Non-zero-sum stochastic games with recursive utilities of risk-sensitive players

Łukasz Balbus¹ ; Anna Jaśkiewicz² ; Andrzej S. Nowak³

¹ Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra Zielona Góra, Poland <a href="https://orcid.org/0000-0002-3181-5187">ORCID: 0000-0002-3181-5187</a>
² Faculty of Pure and Applied Mathematics Wrocław University of Science and Technology Wrocław, Poland
³ Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra Zielona Góra, Poland

Applicationes Mathematicae, Tome 50 (2023) no. 2, pp. 107-121.

Résumé

Recursive utilities constructed by conditional entropic risk measures have recently been considered in various stochastic models and their applications, e.g., in economic dynamics. We study countable state discounted stochastic games played by risk-sensitive players. More precisely, we assume that the players evaluate their payoffs in a recursive way with the aid of the certainty equivalent of an exponential utility function. Under typical continuity and compactness conditions we prove that a stationary Nash equilibrium exists.

Détail

DOI : 10.4064/am2498-1-2024

Keywords: recursive utilities constructed conditional entropic risk measures have recently considered various stochastic models their applications economic dynamics study countable state discounted stochastic games played risk sensitive players precisely assume players evaluate their payoffs recursive aid certainty equivalent exponential utility function under typical continuity compactness conditions prove stationary nash equilibrium exists