Population Games With Erlang Clocks: Convergence to Nash Equilibria For Pairwise Comparison Dynamics
Population Games With Erlang Clocks: Convergence to Nash Equilibria For Pairwise Comparison Dynamics
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DOI：
10.1109/cdc51059.2022.9993228
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
Semih Kara;N. C. Martins;M. Arcak
中科院分区：
文献类型：
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作者：
Semih Kara;N. C. Martins;M. Arcak
流行的方法来分析人口游戏和进化动力学在大人口的限制，假设一个泊松过程（或时钟）固有的每个代理人决定何时可以修改其策略。因此，这种方法的前提是指数分布的修订间隔，是不够的情况下，每个战略需要一系列的子任务（子战略），必须完成之前，一个新的修订时间发生。本文提出了一种方法，这种情况下，一个子策略的持续时间是指数分布的前提下，导致Erlang分布的修订间隔。我们假设一个所谓的成对比较协议捕获代理的修订偏好，使我们的分析具体。子战略的存在带来了与现有模型和结果不相容的额外动态。我们的主要贡献是双重的，都来自一个确定性的近似有效的大人口。我们证明了收敛的人口的状态的纳什均衡集时，一个潜在的游戏产生的策略的回报。我们使用系统理论的被动性，以确定条件下，这种收敛是保证压缩游戏。
The prevailing methodology for analyzing population games and evolutionary dynamics in the large population limit assumes that a Poisson process (or clock) inherent to each agent determines when the agent can revise its strategy. Hence, such an approach presupposes exponentially distributed inter-revision intervals, and is inadequate for cases where each strategy entails a sequence of sub-tasks (sub-strategies) that must be completed before a new revision time occurs. This article proposes a methodology for such cases under the premise that a sub-strategy’s duration is exponentially distributed, leading to Erlang distributed inter-revision intervals. We assume that a so-called pairwise comparison protocol captures the agents’ revision preferences to render our analysis concrete. The presence of sub-strategies brings on additional dynamics that is incompatible with existing models and results. Our main contributions are twofold, both derived for a deterministic approximation valid for large populations. We prove convergence of the population’s state to the Nash equilibrium set when a potential game generates payoffs for the strategies. We use system-theoretic passivity to determine conditions under which this convergence is guaranteed for contractive games.