ORDERED FIELD PROPERTY IN A SUBCLASS OF FINITE SER-SIT SEMI-MARKOV GAMES

Prasenjit Mondal () and Sagnik Sinha ()
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Prasenjit Mondal: Mathematics Department, Jadavpur University, Kolkata-700032, India
Sagnik Sinha: Mathematics Department, Jadavpur University, Kolkata-700032, India

International Game Theory Review (IGTR), 2013, vol. 15, issue 04, 1-20

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 (undiscounted) 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.

Keywords: Two-person semi-Markov games; discounted and undiscounted payoffs; minimax value and Nash equilibrium strategies; Archimedean ordered field property; semi-Markov games with separable reward and state-independent transition; 22E46; 53C35; 57S20 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219198913400264

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