 Zero-sum risk-sensitive stochastic gamesNicole Bäuerle and Ulrich Rieder Stochastic Processes and their Applications, 2017, vol. 127, issue 2, 622-642 Abstract: In this paper we consider two-person zero-sum risk-sensitive stochastic dynamic games with Borel state and action spaces and bounded reward. The term risk-sensitive refers to the fact that instead of the usual risk neutral optimization criterion we consider the exponential certainty equivalent. The discounted reward case on a finite and an infinite time horizon is considered, as well as the ergodic reward case. Under continuity and compactness conditions we prove that the value of the game exists and solves the Shapley equation and we show the existence of optimal (non-stationary) strategies. In the ergodic reward case we work with a local minorization property and a Lyapunov condition and show that the value of the game solves the Poisson equation. Moreover, we prove the existence of optimal stationary strategies. A simple example highlights the influence of the risk-sensitivity parameter. Our results generalize findings in Basu and Ghosh (2014) and answer an open question posed there. Keywords: Risk-sensitive stochastic games; Ergodic reward; Shapley equation; Poisson equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:2:p:622-642 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2016.06.020 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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