We consider a two-person stochastic game of resource extraction. It is assumed that players have identical preferences. A novelty relies on the fact that each player is equipped with the same risk coefficient and calculates his discounted utility in the infinite time horizon in a recursive way by applying the entropic risk measure parametrized by this risk coefficient. Under two alternative sets of assumptions, we prove the existence of a symmetric stationary Markov perfect equilibrium.Mathematics Subject Classification 91A15 · 91A25 · 91A50 · 91B62 · 91B16

This paper deals with Markov decision processes on a general state space under standard compactness-continuity assumptions. The purpose is to obtain a new class of so-called recursive utilities with the aid of the entropic risk measure. Within this framework we show that there exists a stationary policy for a discounted payoff problem in the infinite time horizon. Our result is illustrated by examples.2010 Mathematics Subject Classification: Primary 90C40; Secondary 90C39, 91B70.