Semi-Markov games: a survey and some new results

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发表日期：

2025年10月27日

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P. Mondal,
D. Ghorui,
S. Ghosh

摘要

In this paper, we present some consequences of the theory of semi-algebraic sets for semi-Markov games. We prove that for every stationary strategy of one player, the set of stationary best responses of other player in the \(\beta \) -discounted game is a polytope, the extreme points of which are pure stationary strategies. We define the concept of \(\beta \) -discounted equilibrium, and using Kakutani’s fixed point theorem, we prove that every multiplayer semi-Markov game admits a stationary \(\beta \) -discounted equilibrium, for every discount factor \(\beta \in (0,1)\) . Examples are provided for such games.