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.

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.