Robert W. Rosenthal

A class of games possessing pure-strategy Nash equilibria

A class of noncooperative games (of interest in certain applications) is described. Each game in the class is shown to possess at least one Nash equilibrium in pure strategies.

Games of perfect information, predatory pricing and the chain-store paradox

The thesis of this paper is that finite, noncooperative games possessing both complete and perfect information ought to be treated like one-player decision problems. That is, players ought to assign at every move subjective probabilities to every subsequent choice in the game and ought to make decisions via backward induction. This view is in contrast with the gametheoretic approach of Nash equilibrium. After expanding on this view for games in the abstract in Sections 2 and 3, attention is turned in Section 4 to an example due to Reinhard Selten, called the chain-store paradox, which possesses the flavor of a situation involving a predatory-pricing monopolist. It is argued that for the chain-store game the decision-analytic approach leads, under certain assumptions, to more realistic outcomes than the standard Nash-equilibrium approach.

The network equilibrium problem in integers

In the usual approach to network equilibrium models, the flow variables are modeled as continuous. When the problem under study involves discrete decision makers each controlling an indivisible unit of flow, another approach is called for. We treat the problem as an n-person noncooperative game with pure strategies corresponding to feasible paths through the network. It is shown that pure-strategy Nash equilibria exist and that any solution to an integer-variable analogue of the usual network equilibrium model is such a Nash equilibrium. It is also shown that when individuals can control more than a single unit of flow and want to minimize the sum of their costs, pure-strategy Nash equilibria do not necessarily exist.

A bounded-rationality approach to the study of noncooperative games

A family of solutions for finite noncooperative games is introduced in which players are not confined to use best responses exclusively. Instead, the definition requires that the probability of use of a strategy must be a monotone-nondecreasing function of its expected payoff. For the two-person case, some results characterizing behavior at such solutions are given and some examples are examined.

Sequences of Games with Varying Opponents

This paper considers a problem faced by players who are involved in a sequence of games: not necessarily the same games, not necessarily with the same opponents, and not necessarily under conditions of complete information. The players are assumed to act in response to stationary Markovian hypotheses which they form about the actions of their opponents. Conditions are explored which require that these hypotheses be correct on average and that the players actions be optimal in response to their hypotheses.

Strategic Models of Sovereign-Debt Renegotiations

The sovereign-debt literature has often implicitly assumed that all the power in the bargaining game between debtor and creditor lies with the latter. This paper explores that assumption by analyzing three game-theoretic models of debt renegotiations. In two of the models, both of which are built on the traditional one-sector growth model, all the subgame-perfect equilibria have an extreme form in which the games surplus is captured by the creditor. The third game has many subgame-perfect equilibria that do not have this feature, however. The roles of various assumptions in all three games are examined.

Arbitration of Two-Party Disputes Under Ignorance

When an arbitrator lacks complete information about the dispute in question, he may have to turn to the disputants themselves to provide information. If they know how the information is to be used, they may have incentives to hide the truth. By using the players reports as checks on each other, a completely ignorant arbitrator of a dispute between two completely informed players can induce truthful revelation in the sense that the truth is a Nash equilibrium of the game which the arbitrators decision process imposes on the players. Such a scheme may be used in conjunction with any one from a class of functions which select Pareto-optimal, individually-rational outcomes in two-person normal-form games.

Asking Prices as Commitment Devices

This paper explores the implications of the hypothesis that an asking price is a ceiling to which a seller commits in order to provide incentives for potential buyers to incur search costs. Having attracted such a potential buyer, the seller must also determine how low to set the floor price, below which it is preferable to wait for another customer. This decision is affected by expectations about the characteristics of future buyers, which are, in turn, affected by the asking price. All of this is embedded in models of monopoly and of duopolistic competition. Copyright 1996 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Cooperative games in effectiveness form

The primary vehicle for the analysis of cooperative games has been the characteristicfunction form. This paper seeks to point out certain deficiencies inherent in a characteristic-function type of representation for some cooperative games. A more general form, the effectiveness form, is proposed to correct the inadequacies of the characteristic-function representation. In addition, concepts of stability for effectiveness-form games are suggested; and some examples are studied. Section 2 establishes notation and introduces some basic definitions and references. In Section 3 the rationale for the effectiveness form is discussed. A formal description of the form is presented in Section 4. Section 5 deals with some possible concepts of stability. Section 6 analyzes a few examples of interest.

Beyond chopsticks: Symmetric equilibria in majority auction games

Majority auction games are simultaneous sealed-bid auctions of identical objects among identical bidders who each want to win a specified fraction (more than a half) of the objects. Each bidder receives no benefit from winning less than the specified fraction and no additional benefit from winning more than it. Symmetric equilibria having simple, intuitive forms are shown to exist in first-price, second-price and all-pay versions of such games when the number of bidders is sufficiently large. This contrasts with earlier results for the two-bidder “pure chopstick” majority auction games where the only known equilibria are more complicated.