This paper proposes a model of the process by which players learn to play repeated coordination games, with the goal of understanding the results of some recent experiments.In those experiments the dynamics of subjects' strategy choices and the resulting patterns of discrimination among equilibria varied systematically with the rule for determining payoffs and the size of the interacting groups, in ways that are not adequately explained by available methods of analysis.The model suggests a possible explanation by showing how the dispersion of subjects' beliefs interacts with the learning process to determine the probability distribution of its dynamics and limiting outcome.
The authors present three distinct approaches to perfect and proper equilibria for infinite normal form games. In the first two approaches, players 'tremble' in the infinite game playing full support approximate best responses to others' strategies. In the strong approach, a tremble assigns high probability to the set of pure best responses; in the weak approach, it assigns high probability to a neighborhood of this set. The third, limit-of-finite approach applies traditional refinements to sequences of successively larger finite games. Overall, the strong approach to equilibrium refinement most fully respects the structure of infinite games. Copyright 1995 by The Econometric Society.
We analyze optimal mechanisms in environments where sellers are privately informed about quality. A methodology is provided for deriving conditions that are necessary and sufficient to determine when two simple trading environments maximize either social or private surplus. The commonly used auction mechanism is frequently inefficient in procurement environments. Often, the optimal mechanism is simply to order potential suppliers and to tender take-it-or-leave-it offers to each sequentially. We completely characterize the environments in which either mechanism is optimal. In doing so, we develop a general methodology that determines when and if a given trading institution is optimal.
A new asymptotic theory of regression is introduced for possibly nonstationary time series. The regressors are assumed to be generated by a linear process with martingale difference innovations. The conditional variances of these martingale differences are specified as autoregressive stochastic volatility processes with autoregressive roots that are local to unity. The author finds conditions under which the least squares estimates are consistent and asymptotically normal. A simple adaptive estimator is proposed which achieves the same asymptotic distribution as the generalized least squares estimator without requiring parameter assumptions for the stochastic volatility process. Copyright 1995 by The Econometric Society.
Rubinstein's alternating-offers bargaining model is enriched by assuming that players' payoffs in disagreement periods are determined by a normal form game. It is shown that such a model can have multiple perfect equilibria, including inefficient ones, provided that players are sufficiently patient. Delay is possible even though there is perfect information and the players are fully rational. The length of delay depends only on the payoff structure of the disagreement game and not on the discount factor. Not all feasible and individually rational payoffs of the disagreement game can be supported as average disagreement payoffs. Indeed, some negotiation games have a unique perfect equilibrium with immediate agreement.
[This study demonstrates the possibility of ergodically chaotic optimal accumulation in the case in which future utilities are discounted arbitrarily weakly. For this purpose, we use a two-sector model with Leontief production functions and construct a condition under which the optimal transition function is unimodal and expansive. We demonstrate that the set of parameter values satisfying that condition is nonempty no matter how weakly the future utilities are discounted.]
This paper elucidates the logic behind recent papers which show that a unique equilibrium is selected in the presence of higher order uncertainty, i.e., when players lack common knowledge.We introduce two new concepts: belief potential of the information system and p-dominance of Nash-equilibria of the game, and show that a Nash-equilibrium is uniquely selected whenever its p-dominance is below the belief potential.This criterion applies to many-action games, not merely 2 x 2 games.It also applies to games without dominant strategies, where the set of equilibria is shown to be smaller and simpler than might be initially conjectured.Finally, the new concepts help understand the circumstances under which the set of equilibria varies with the amount of common knowledge among players.
In a recent paper Rubinstein, Safra, and Thomson (RST) have provided an interesting re-examination of the widely applied Nash solution for a two-person bargaining problem. They recast the usual Nash bargaining problem into a more natural setting of feasible alternatives with a disagreement outcome. The two players are then described by their risk preferences defined on the set of lotteries over the alternatives and the disagreement outcome. This enables them to define an ordinal Nash solution in terms of the agents' risk preferences. Essentially, their ordinal solution is an outcome that is immune against possible objections. Freeing the definition of the Nash solution from utility naturally led RST to extending its scope to Non-Expected Utility (NEU) preferences. We contend, however, that the family of NEU preferences considered by RST is unduly restrictive. The assumptions imposed on the risk preferences by RST essentially exclude any members of the Rank Dependent Expected Utility (RDEU) and betweenness families that can accommodate the very choice paradoxes that stimulated the development of NEU theory. As these are two of the most extensively analyzed and widely applied NEU models in the literature, this seems to cast doubt on how broad an extension to NEU preferences the RST approach affords. We demonstrate, however, that RST's analysis can be modified so that their conclusion is valid in a wider class of preferences that can include examples of RDEU preferences. This class consists of preferences that admit what we term a disagreement linear representation.