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<p>In this paper we study constrained discrete-time nonzero-sum games with a Borel state space and possibly unbounded cost functions. The transition law is absolutely continuous with respect to some probability measure. Due to the uncountability of the state space, we endow the set of all stationary strategies with the Young topology. For the expected discounted cost criteria, we show the existence of a stationary constrained discount Nash equilibrium via constructing an approximating sequence of the game models. For the expected average cost criteria, we first obtain the continuity of the expected average cost functions with respect to the stationary strategy profile. Then employing the vanishing discount approach we prove that any limit point of the stationary constrained discount Nash equilibrium is a constrained average Nash equilibrium.</p>

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Nonzero-sum constrained discrete-time stochastic games with uncountable state spaces

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • Qingda Wei,
  • Xian Chen

摘要

In this paper we study constrained discrete-time nonzero-sum games with a Borel state space and possibly unbounded cost functions. The transition law is absolutely continuous with respect to some probability measure. Due to the uncountability of the state space, we endow the set of all stationary strategies with the Young topology. For the expected discounted cost criteria, we show the existence of a stationary constrained discount Nash equilibrium via constructing an approximating sequence of the game models. For the expected average cost criteria, we first obtain the continuity of the expected average cost functions with respect to the stationary strategy profile. Then employing the vanishing discount approach we prove that any limit point of the stationary constrained discount Nash equilibrium is a constrained average Nash equilibrium.