Two‐strategy evolutionary games with stochastic adaptive control. (1st July 2021)

• Record Type: Journal Article
• Authors: Liang, Haili; Cui, Ying; Zhou, Zhao; Ding, Baogang
• Other Names: Baldi Simone guestEditor.; Kosmatopoulos Elias guestEditor.; Roy Spandan guestEditor.; Yuan Shuai guestEditor.; Roy Sayan Basu guestEditor.; Li Le guestEditor.
• Is Part Of: International journal of adaptive control and signal processing. Volume 36:Number 2(2022)
• Page Start: 251
• Page End: 263
• Publication Date: 2021-07-01
• Subjects: adaptive control -- evolutionary games -- stochastic stability -- time delay; Adaptive control systems -- Periodicals; Adaptive signal processing -- Periodicals; 629.836
• DOI: 10.1002/acs.3301
• Languages: English
• ISSNs: 0890-6327

Abstract

Summary: We investigate the stochastic stability of replicator dynamics for evolutionary games with multiplicative noises and time delay in this article. We study evolutionary games in infinite well‐mixed populations, among which each individual has two strategies, to cooperate or defect, each time when it is matched up with other individuals to play the two‐strategy game together. This article is concerned with the extension of the well‐known two‐strategy evolutionary games to the stochastic case with adaptive control. We analyze the stochastic replicator dynamics with time delays and provide conservative bounds on the strength of noise and the time delay for the almost sure exponential stability of stochastic systems. Finally, numerical simulations based on triple classical game models (snowdrift game, hunt stag game, and prisoner's dilemma game) are given to illustrate the preceding theoretical results.