Nonzero-sum Risk-Sensitive Average Stochastic Games: The Case of Unbounded Costs

Qingda Wei () and Xian Chen ()
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Qingda Wei: Huaqiao University
Xian Chen: Xiamen University

Dynamic Games and Applications, 2021, vol. 11, issue 4, No 8, 835-862

Abstract: Abstract In this paper, we study discrete-time nonzero-sum stochastic games under the risk-sensitive average cost criterion. The state space is a denumerable set, the action spaces of players are Borel spaces, and the cost functions are unbounded. Under suitable conditions, we first introduce the risk-sensitive first passage payoff functions and obtain their properties. Then, we establish the existence of a solution to the risk-sensitive average cost optimality equation of each player for the case of unbounded cost functions and show the existence of a randomized stationary Nash equilibrium in the class of randomized history-dependent strategies. Finally, we use a controlled population system to illustrate the main results.

Keywords: Nonzero-sum game; Risk-sensitive average cost criterion; Unbounded cost; Nash equilibrium; 91A15; 91A25 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13235-021-00380-5

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