Ariel Rubinstein

PERFECT EQUILIBRIUM IN A BARGAINING MODEL

Focuses on a study which examined perfect equilibrium in a bargaining model. Overview of the strategic approach adopted for the study; Details of the bargaining situation used; Discussion on perfect equilibrium. (From Ebsco)

Finite automata play the repeated prisoner's dilemma

The paper studies two-person supergames. Each player is restricted to carry out his strategies by finite automata. A player’s aim is to maximize his average payoff and subject to that, to minimize the number of states of his machine. A solution is defined as a pair of machines in which the choice of machine is optimal for each player at every stage of the game. Several properties of the solution are studied and are applied to the repeated prisoner’s dilemma. In particular it is shown that cooperation cannot be the outcome of a solution of the infinitely repeated prisoner’s dilemma.

Equilibrium in a Market with Sequential Bargaining

This paper considers a market where pairs of agents who are interested in carrying out a transaction are brought together by a stochastic process and, upon meeting, initiate a bargaining process over the terms of the transaction. The basic bargaining problem is treated with the strategic approach. The paper derives the steady state equilibrium agreements; analyzes their dependence on market conditions such as the relative numbers of agents of different types; and discusses their relations with the competitive equilibrium outcome and other results in the search equilibrium literature. THIS PAPER CONSIDERS a market that operates in the following way. Pairs of agents who have mutual interest in carrying out a transaction are brought together by a stochastic process. When two agents meet, they initiate a bargaining process over the terms of the transaction. If two agents reach an agreement a transaction takes place and they leave the market. Of course, the bargaining positions and hence the agreement reached in any particular meeting will be affected by the conditions prevailing in the market. These will include the chances that each of the negotiating parties have of meeting other partners in the event that the agreement in the current negotiations is delayed; also the expected length of time required to achieve an alternative transaction, and the expected behavior of alternative partners. The study of such a market mechanism is of interest for two reasons. Firstly, it captures some realistic aspects of the trade in certain specific markets (e.g., asset markets such as housing and some labor markets). Secondly, it contributes to an understanding of the micro-mechanisms of price formation and their role in shaping market outcomes. In both cases, the features studied are largely neglected in the traditional market equilibrium analyses. The related literature includes the articles by Diamond [4, 5], Diamond and Maskin [6], Mortensen [8, 9], and Zusman and Bell [13]. These articles consider markets of the type described above, in which transactions are concluded at pairwise meetings of agents. The major difference between our work and these articles is in the approach to the basic bargaining problem. In the cited articles it is assumed that a meeting is concluded with an instantaneous agreement which divides the associated surplus in an arbitrary predetermined way (when the surplus is assumed to be divided equally, the division rule is, in fact, Nashs axiomatic bargaining solution). In contrast, the present paper treats the basic bargaining problem with the strategic approach (see Rubinstein [19]) which constitutes an attempt to look into the bargaining black-box. This approach explicitly models the time dimension of the bargaining process, describes in-detail the bargaining procedure, and justifies the agreement as a perfect equilibrium in

Equilibrium in supergames with the overtaking criterion

Discusses the equilibrium in supergames with evaluation relations determined according to overtaking criterion. Differences between the situation of players undertaking to play a single game, and players who know that they will play the same game repeatedly in the future; Influence of the power of the threats on the existence of equilibrium points.

Instinctive and Cognitive Reasoning: A Study of Response Times

Lecture audiences and students were asked to respond to virtual decision and game situations at gametheory.tau.ac.il. Several thousand observations were collected and the response time for each answer was recorded. There were significant differences in response time across responses. It is suggested that choices made instinctively, that is, on the basis of an emotional response, require less response time than choices that require the use of cognitive reasoning.

Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)

Abstract It is argued that the Allais paradox reveals a certain property of the decision scheme we use to determine the preference of one lottery over another. The decision scheme is based on the use of similarity relations on the probability and prize spaces. It is proved that for every pair of similarity relations there is essentially only one preference consistent with the decision scheme and the similarities. It is claimed that the result shows a basic difficulty in reconciling utility theory with experimental data.

Repeated Insurance Contracts and Moral Hazard

Abstract An attempt is made to account for the frequently observed phenomenon of insurance companies offering discounts to clients who possess a favorable record of past claims. We argue that such discounts provide a mechanism which enables both insurer and insured to counteract the inefficiency which arises from moral hazard.

Decentralized Trading, Strategic Behaviour and the Walrasian Outcome

For a market with a finite number of agents, pairwise matching and bargaining, it is shown that, even when the market is frictionless, the equilibrium is not necessarily competitive. It depends on the amount of information agents use. If their behaviour is conditioned only on the sets of agents present and the time, the competitive solution is the unique subgame perfect equilibrium. If agents have full information and condition their behaviour on some of it, there are also noncompetitive equilibria in which behaviour depends on specific information such as the identity of the trading partner and past events.

Noncooperative models of bargaining

Publisher Summary This chapter focuses on the noncooperative models of bargaining. John Nashs (1950) path- breaking paper introduces the bargaining problem, and his pioneering work on noncooperative bargaining theory was taken up again and developed by numerous authors. The target of such a noncooperative theory of bargaining is to find theoretical predictions of what agreement, if any, will be reached by the bargainers, thereby to explain the manner in which the bargaining outcome depends on the parameters of the bargaining problem and to shed light on the meaning of some of the verbal concepts that are used when bargaining is discussed in ordinary language. Three directions in which progress has been particularly fruitful are (1) sequential models have been introduced in studying specific bargaining procedures, (2) refinements of Nash equilibrium have been applied, and (3) bargaining models have been embedded in market situations to provide insights into markets with decentralized trading. In spite of this progress, important challenges are still ahead. The most pressing is that of establishing a properly founded theory of bargaining under incomplete information. A resolution of this difficulty must presumably await a major breakthrough in the general theory of games of incomplete information. From the perspective of economic theory in general, the main challenge remains the modeling of trading institutions (with the nature of money as the most obvious target).

On the Interpretation of the Nash Bargaining Solution and Its Extension to Non-expected Utility Preferences

This paper questions the interpretation of the Nash bargaining solution. A new definition is suggested. Revisions of Nash axioms characterize the solution. The definition makes possible its extension to non-expected-utility preferences. It also reveals the logic behind the comparative statics of risk aversion and the connection between the Nash bargaining solution and strategic models. Copyright 1992 by The Econometric Society.