The concept of coalition proof Nash equilibrium was introduced by Bernheim, Peleg and Whinston. In the present paper, we consider the representation problem for coalition proof Nash equilibrium: For a given effectivity function, describing the power structure or the system of rights of coalitions in society, it is investigated whether there is a game form which gives rise to this effectivity function and which is such that for any preference assignment, there is a coalition proof Nash equilibrium. It is shown that the effectivity functions which can be represented in coalition proof Nash equilibrium are exactly those which satisfy the well-known properties of maximality and superadditivity. As a corollary of the result, we obtain necessary conditions for implementation of a social choice correspondence in coalition proof Nash equilibrium which can be formulated in terms of the associated effectivity function.

Contrary to a common picture of relationships in a market economy, people often express communal and membership-seeking impulses via consumption choices, purchasing goods and services because other people are doing so as well. Shared identities are maintained and created in this way. Solidarity goods are goods whose value increases as the number of people enjoying them increases. Exclusivity goods are goods whose value decreases as the number of people enjoying them increases. Distinctions can be drawn among diverse value functions, capturing diverse relationships between the value of goods and the value of shared or unshared consumption. Though markets spontaneously produce solidarity goods, individuals sometimes have difficulty in producing such goods on their own, or in coordinating on choosing them. Here law has a potential role. There are implications for trend setting, clubs, partnerships, national events, social cascades and compliance without enforcement.

In the framework of a first-price private-value auction, we study the seller as a player in a game with the buyers in which he has private information about their realized valuations. We find that depending upon his information, set of signals, and commitment power, he may strategically transmit messages to buyers in order to increase his revenue. In an environment where the seller knows the rankings and lacks any commitment power, we find that the seller is unable to exploit his information. However, in an environment where the seller knows the realized valuations and can credibly annouce either the true rankings or the true values (or announce nothing at all) but cannot commit as to which of these truthful messages to announce, then it is indeed possible to increase his revenue. If the seller, in addition, can commit to the full signaling strategy, then his expected revenue will be even higher. We believe that this line of research is fruitful for both better understanding behavior in auctions and finding paths to higher seller revenue.

Subjective probabilities are probabilities people express for uncertain events or outcomes. They are generated, or judged, by two major heuristics: 1. When outcomes are unique (e.g., the guilt of some defendant) or set in the future (e.g., the winner of the next election), the approach is "theoretical". People pull together whatever they know, or believe, to be relevant, and judge the probabilities of the possible outcomes by the closeness of the match between them and whatever "prediction model" they have built in their heads. This heuristic is called representativeness. 2. When outcomes are grouped in categories or by features (e.g., the percent of convictions for a given charge, or the percent of elections won by incumbents), the approach is "empirical": Let's sample what's out there and count. If the sampling is done in one's head, and the probabilities judged by the number of examples that come to mind, or by the ease – real or anticipated – with which they come to mind, the heuristic is that of availability. These heuristics have distinct signatures. They lead to predictable and systematic biases, among them: the extension fallacy, the base-rate fallacy, sample size neglect, regression neglect, the unpacking effect, overconfidence, hindsight bias and more.

We present a simplified model of the evolution of a society which is regulated by a formal unanimity voting procedure. We examine several protocols, which depend on whether admission or expulsion are permissible, and on the order with which they are implemented. Conditions which ensure the existence of pure-strategy perfect equilibrium profiles for some voting protocols, and counter examples for the existence of such profiles in other protocols are presented. Finally, we prove that the original founders would prefer a protocol in which expulsion precedes admission to protocols in which admission precedes expulsion, or the two are treated simultaneously.

We exhibit and characterize an entire class of simple adaptive strategies,in the repeated play of a game, having the Hannan-consistency property: In the long-run, the player is guaranteed an average payoff as large as the best- reply payoff to the empirical distribution of play of the other players; i.e., there is no "regret." Smooth fictitious play (Fudenberg and Levine [19951) and regret-matching (Hart and Mas-Colell [1998]) are particular cases. The motivation and application of this work come from the study of procedures whose empirical distribution of play is, in the long-run, (almost) a correlated equilibrium. The basic tool for the analysis is a generalization of Blackwell's [1956a) approachability strategy for games with vector payoffs. Keywords: adaptive strategies, approachability, correlated equilibrium, fictitious play, regret. Journal of Economic Literature Classification: C7, D7, C6

A curious connection exists between the theory of optimal stopping for independent random variables, and branching processes. In particular, for the branching process Zn with offspring distribution Y, there exists a random variable X such that the probability P(Zn = 0) of extinction of the n-th generation in the branching process equals the value obtained by optimally stopping the sequence X-i_,...,Xn, where these variables are i.i.d distributed as X. Generalizations to the inhomogeneous and infinite horizon-cases are also considered. This correspondence furnishes a simple 'stopping rule' method for computing various characteristics of branching processes, including rates of convergence of the n-th generation's extinction probability to the eventual extinction probability, for the supercritical, critical and subcritical Galton-Watson process. Examples, bounds, further generalizations and a connection to classical prophet inequalities are presented. Throughout, the aim is to show how this unexpected connection can be used to translate methods from one area of applied probability to another, rather than to provide the most general results.

An analogue of Vickrey's (1961) multi-unit auction is provided when bidders have interdependent values. The analogue is strategically equivalent to a collection of two-bidder single-unit second-price auctions and it possesses an ex-post efficient equilibrium. As an application of this result, it is shown that the FCC auction possesses an efficient equilibrium in the case of homogeneous goods. Conditions are provided under which the new auction (and also the FCC auction) revenue-dominates all ex-post equilibria of ex-post efficient individually rational mechanisms.

This paper exhibits to any noncooperative game in strategic or normal form a 'canonical' game in extensive form that preserves all symmetries of the former one. The operation defined this way respects the restriction of games to subgames and yields a minimal total rank of the tree involved. Moreover, by the above requirements the 'canonical extensive game form' is uniquely defined. Key words: Games, Extensive Form, Normal Form, Strategic Form. AMS(MOS) Subject Classification: 90D10, 90D35, 05C05

In standard rational choice modelling decisions are made according to given information and preferences. In the model presented here the 'information technology' of individual decision makers as well as their preferences evolve in a dynamic process. In this process decisions are made rationally by players who differ in their informational as well as in their preference type. Relative success of alternative decisions feeds back on the type composition of the population which in turn influences rational decision making. An indirect evolutionary analysis of an elementary yet important basic game of trust shows that under certain parameter constellations the population dynamics of the evolutionary process specify a unique completely mixed rest point. However, as opposed to previous studies of preference formation in the game of trust there is no convergence to but only cycling around the rest point if the informational status of individuals evolves rather than being chosen strategically.

We show existence and uniqueness of cost allocating mechanisms, satisfying standard axioms, on three classes of cost functions with major nondifferentiabilities. Two of the classes consist of nondecreasing convex functions, which exhibit either increasing or constant costs to scale. The third is the space of piecewise linear cost functions.

We report an experiment on the covered response ultimatum game, in which the proposer is not informed about the responder's reaction to an unequal offer. In this game, no education of proposers is possible. A control experiment with informed proposers was also conducted. We observe high rejection rates with covered response. These are explained by responders' resistance to unfairness. But the rejection rates are lower than in the control group, due to the lacking possibility of educative punishment. Proposers in the open response treatment test responders' propensity to reject by making more unequal offers. We conclude that both resistance to unfairness and educative punishment are determinants of behaviour, but neither is sufficient on its own. Keywords Ultimatum bargaining, fairness, punishment, experimental economics.

We report an experiment on individual and group behavior in intergroup conflict as modeled by the Intergroup Prisoner's Dilemma (IPD) game (Bornstein, 1992). The game was played repeatedly either with or without intra-group communication in an attempt to distinguish the dynamic process associated with reciprocation at the intergroup level from that resulting from adaptation at the individual level. We found that without communication, individuals gradually learned that it does not pay to contribute. The overall effect of within-group communication was to increase individual contribution. However, this effect varied greatly in later stages of the game. In some cases intragroup communication eliminated individual contribution, rewarding the members of both teams with the mutually cooperative outcome, while in other cases it intensified the intergroup conflict to its maximal level of full contribution. The implications for these findings to conflict resolution are discussed.

The backward induction (or subgame-perfect) equilibrium of a perfect information game is shown to be the unique evolutionarily stable outcome for dynamic models consisting of selection and mutation, when the mutation rate is low and the populations are large. Keywords: games in extensive form, games of perfect information, backward induction equilibrium, subgame-perfect equilibrium, evolutionary dynamics, evolutionary stability, mutation, selection, population games. Journal of Economic Literature Classification: C7, D7, C6.

We consider an infinitely repeated zero-sum two-person game with incomplete information on one side, in which the maximizer is the (more) informed player. Such games have value Vx(p) for all 0

We show that standard axioms determine uniquely the marginal cost pricing rule on homogeneous, convex and continuously differentiable cost functions.

We derive an explicit formula for a marginalist and efficient value for a TU game which possesses the -player property and is either continuous or monotonic. We show that every such a value has to be additive and covariant as well. It follows that the set of all marginalist, efficient, and monotonic values possessing the -player property coincides with the set of random-order values, and thereby the last statement provides an axiomatization without the linearity axiom for the latter which is similar to that of Young for the Shapley value. Another axiomatization without linearity for random-order values is provided by marginalism, efficiency, monotonicity, and covariance. Keywords: Transferable utility game; Value; Axiomatic characterization; Efficiency; Mar- ginalism

This paper considers the set of Lorenz-maximal imputations in the core of a balanced cooperative game as a solution concept. It is shown that the Lorenz-solution concept satisfies a number of suitable properties such as desirability, continuity and the reduced game property. Moreover, the paper considers alternative characterizations where it is shown that Lorenz-fairness is tantamount to the existence of an additive, strictly increasing and concave social welfare function. Finally the paper also provides axiomatic characterizations as well as two examples of application.

We develop an axiomatization of a single-valued solution for finite-type perfectly competitive economies. The solution is a competitive payoff selection. Our axioms are similar to those of Dubey and Neyman for solutions of differentiable economies, and they give rise to the Mertens value.

We show that for voting systems containing at least three voters the set of all marginalist, efficient, and monotonic power indices possessing the -player property coincide with the set of random-order power indices, and thereby the last statement spreads to simple games the result of Khmelnitskaya concerning an axiomatization without the linearity assumption for random-order values for the entire class of TU games. We also give evidence that every marginalist, efficient, and symmetric power index is just the Shapley-Shubik power index what provides an axiomatization for the latter similar to that of Young for the Shapley value; in symmetric case there is no restriction for a number of players to be not less than three. Keywords: Simple game; Power index; Axiomatic characterization; Efficiency; Marginalism