51. Continuous stochastic games
- Author
-
Matthew J. Sobel
- Subjects
Equilibrium point ,Statistics and Probability ,Computer Science::Computer Science and Game Theory ,Generalization ,General Mathematics ,010102 general mathematics ,Stochastic game ,ComputingMilieux_PERSONALCOMPUTING ,Markov process ,TheoryofComputation_GENERAL ,Sobel operator ,01 natural sciences ,Dynamic programming ,010104 statistics & probability ,symbols.namesake ,Metric space ,Compact space ,symbols ,0101 mathematics ,Statistics, Probability and Uncertainty ,Mathematical economics ,Mathematics - Abstract
Nonzero-sum N-person stochastic games are a generalization of Shapley's two-person zero-sum terminating stochastic game. Rogers and Sobel showed that an equilibrium point exists when the sets of states, actions, and players are finite. The present paper treats discounted stochastic games when the sets of states and actions are given by metric spaces and the set of players is arbitrary. The existence of an equilibrium point is proven under assumptions of continuity and compactness. NONCOOPERATIVE STOCHASTIC GAME; DISCOUNTED MARKOVIAN DECISION PROCESS; EQUILIBRIUM POINT; DYNAMIC PROGRAMMING
- Published
- 1973