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Conference Paper (international conference)

Risk-Sensitive Optimality in Markov Games

Sladký Karel, Martínez Cortés V. M.

: Proceedings of the 35th International Conference Mathematical Methods in Economics (MME 2017), p. 684-689

: MME 2017. International Conference Mathematical Methods in Economics /35./, (Hradec Králové, CZ, 20170913)

: GA13-14445S, GA ČR

: two-person Markov games, communicating Markov chains, risk-sensitive optimality, dynamic programming

: http://library.utia.cas.cz/separaty/2017/E/sladky-0480036.pdf

(eng): 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.

: AH

: 50202

07.01.2019 - 08:39