Competitive and Cooperative Games of Variable-Structure Stochastic Automata

Abstract

Abstract The collective behavior of variable-structure stochastic automata in competitive and cooperative game situations is investigated. In competitive games, it is demonstrated that when the automata use optimal reinforcement schemes, the Von Neumann value is achieved for games against nature as well as for two-player zero-sum games having a saddle point. For games without a saddle point the value of the game oscillates about the Von Neumann value in mixed strategies. For two-player cooperative games, the participating automata are shown to exhibit a locally optimal collective behavior and conditions are derived for achieving global optimality. The results of extensive computer studies are described briefly by considering five typical examples which reveal many interesting aspects of the collective behavior of automata.