last visited flower) as long as the nectar yield is high enough, and go "far" otherwise. Here we show that under certain conditions, such a strategy can be evolutionary stable. Furthermore, prior patchiness in the nectar distribution is not a necessary condition for the evolutionary stability of a near-far search. It turns out that during near-far foraging, some patchiness is created by the foraging process itself, which the near-far forager can exploit later on. To show the evolutionary stability of near-far search, various foraging strategies were compared, according to two, slightly different optimality criteria : the number of flowers emptied during a fixed length bout, and the number of flowers visited until total extraction of the entire inflorescence. We find that long enough bouts (in the case of a single forager) or a substantial probability of revisits to the same inflorescence (in the case of multipleforagers) are necessary for near-far to be an ESS.

We consider the class of hyperplane coalition games (H-games): the feasible set of each coalition is a half-space, with a slope that may vary from one coalition to another. H-games have turned out in various approaches to the value of general non-transferable utility (NTU) games. In this paper we introduce a simple model – prize games – that generates the hyperplane games. next, we provide an axiomatization for the Maschler & Owen (1989) consistent value of H-games.