Large deviations and Stochastic stability in Population Games

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Mathias Staudigl, S. Arigapudi, W. Sandholm
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引用次数: 2

Abstract

In this article we review a model of stochastic evolution under general noisy best-response protocols, allowing the probabilities of suboptimal choices to depend on their payoff consequences. We survey the methods developed by the authors which allow for a quantitative analysis of these stochastic evolutionary game dynamics. We start with a compact survey of techniques designed to study the long run behavior in the small noise double limit (SNDL). In this regime we let the noise level in agents' decision rules to approach zero, and then the population size is formally taken to infinity. This iterated limit strategy yields a family of deterministic optimal control problems which admit an explicit analysis in many instances. We then move in by describing the main steps to analyze stochastic evolutionary game dynamics in the large population double limit (LPDL). This regime refers to the iterated limit in which first the population size is taken to infinity and then the noise level in agents' decisions vanishes. The mathematical analysis of LPDL relies on a sample-path large deviations principle for a family of Markov chains on compact polyhedra. In this setting we formulate a set of conjectures and open problems which give a clear direction for future research activities.
人口博弈中的大偏差和随机稳定性
在本文中,我们回顾了一般噪声最佳响应协议下的随机进化模型,该模型允许次优选择的概率取决于它们的收益结果。我们调查了作者开发的方法,这些方法允许对这些随机进化博弈动力学进行定量分析。我们首先简要介绍了用于研究小噪声双极限(SNDL)长期行为的技术。在这种情况下,我们让智能体决策规则中的噪声水平接近于零,然后将总体规模正式取为无穷大。这种迭代极限策略产生了一系列确定性最优控制问题,在许多情况下可以进行明确的分析。然后,我们通过描述在大种群双极限(LPDL)下分析随机进化博弈动力学的主要步骤进入。这种状态指的是一种迭代极限,在这种极限下,首先种群规模趋于无穷大,然后智能体决策中的噪声水平消失。LPDL的数学分析依赖于紧多面体上马尔可夫链族的样本路径大偏差原理。在这种情况下,我们制定了一套猜想和开放性问题,为未来的研究活动提供了明确的方向。
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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