Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games

Beatris Escobedo-Trujillo (), Daniel López-Barrientos () and Onésimo Hernández-Lerma ()
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Beatris Escobedo-Trujillo: CINVESTAV-IPN
Daniel López-Barrientos: CINVESTAV-IPN
Onésimo Hernández-Lerma: CINVESTAV-IPN

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 3, No 8, 662-687

Abstract: Abstract This paper deals with zero-sum stochastic differential games with long-run average payoffs. Our main objective is to give conditions for existence and characterization of bias and overtaking optimal equilibria. To this end, first we characterize the family of optimal average payoff strategies. Then, within this family, we impose suitable conditions to determine the subfamilies of bias and overtaking equilibria. A key step to obtain these facts is to show the existence of solutions to the average payoff optimality equations. This is done by the usual “vanishing discount” approach. Finally, a zero-sum game associated to a certain manufacturing process illustrates our results.

Keywords: Average (or ergodic) payoff criteria; Bias optimality; Zero-sum stochastic differential games; Overtaking optimality (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9974-4

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