Stable degree analysis for strategy profiles of evolutionary networked games

Abstract

In this paper, we investigate the stable degree of strategy profile for evolutionary networked games by using the semi-tensor product method, and present a number of new results. First, we propose the concept of k-degree stability for strategy profiles based on a normal evolutionary networked game model. Second, using the semi-tensor product of matrices, we convert the game dynamics with "best imitate" strategy updating rule into an algebraic form. Third, based on the algebraic form of the game, we analyzed the stable degree of strategy profile, and proposed two necessary and sufficient conditions for the k-degree stability of strategy profile. Furthermore, we discuss the computation problem of the transient time within which a disturbed strategy profile can be restored, and also establish an algorithm for the verification of the stable degree of strategy profile. The study of an illustrative example shows that the new results obtained in this paper are very effective.

A survey on applications of semi-tensor product method in engineering

“…On the other hand, STP method has wide applications in the engineering related field. These applications include gene regulation [124,125], power system [126][127][128][129], wireless communication [130][131][132], smart grid [133][134][135][136][137][138][139], finite automata [140][141][142][143][144], information security [145][146][147], vehicle control [148][149][150], indoor thermal comfort [151][152][153][154], fault detection of circuits [155,156], spacecraft [157], epidemic vaccination [158], mobile robot [159]. The aim of this paper is to present a comprehensive survey on these applications.…”

Modeling and analysis of colored petri net based on the semi-tensor product of matrices

“…In [21,22], the semi-tensor product of matrices was applied to finite automata, and the control problem of finite automata was studied. Additionally, the semi-tensor product of matrices can be used in game theory [23][24][25][26], fuzzy control problems [27].…”

Linear dynamic games with polytope strategy sets

“…In the logical dynamical system framework, the STP has been successfully used in various fields, including Boolean control networks [8–15] and internal combustion engines [16, 17]. Recently, the applications of the STP have been extended to game theory and obtained a series of interesting results, including verification of finite potential game [18]; the space structure of non‐cooperative finite games [19]; modelling, analysis and control of networked evolutionary games (NEG) [20]; and the stable degree of strategy profile for NEG [21], etc.…”