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Original title:
Risk-Sensitive Optimality in Markov Games
Authors: Sladký, Karel ; Martínez Cortés, V. M.
Document type: Papers
Conference/Event: MME 2017. International Conference Mathematical Methods in Economics /35./, Hradec Králové (CZ), 20170913
Year: 2017
Language: eng
Abstract: 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.
Keywords: communicating Markov chains; dynamic programming; risk-sensitive optimality; two-person Markov games
Project no.: GA13-14445S (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of the 35th International Conference Mathematical Methods in Economics (MME 2017), ISBN 978-80-7435-678-0
Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2017/E/sladky-0480036.pdf
Original record: http://hdl.handle.net/11104/0276771
Permalink: http://www.nusl.cz/ntk/nusl-369593
The record appears in these collections:
Research > Institutes ASCR > Institute of Information Theory and Automation
Conference materials > Papers
Authors: Sladký, Karel ; Martínez Cortés, V. M.
Document type: Papers
Conference/Event: MME 2017. International Conference Mathematical Methods in Economics /35./, Hradec Králové (CZ), 20170913
Year: 2017
Language: eng
Abstract: 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.
Keywords: communicating Markov chains; dynamic programming; risk-sensitive optimality; two-person Markov games
Project no.: GA13-14445S (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of the 35th International Conference Mathematical Methods in Economics (MME 2017), ISBN 978-80-7435-678-0
Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2017/E/sladky-0480036.pdf
Original record: http://hdl.handle.net/11104/0276771
Permalink: http://www.nusl.cz/ntk/nusl-369593
The record appears in these collections:
Research > Institutes ASCR > Institute of Information Theory and Automation
Conference materials > Papers
Record created 2017-12-07, last modified 2022-09-29