In a repeated game of incomplete information, myopic players form beliefs on next-period play and choose strategies to maximize next-period payoffs. Beliefs are treated as forecast of future plays. Forecast accuracy is assessed using calibration tests, which measure asymptotic accuracy of beliefs against some realizations. Beliefs are calibrated if they pass all calibration tests. For a positive Lebesgue measure of payoff vectors, beliefs are not calibrated. But, if payoff vector and calibration test are drawn from a suitable product measure, beliefs pass the calibration test almost surely.
This paper surveys implementation theory when players have incomplete or asymmetric information, especially in economic environments. After the basic problem is introduced, the theory of implementation is summarized. Some coalitional considerations for implementation problems are discussed. For economies with asymmetric information, cooperative games based on incentive compatibility constraints or Bayesian incentive compatible mechanisms are derived and examined.
We document and attempt to explain the observation that automobile insurance premiums vary dramatically across local markets. We argue high premiums can be attributed to the large numbers of uninsured motorists in some cities, while at the same time, the uninsured motorists can be attributed to high premiums. We construct a simple noncooperative equilibrium model, where limited liability can generate inefficient equilibria with uninsured drivers and high, yet actuarially fair, premiums. For certain parameterizations, an optimal full insurance equilibrium and inefficient high price equilibria with uninsured drivers exist simultaneously, consistent with the observed price variability across seemingly similar cities.
Game theory is both at the heart of economics and without a definitive solution. This paper proposes a solution. It is argued that a dominance criterion generates a, and perhaps the, generalized equilibrium solution for game theory. First we provide a set theoretic perspective from which to view game theory, and then present and discuss the proposed solution.
A new approach to market behavior is suggested. This approach has a coherent game theoretic foundaton, addresses such anomalous economic behaviors as strikes, rigid wages and unemployment, regulation of financial markets, depresssion, and nonmarket allocation, and, more generally, provides insights for Finance, Oligopoly Theory, Industrial Organization, and Macroeconomics. The central theme of the approach is that exchange technologies are a basic building block in a model, as are tastes, endowments, and production technologies. Moreover, the key feature of an institution of exchange is that it allows the making of a binding final offer.
Game theory addresses a problem which is central to economics. Yet, according to the folklore of economics, game theory has failed. This paper argues that this is an incorrect interpretation of the game theory literature. When faced with a well-posed problem, game theory provides a solution. Procedures for facing game theory with well-posed problems are suggested, and examples of economic applications provided. The applications are Samuelson's fiat money model, Phelps' capital overaccumulation problem, multiple rational expectations equilibria, and a bargaining problem.