Risk-Sensitive Optimality in Markov Games

0480036 - ÚTIA 2018 RIV CZ eng C - Conference Paper (international conference)
Sladký, Karel - Martínez Cortés, V. M.
Risk-Sensitive Optimality in Markov Games.
Proceedings of the 35th International Conference Mathematical Methods in Economics (MME 2017). Hradec Králové: University of Hradec Králové, 2017, s. 684-689. ISBN 978-80-7435-678-0.
[MME 2017. International Conference Mathematical Methods in Economics /35./. Hradec Králové (CZ), 13.09.2017-15.09.2017]
R&D Projects: GA ČR GA13-14445S
Institutional support: RVO:67985556
Keywords : two-person Markov games * communicating Markov chains * risk-sensitive optimality * dynamic programming
OECD category: Applied Economics, Econometrics
http://library.utia.cas.cz/separaty/2017/E/sladky-0480036.pdf

The article is devoted to risk-sensitive optimality in Markov games. Attention is focused on Markov games evolving on communicating Markov chains with two-players with opposite aims. Considering risk-sensitive optimality criteria means that total reward generated by the game is evaluated by exponential utility function with a given risk-sensitive coefficient. In particular, the first player (resp. the secondplayer) tries to maximize (resp. minimize) the long-run risk sensitive average reward. Observe that if the second player is dummy, the problem is reduced to finding optimal policy of the Markov decision chain with the risk-sensitive optimality. Recall that for the risk sensitivity coefficient equal to zero we arrive at traditional optimality criteria. In this article, connections between risk-sensitive and risk-neutral Markov decisionchains and Markov games models are studied using discrepancy functions. Explicit formulae for bounds on the risk-sensitive average long-run reward are reported. Policy iteration algorithm for finding suboptimal policies of both players is suggested. The obtained results are illustrated on numerical example.
Permanent Link: http://hdl.handle.net/11104/0276771