CONTINUOUS STOCHASTIC GAMES OF CAPITAL ACCUMULATION WITH CONVEX TRANSITIONS

We consider a discounted stochastic game of common-property capital ac cumulation with nonsymmetric players, bounded one-period extraction ca pacities, and a transition law satisfying a general strong convexity c ondition. We show that the infinite-horizon problem has a Markov-stati onary (subgame-perfect) equilibrium and that every finite-horizon trun cation has a unique Markovian equilibrium, both in consumption functio ns which are continuous and nondecreasing and have all slopes bounded above by 1. Unlike previous results in strategic dynamic models, these properties are reminiscent of the corresponding optimal growth model. (C) 1996 Academic Press, Inc.