Ordered Field Property for Semi-Markov Games when One Player Controls Transition Probabilities and Transition Times

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

International Game Theory Review (IGTR), 2015, vol. 17, issue 02, 1-26

Abstract: Two-person finite semi-Markov games (SMGs) are studied when the transition probabilities and the transition times are controlled by one player at all states. For the discounted games in this class, we prove that the ordered field property holds and there exist optimal/Nash equilibrium stationary strategies for the players. We illustrate that the zero-sum SMGs where only transition probabilities are controlled by one player, do not necessarily satisfy the ordered field property. An algorithm along with a numerical example for the discounted one player control zero-sum SMGs is given via linear programming. For the undiscounted version of such games, we exhibit with an example that if the game ceases to be unichain, an optimal stationary or Markov strategy need not exist, (though in this example of a one-player game we exhibit a semi-stationary optimal strategy/policy). Lastly, we prove that if such games are unichain, then they possess the ordered field property for the undiscounted case as well.

Keywords: Semi-Markov games; semi-Markov decision processes; semi-Markov policies; discounted and limiting average payoffs; ordered field property; multichain structure; finite step algorithms for semi-Markov games; 22E46; 90C40; 53C35; 57S20 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219198915400228
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:igtrxx:v:17:y:2015:i:02:n:s0219198915400228

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219198915400228

Access Statistics for this article

International Game Theory Review (IGTR) is currently edited by David W K Yeung

More articles in International Game Theory Review (IGTR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().