Two teams meet every day to play the same matrix game. Every entry in the matrix contains five numbers: a payoff that each player in the first team receives whenever this entry is chosen, a similar payoff for the players of the second team, a probability that once this entry is chosen the game becomes "static", a payoff that each player in the first team receives in each future day if the game becomes "static" by this entry, and a similar payoff for the players of the second team.We prove that every such game has an equilibrium payoff.

This article concerns infinitely repeated and un-discounted two-person non-zero-sum games of incomplete information on one side. Following the spirit of the Folk Theorem it establishes sufficient conditions for the existence of Nash equilibria with payoffs superior to what the players would receive from observable deviation. Examples are presented that show both the difficulty and the desirability for stronger results than those presented here.

We study fundamental properties of monotone network enterprises which contain public vertices and have positive and negative costs on edges and vertices. Among the properties studied are the nonemptiness of the core, characterization of nonredundent core constraints, ease of computation of the core and the nucleolus, and cases of decomposition of the core and the nucleolus.

In the present paper we consider recursive games that satisfy an absorbing property defined by Vieille. We give two sufficient conditions for existence of an equilibrium payoff in such a game, and prove that if the game has at most two non- absorbing states, then at least one of the conditions is satisfied. Using a reduction of Vieille, we conclude that every stochastic game which has at most two non-absorbing states has an equilibrium payoff.

In making major decisions (e.g., about medical treatment, acceptance of manuscripts for publication, or investment), decision makers frequently poll the opinions and subjective estimates of other judges. The aggregation of these opinions is often beset by difficulties. First, decision makers often encounter conflicting subjective estimates. Second, estimates are often expressed with a measure of uncertainty. The decision maker thus needs to reconcile inconsistencies among judgmental estimates and determine their influence on the overall aggregate judgement. In the empirical studies, I examine the idea that weighting and trimming are two important heuristics in the aggregation of opinions under uncertainty. The results from these studies are contrasted with the findings of a normative study using a computer simulation that was designed to assess the objective effects of weighting and trimming operations on the accuracy of estimation.

Survival of the fittest means that phenotypes behave as if they would maximize reproductive success. An indirect evolutionary analysis allows for stimuli which are not directly related to reproductive success although they affect behavior. One first determines the solution for all possible constelations of stimuli and then the evolutionarily stable stimuli. Our general analysis confirms the special results of former studies that survival of the fittest in case of commonly known stimuli requires either that own success does not depend on other's behavior or that other's behavbior is not influenced by own stimuli. When stimuli are private information one can derive similar necessary conditions for the survival of the fittest.

In Rosenthal's Centipede Game, if it is commonly known that the players choose rationally at vertices that are actually reached, then the first player "goes out" at the first move.

The example of the "absent-minded driver" was introduced by Piccione & Rubinstein [1995] in the context of games and decision problems with imperfect recall. They claim that a "paradox" or "inconsistency" arises when the decision reached at the "planning stage" – before the game is played – is compared with that at the "action stage" – when the game is played. Though the example is provocative and worth having, their analysis is unsound. A careful analysis reveals that while the considerations at the planing and action stages do differ, there is no paradox or inconsistency. 94R. Robert J. Aumann, Sergiu Hart & Motty Perry, "The Absent-Minded Driver" (Revised, December 1996). The example of the "absent-minded driver" was introduced by Piccione & Rubinstein [1995] in the context of games and decision problems with imperfect recall. They claim that a "paradox" or "inconsistency" arises when the decision reached at the "planning stage" is compared with that at the "action stage". Though the example is provocative and worth having, their analysis is questionable. A careful analysis reveals that while the considerations at the planing and action stages do differ, there is no paradox or inconsistency.

This paper analyzes a dynamic model of a firm in which the wage of each employee is determined in separate bilateral negotiations with the firm. The contractsbetween the firm and its employees are non-binding in the sense that they can be repeatedly renegotiated to adjust to changing situations. The Bargaining power of an employee stems from the threat of quitting that will deprive the firm of this worker's marginal contribution and will put the firm in a weaker position against the remaining workers. This threat is offset to some extent by the replacement opportunities that the firm has, but these are only imperfect in the sense that replacement of quits requires time and effort. The paper characterizes a class of equilibria for this scenario and examines their features. These include a sharp decline of the wage at the firm's target employment level, a mark-up of the wage over the employees' reservation wage and over-employment.

The bankruptcy problem from the Talmud is modelled as a game (in coalitional form with transferable utility) which differs from the "standard bankruptcy game". A non-game theoretic solution to the bankruptcy problem is recovered by two different game theoretic approaches applied to the alternative game. The major game theoretic approach enables to interpret pairwise greedy or modest claims of creditors as largest or smallest core-allocations to creditors in the alternative game. A theory of consistency is elucidated with elementary game theoretic tools and proofs. As a separate topic, the indirect function of the "standard bankruptcy game" is determined and interpreted in an economic manner. The indirect function may be helpful to describe the game itself as well as its core (due to the duality between games and indirect functions).

Part I of a non-technical account, written in Hebrew for the Rabbinic Community, of "Game Theoretic Analysis of a Bankruptcy Problem from the Talmud", by R. Aumann and M. Maschler, Journal of Economic Theory 36 (1985), 195-213. The Talmudic passage in question is explained in more detail than in the JET paper, and additional Talmudic sources are adduced.

We provide a characterization of the set of equilibria of two-person cheap-talk games with incomplete information on both sides. Each equilibrium generates a martingale with certain properties and one can obtain an equilibrium from each such martingale. Moreover, the characterization depends on the number of possible messages. It is shown that for every natural number n, there exist equilibrium payoffs that can be obtained only when the number of possible messages is at least n.

Cheap-Talk with Random Stopping is a Cheap-Talk game in which after each period of communication, with probability 1- %, the talk ends and the players play the original game (i.e., choose actions and receive payoffs). In this paper the relations between Cheap-Talk games and Cheap-Talk with Random Stopping are analyzed.

We introduce two ways of comparing two information structures, say I and J. First, I is richer than J when for every compact game G, all correlated equilibrium distributions of G induced by J are also induced by I. Second, J is faithfully reproducible from I when all the players can compute from their information in the I "new information" that reproduces what they could have from J. We prove that I is richer than J if and only if J is faithfully reproducible from I.

This paper surveys results concerning online algorithms for solving problems related to the management of money and other assets. In particular, the survey focuses on search, replacement and portfolio selection problems.

This paper introduces a new team game where players are engaged in simultaneous games of Chicken between and within teams. The intergroup Chicken game is proposed as a model of intergroup confrontations (e.g., military Conflicts, industrial disputes) involving bilateral threats where a failure on the part of either side to yield leads to an outcome (e.g., war, strike) that is disastrous to both sides. We report an experiment in which an intergroupChicken game with two players in each team was compared with a two-person Chicken and a (single-group) four-person Chicken. The games were played repeatedly and each round was preceded by a pre-game period in which players could signal their intention to cooperate or not. Our interest was in assessing the ability of the participants in the different games to cooperate, i.e., achieve the coordination necessary for the optimal realization of their mutual interests. We found that subjects were considerably less cooperative in the inter-group Chicken game than in either the two-person or the four-person game. Since the coordination problem in the intergroup game is of the same magnitude as that in the four-person game, we attribute most of the competitiveness observed in the intergroup conflict to the strategic properties of the game rather than the number of players involved.

In this paper we offer an axiomatic approach for the investigation of rights by means of game forms. We give a new definition of constitution which consists of three components: the set of rights, the assignment of rights to groups of members of the society, and the distribution of power in the society (as a function of the distribution of rights). Using the forgoing definition we investigate game forms that faithfully represent the distribution of power in the society, and allow the members of the society to exercise their rights simultaneously. Several well-known examples are analyzed in the light of our framework. Finally, we find a connection between Sen's minimal liberalism and Maskin's result on implementation by Nash equilibria.

We report an experiment in which the Intergroup Prisoner's Dilemma (IPD) game was contrasted with a structurally identical (single-group) Prisoner's Dilemma (PD). The games were played repeatedly for 40 rounds. We found that subjects were initially more likely to cooperate in the IPD game than in the PD game. However, cooperation rates decreased as the game progressed and, as a result, the differences between the two games disappeared. This pattern is consistent with the hypothesis that subjects learn the structure of the game and adapt their behavior accordingly. Computer simulations based on a simple learning model by Roth & Erev (1995) support this interpretation.

Foraging can be viewed as a dual activity: a food-collection process, and an exploration process, which enables foragers to collect information on food resources. Exploration of food sources may involve patch sampling, as well as sampling of various food sources within heterogeneous patches. The present study aimed to quantify exploration effort in relation to the spatial distribution of the food sources. Exploration effort was measured in two-stage laboratory experiments on naive bumblebees, Bombus terrestris (L.). In the first stage the bees were allowed to forage on three types of color-distinct artificial flowers. In the second stage a new type of artificial flowers ("exploratory flowers"), which were non-rewarding, was added. The four types of artificial flowers were either arranged in spatially distinct clusters or randomly intermingled. Two reward schedules were used in each spatial arrangement: constant refilling of visited flowers and probabilistic refilling. The bees' visit to the exploratory flowers were recorded as a measure of exploratory activity, and were related to their previous foraging experience. Bees which experienced a probabilistic reward schedule explored more than bees from the constant-reward treatments. Bees which foraged on clustered flowers directed a larger proportion of their flights to exploratory flowers, and made more visits to these flowers, than bees that foraged on intermingled flowers. This tendency was obtained both in the probabilistic and in the constant reward schedules. The results suggest that bees allocate more effort to the exploration of novel feeding patches than to the exploration of new food types within a known patch.

We consider an augmented version of the symmetric private value auction model with independent types. The augmentation, intended to illustrate reality, concerns information bidders have about their opponents. To the standard assumption that every bidder knows his type and the distribution of types is common knowledge we added the assumption that the ranking of bidders' valuations is common knowledge. This set-up induces a particular asymmetric auction model that raises serious technical difficulties. We prove existence and uniqueness of equilibrium in pure strategies in the two bidder case. We also show that the model generally has no analytic solution. If the distribution of valuations is uniform, both bidders bid pointwise more aggressively relative to the standard symmetric case. However, this property does not apply to all distributions of valuations. Finally, we also provide a numerical solution of equilibrium bid functions for the uniform distribution case.