In this paper,we study the expected average criterion in discrete-time Markov games with Borel spaces.For the general case of unbounded reward functions,we first replace the corresponding Shapley equation for the average criterion with average-optimality two-inequalities.Then,by using the relative difference of the values of the discounted games,we give a new set of optimality conditions,which are weaker than the geometric ergodicity condition in the existing literature.Under these new conditions,we not only establish the solvability of the average-optimality two-inequalities but also show the existence of both the value and a Nash equilibrium of the game.Moreover,under the stronger geometric ergodicity condition,by the average-optimality two-inequalities,we also establish the solvability of the Shapley equation.Finally,we present two examples of renewable resources and financial insurance to verify the conditions and illustrate the results in this paper.
关键词
零和平均随机博弈/最优性条件/平均最优双不等式/Shapley方程/Nash均衡策略
Key words
zero-sum average stochastic game/optimality conditions/average-optimality two-inequalities/Shapley equation/Nash equilibrium
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