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<p>In this paper, we consider nonzero-sum <i>N</i>-player continuous-time Markov games with constraints and countable states. Players aim to maximize their total expected rewards on the finite horizon, while keeping their finite-horizon expected costs bounded by given constants. For the model with unbounded transition and reward/cost rates, we introduce correlated strategies and associate them with occupation measures. Under suitable continuity-compactness conditions, we obtain some topological properties of the occupation measures. Using these properties and the Kakutani-Fan-Glicksberg fixed point theorem, we prove the existence of constrained Nash equilibria for auxiliary games. These Nash equilibria for auxiliary games are then shown to converge to a constrained Nash equilibrium for our original game. Furthermore, we use a controlled birth and death system to illustrate our main result.</p>

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Constrained continuous-time nonzero-sum Markov games on the finite horizon

  • 期刊论文

  • 发表日期：

    2026年4月9日

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  • Weicheng Wang,
  • Xianping Guo

摘要

In this paper, we consider nonzero-sum N-player continuous-time Markov games with constraints and countable states. Players aim to maximize their total expected rewards on the finite horizon, while keeping their finite-horizon expected costs bounded by given constants. For the model with unbounded transition and reward/cost rates, we introduce correlated strategies and associate them with occupation measures. Under suitable continuity-compactness conditions, we obtain some topological properties of the occupation measures. Using these properties and the Kakutani-Fan-Glicksberg fixed point theorem, we prove the existence of constrained Nash equilibria for auxiliary games. These Nash equilibria for auxiliary games are then shown to converge to a constrained Nash equilibrium for our original game. Furthermore, we use a controlled birth and death system to illustrate our main result.