Name
Abstract | ||
|---|---|---|
In this paper, we deal with a subclass of two-person finite SeR-SIT (Separable Reward-State Independent Transition) semi-Markov games which can be solved by solving a single matrix/bimatrix game under discounted as well as limiting average (undis-counted) payoff criteria. A SeR-SIT semi-Markov game does not satisfy the so-called (Archimedean) ordered field property in general. Besides, the ordered field property does not hold even for a SeR-SIT-PT (Separable Reward-State-Independent Transition Probability and Time) semi-Markov game, which is a natural version of a SeR-SIT stochastic (Markov) game. However by using an additional condition, we have shown that a subclass of finite SeR-SIT-PT semi-Markov games have the ordered field property for both discounted and undiscounted semi-Markov games with both players having state-independent stationary optimals. The ordered field property also holds for the nonzero-sum case under the same assumptions. We find a relation between the values of the discounted and the undiscounted zero-sum semi-Markov games for this modified subclass. We propose a more realistic pollution tax model for this subclass of SeR-SIT semi-Markov games than pollution tax model for SeR-SIT stochastic game. Finite step algorithms are given for the discounted and for the zero-sum undiscounted cases. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1142/S0219198913400264 | INTERNATIONAL GAME THEORY REVIEW |
Keywords | Field | DocType |
Two-person semi-Markov games, discounted and undiscounted payoffs, mini-max value and Nash equilibrium strategies, Archimedean ordered field property, semi-Markov games with separable reward and state-independent transition | Mathematical economics,Ordered field,Subclass,Matrix (mathematics),Markov chain,Bimatrix game,Separable space,Limiting,Mathematics,Stochastic game | Journal |
Volume | Issue | ISSN |
15 | 4 | 0219-1989 |
Citations | PageRank | References |
3 | 0.57 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Prasenjit Mondal | 1 | 3 | 2.26 |
| Sagnik Sinha | 2 | 20 | 3.29 |