In this paper we introduce the notion of a rematching-proof equilibrium for a two-sided matching market to resolve Roth's open question: What kind of equilibria of the game induced by any stable mechanism with respect to misreported profiles produce matchings that are stable with respect to the true profile. We show that the outcome of a rematching-proof equilibrium is stable with respect to the true profile even though the equilibrium profile may contain misreported preferences. We show that a rematching-proof equilibrium exists. Moreover, we extend these two results to the strong equilibria. Furthermore, the Nash equilibria in Roth [11] are shown to be rematching-proof equilibria. The relation between the rematching-proof equilibria and the strong equilibria is discussed as well.

The notion of a strict equilibrium set is introduced as a natural extension of the notion of a strict equilibrium point. The evolutionary stable sets of a truly asymmetric contest are shown to be behaviorally equivalentto the strict equilibrium sets of an "agent representation" of the contest. Using variants of the replicator dynamic we provide dynamic characterizations of strict equilibrium sets. We do this both for truly asymmetric contests and for arbitrary normal form games modelling conflicts between several distinct species.

We examine a sequential mechanism which is a simple modification of the normal form mechanism introduced by Abreu and Matsushima (1992). We show that almost any social choice function can be virtually implemented via a finite sequential game of perfect information. The solution concept assumed is Subgame Perfect Equilibrium or Iterative Elimination of Strictly Dominated Strategies. In particular, any social choice function that is virtually implementable via the Abreu-Matsushima's mechanism is also virtually implementable by a sequential mechanism.

The consequences of veto power in committees is analyzed using the approach of non-cooperative bargaining theory. It is first shown that in equilibrium non-veto players do not share in the benefits gained by the decision making of the committee, i.e, in every equilibrium outcome of the bargaining game non-veto players earn zero. Some measures for reducing the excessive power of veto members in committees are analyzed. Specifically, we study the effects of imposing a deadline on negotiations and of expanding the committee by increasing the number of non-veto players.

We introduce a new operator on information structures which we call `Knowing whether' as opposed to the standard knowledge operator which may be called `Knowing that'. The difference between these operators is simple. Saying that an agent knows that a certain event occurred implies that this event indeed occurred, while saying that the agent knows whether an event occurred does not imply that the event occurred. (Formally, knowing whether X means that either it is known that X occurred or it is known that X did not occur). We show that iterating `Knowing whether' operators of different agents has a remarkable property that iterations of `knowing that' do not have. When we generate a sequence of events, starting with a given event and then applying `Knowing that' or `not knowing that' to the previous event, then the events in this sequence may be, somewhat surprisingly, contradictory. In contrast, any sequence of this type, generated with `knowing whether' and `not knowing whether' is never contradictory. We use this property of the `knowing whether' operator to construct a simple and natural state space and information structures for two agents, such that: (1) any two states are distinct relative to some interactive knowledge of a fixed event, (2) the space has the cardinality of the continuum. This result - originally proved in a complicated manner by Aumann (1989) - demonstrates the usefulness of the `knowing whether' operator.

We introduce a game form that captures a non-cooperative dimension of the consistency property of bankruptcy rules. Any consistent and monotone rule is fully characterized by a bilateral principle and consistency. Like the consistency axiom, our game form, together with a bilateral principle, yields the respective consistent bankruptcy rule as a result of a unique outcome of subgame perfect equilibria. The result holds for a large class of consistent and monotone rules, including the Constrained Equal Award, the Proportional and many other well-known rules. Moreover, for a large class of rules, all the subgame perfect equilibria are coalition-proof.

Varying quantities of a single good can be produced using at least two and at most n factors of production. The problem of allocating the surplus is studied in a dynamic model with adaptive behavior. Representatives for the factors (referred to as players) make wage demands based on precedent and ignorant of each others utilities for this good. Necessary and sufficient conditions are provided under which the long-run equilibria coincide with the core allocations. Moreover, allowing for the possibility of mistakes by the players, it is shown that the unique limiting stochastically stable outcome maximizes the product of the players' utilities subject to being in the core of the technology.

In this paper we discuss two types of foraging strategies for bees. Each of these explicit strategies explains that in the environment of a monomorphic bee community the bees will distribute themselves over the available homogeneous nectar sources according to the Ideal Free Distribution. At the same time these strategies explain that in single-bee experimental settings a bee will match, by its number of visits, the nectar supply from the available sources (the Matching Law). Moreover, both strategies explain that in certain situations the bees may behave as if they are risk averse, i.e spend more time on the flower type with the lower variance in nectar supply.

The literature on Nash equilibrium refinements provides several ways to check the stability of a Nash equilibrium against deviations from equilibrium play. Stability, however, is a function of how a deviation is being interpreted. An equilibrium that is stable under one interpretation may cease to be stable under another, but the refinement literature provides no general criterion to judge the plausibility of different interpretations of off-equilibrium play. This paper specifies a model of belief revision that minimizes the loss of useful information. When several interpretations are compatible with off-equilibrium play, the one that requires the least costly belief revision (in terms of informational value) will be chosen by the players. This model of belief revision generates a plausibility ranking of interpretations of deviations, hence it also provides a ranking of Nash equilibrium refinements.

Criminal law is traditionally described as directing its injunctions exclusively to actual or potential criminals. This article will argue that the traditional view is normatively unjustified both on efficiency and fairness grounds. To disregard the victim's conduct in determining the sanctions of criminals is both inefficient and unfair. It is inefficient because dismissing the behavior of the victim as irrelevant to the concerns of the criminal justice system does not provide optimal incentives for victims to take precautions against crime. It is unfair to disregard the victim's conduct because given the greater likelihood that careless potential victims (relative to cautious ones) will become actual victims of crime, the expected costs of protecting careless victims are higher than the expected costs of protecting cautious ones. Hence, under the current system, cautious victims are exploited for the sake of protecting careless ones. Both efficiency and fairness considerations suggest that criminal law should adopt a criminal law doctrine of comparative fault, under which criminals who act against careless victims would be exculpated or their punishment mitigated.

We define a desirability effect as the inflation of the judged probability of desirable events and the diminution of the judged probability of undesirable events. A series of studies designed to detect this effect is reported. In the first four experiments, subjects were presented with visual stimuli (a grid matrix in two colors, or a jar containing beads in two colors), and asked to estimate the probability of drawing at random one of the colors. The estimated probabilities for a defined draw were not higher when the draw entailed a gain than when it entailed a loss. In the fifth and sixth experiment, subjects read short stories each describing two contestants competing for some desirable outcome (e.g., firms competing for a contract). Some judged the probability that A would win, others judged the desirability that A would win. Story elements which enhanced a contestant's desirability without having normative bearing on its winning probability did not cause the favored contestant to be judged more likely to win. Only when a contestant's desirability was enhanced by promising the subject a monetary prize contingent on that contestant's win was there some slight evidence for a desirability effect: contestants were judged more likely to win when the subject expected a prize if they won than when the subject expected a prize if the other contestant won. In the last experiment, subjects estimated the probability of an over-20 point weekly change in the Dow Jones average, and were promised monetary prizes contingent on such a change either occurring, or failing to occur. They were also given a monetary incentive for accuracy. Subjects who desired a large change did not judge it more likely to occur than subjects who desired a small change. We discuss the difficulty of obtaining a desirability effect on probabilities, and argue that apparently wishful thinking– in the form of optimistic cognitions – can occur without affecting the evaluation of evidence.

We present an axiomatic approach for a class of finite, extensive form games of perfect iformation that makes use of notions like "rationality at a node" and "knowledge at a node". We show that, in general, a theory that is sufficient to infer an equilibrium must be modular: for each subgame G' of a game G the theory of game G must contain just enough information about the subgame G' to infer an equilibrium for G'. This means, in general, that the level of knowledge relative to any subgame of G must not be the same as the level of knowledge relative to the original game G. We show that whenever the theory of the game is the same at each node, a deviation from equilibrium play forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not cause any revision of the theory of the game.

Game theoretical models and analysis are provided for the sequential material accountancy problem. We model the n-period problem as a general sequential game played between the Operator and the Inspector. The game is analyzed through the solution concept of (Nash) equilibrium. We study several versions of the game corresponding to various assumption on the payoffs and the strategy sets. The first model solved is what we refer to as the static game. This is a game in which detection time is unimportant and the operator has to decide about his diversion plan at the beginning of the game (and he cannot deviate from it in a later stage). The solution of this game is obtained by its decomposition into two simpler game: a zero-sum game which determines the diversion plan and the statistical test (which turned out to be the CUMUFtest) and a second, non zero-sum game which determines the diversion probability and the false alarm probability. Next we return to the sequential game and prove that under the assumptions underlying the statistical analysis, the CUMUFtest emerges as part of the solution of the game i. e., as the inspector's strategy in equilibrium. Then we consider a `really sequential' game in which early detection is important and in which the operator can retreat (in view of high observed intermediate MUF) from completing a diversion plan that he have started. We find the structure of the equilibrium and the equilibrium equations of this game. These equations turn out to be too complex to be solved analytically, hence we provide numerical solutions which give interesting insight into the problem.

We consider the relations between the competitive equilibria in economies with many agents and the value allocations of the resulting coalition games. In particular, we provide a (smooth and robust) example where the "value principle" does not hold for the Harsanyi NTU-value: there is a unique competitive equilibrium, which however does not belong to the (non-empty) set of Harsanyi value allocations.

Loan contracts with collateral are a common instrument to allocate credit to entrepreneurs who invest in risky projects. Collateral provides lenders with partial insurance against bad outcomes. Since typically, credit is provided under incomplete information about the nature of the project to be undertaken, we investigate in this paper whether collateral can be used as an instrument to identify projects which the bank may consider to be 'bad'. We prove that the ability of collateral to serve as a screening device depends on whether the entrepreneurs and the bank have similar ranking of project quality. If they do not, collateral is less effective as a signal. Within each regime, we identify conditions under which separating and pooling equilibria take place and we characterize the properties of these equilibria. When credit is scarce, we derive equilibria in which credit is rationed. A rationing regime eliminates pooling equilibria and generates more surplus to the bank on every project for which a loan was granted.

The classic Option Pricing Model is generalized to a more realistic, imperfect, dynamically incomplete capital market with different interest-rates for borrowing and for lending and a return differential between long and short positions in stock. It is found that in the absence of arbitrage opportunities, the equilibrium price of any contingent claim, or of a portfolio of such claims, must lie within an arbitrage-band. The boundaries of an arbitrage-band are computed as solutions to a quasi-linear partial-differential-equation, and, in general, each end-point of such a band depends on both interest-rates for borrowing and for lending. This, in turn, implies that the vector of concurrent equilibrium prices of different contingent-claims - even claims that are written on different underlying assets - must lie within a computable oval in the price space.

We introduce the notion of the partnered core of a game. A payoff is partnered if there are no asymmetric dependencies between any two players. A payoff is in the partnered core of a game if it is partnered, feasible and cannot be improved upon by any coalition of players. We show that the relative interior of the core of a game with side payments is contained in the partnered core. For quasi-strictly convex games the partnered core coincides with the relative interior of the core. When there are no more than three partnerships, the sums of the payoffs to partnerships are constant across all core payoffs. When there are no more than three players, the partner core satisfies additional properties.

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.