Name
Abstract | ||
|---|---|---|
The infinite horizon risk-sensitive discounted-cost and ergodic-cost nonzero-sum stochastic games for controlled Markov chains with countably many states are analyzed. For the discounted-cost game, we prove the existence of Nash equilibrium strategies in the class of Markov strategies under fairly general conditions. Under an additional weak geometric ergodicity condition and a small cost criterion, the existence of Nash equilibrium strategies in the class of stationary Markov strategies is proved for the ergodic-cost game. The key nontrivial contributions in the ergodic part are to prove the existence of a particular form of a (relative) value function solution to a player's Bellman equation and the continuity of this solution with respect to the opponent's strategies. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1287/moor.2017.0870 | MATHEMATICS OF OPERATIONS RESEARCH |
Keywords | Field | DocType |
noncooperative stochastic games,risk-sensitive payoff,Bellman equations,Nash equilibria,geometric ergodicity | Correlated equilibrium,Discrete mathematics,Mathematical optimization,Risk dominance,Epsilon-equilibrium,Markov chain,Best response,Normal-form game,Nash equilibrium,Mathematics,Stochastic game | Journal |
Volume | Issue | ISSN |
43 | 2 | 0364-765X |
Citations | PageRank | References |
2 | 0.38 | 11 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Arnab Basu | 1 | 10 | 3.05 |
| Mrinal K. Ghosh | 2 | 28 | 9.78 |