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首页> 外文期刊>Annales de l'Institut Henri Poincare. Probabilites et Statistiques >N-Player games and mean-field games with smooth dependence on past absorptions
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N-Player games and mean-field games with smooth dependence on past absorptions

机译：N播放机游戏和卑鄙的野外游戏，对过去的吸收相比顺利依赖

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摘要

Mean-field games with absorption is a class of games that has been introduced in (Ann. Appl. Probab. 28 (2018) 2188-2242) and that can be viewed as natural limits of symmetric stochastic differential games with a large number of players who, interacting through a mean-field, leave the game as soon as their private states hit some given boundary.In this paper, we push the study of such games further, extending their scope along two main directions. First, we allow the state dynamics and the costs to have a very general, possibly infinite-dimensional, dependence on the (non-normalized) empirical subprobability measure of the survivors' states. This includes the particularly relevant case where the mean-field interaction among the players is done through the empirical measure of the survivors together with the fraction of absorbed players over time. Second, the boundedness of coefficients and costs has been considerably relaxed including drift and costs with linear growth in the state variables, hence allowing for more realistic dynamics for players' private states. We prove the existence of solutions of the MFG in strict as well as relaxed feedback form, and we establish uniqueness of the MFG solutions under monotonicity conditions of Lasry-Lions type. Finally, we show in a setting with finite-dimensional interaction that such solutions induce approximate Nash equilibria for the N-player game with vanishing error as N - infinity.
机译：具有吸收的平均野外游戏是一类已经在（Ann.Phop.Popl.Popl.Pogl.Pog.28（2018）2188-2242）中，可以被视为具有大量玩家的对称随机差动游戏的自然限制谁，通过平均字段互动，一旦私人国家击中一些给定边界，就会离开游戏。在本文中，我们进一步推动了这种游戏的研究，沿两个主要方向延伸了它们的范围。首先，我们允许国家动态和成本具有非常一般的，可能无限的维度，依赖于幸存者状态的（非标准化）的经验副资料衡量。这包括特别相关的情况，其中通过幸存者的经验测量与吸收的球员随时间的分数一起完成球员之间的平均场相互作用。其次，系数和成本的有界已经很大放松，包括漂移和成本，状态变量在线性生长，因此允许为玩家的私有国家进行更现实的动态。我们证明了MFG的解决方案的存在性能，以及放宽的反馈形式，我们在激光狮子型单调条件下建立了MFG解决方案的唯一性。最后，我们在具有有限尺寸相互作用的环境中显示了这种解决方案诱导N播放器游戏的近似NASH均衡，随着N-＆GT的消失误差。无限。

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