Stochastic Dynamical Games with Information of Various Types

Dynamic discrete-time games are generalized to a stochastic environment, in order to examine the influence of various types of information structures on the course of a game. It is shown that the information structure of a game, i.e., type and amount of information available to players and, in particular, asymmetry of information, may lead to unexpected and sometimes counter-intuitive effects on the game result, i.e., the players' payoffs. The paper also develops algorithms for obtaining the Nash equilibrium strategies in such games. These involve reducing optimal reaction policies to the corresponding dynamic programming algorithms and generalizing the classical optimal control technique. Results of computer simulations for a variant of fishery harvesting game are presented.