Markovian Equilibrium in a Class of Stochastic Games: Existence Theorems for Discounted and Undiscounted Models
AbstractWe study a strategic version of the neoclassical growth model under possible production uncertainty. For a general specification of the problem, we establish (1) the existence of stationary Markov equilibria in pure strategies for the discounted game, and (2) the convergence, under a boundedness condition, of discounted equilibrium strategies to a pure strategy stationary Markovian equilibrium of the undiscounted game as the discount factor tends to unity. The same techniques can be used to prove that such convergence also obtains in all finite-state, finite-action stochastic games satisfying a certain "full communicability" condition. These results are of special interest since there are well known examples in the literature in which the limit of discounted.equilibria fails to be an equilibrium of the undiscounted game.
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Volume (Year): 2 (1992)
Issue (Month): 2 (April)
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