Dynamics and stability for a class of evolutionary games with time delays in strategies

一类具有时滞策略的演化博弈的动力学和稳定性

Abstract

This paper investigates the modeling and stability of a class of finite evolutionary games with time delays in strategies. First, the evolutionary dynamics of a sequence of strategy profiles, named as the profile trajectory, is proposed to describe the strategy updating process of the evolutionary games with time delays. Using the semi-tensor product of matrices, the profile trajectory dynamics with two kinds of time delays are converted into their algebraic forms respectively. Then a sufficient condition is obtained to assure the stability of the delayed evolutionary potential games at a pure Nash equilibrium.

摘要

创新点

针对策略存在时间延迟的有限演化博弈, 本文研究了其动态演化过程和稳定性。 首先, 利用矩阵的半张量积这一数学工具, 将策略存在常时滞和变时滞两种不同情况下的逻辑动态演化过程分别转化为相应的代数表达形式。 其次, 利用势博弈的优点, 给出了时滞演化的有限势博弈收敛到纳什均衡点的充分条件。

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Correspondence to Yuanhua Wang.

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Wang, Y., Cheng, D. Dynamics and stability for a class of evolutionary games with time delays in strategies. Sci. China Inf. Sci. 59, 92209 (2016). https://doi.org/10.1007/s11432-016-5532-x

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Keywords

  • evolutionary game
  • time delays
  • potential game
  • semi-tensor product of matrices
  • stability

关键词

  • 演化博弈
  • 时滞
  • 势博弈
  • 矩阵的半张量积
  • 稳定性