Core Discussion Paper 2001/59 Stochastic Games in Economics: the Lattice-theoretic Approach

This chapter considers a recent trend in the application of stochastic games to economics characterized by the use of the lattice-theoretic approach to capture the monotonic properties of Markovian equilibria. The topics covered are: (i) a general framework for discounted stochastic games with Liptchitz-continuous and monotone equilibrium strategies and values, (ii) a model of capital accumulation, (iii) two classes of games with perfect information, in strategic bequests and oligopoly with commitment. In view of the restriction to pure-strategy equilibria and of the natural monotonicity property of strategies and value functions in most economic applications, this approach appears most promising. JEL Classification: C72, L13, O31. CORE, Université catholique de Louvain, Belgium. E-mail: [email protected] I would like to thank Jean-François Mertens, Wolfgang Leininger, Abraham Neyman, Robert Rosenthal, Matt Sobel, and Sylvain Sorin for helpful suggestions concerning the material covered here. This paper was prepared for presentation at the NATO Advanced Summer Institute on stochastic games held at SUNY-Stony-Brook in July 1999. This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the author.