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.

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.