Robust Consensus of Networked Evolutionary Games with Attackers and Forbidden Profiles †

Abstract

Using the algebraic state space representation, this paper studies the robust consensus of networked evolutionary games (NEGs) with attackers and forbidden profiles. Firstly, an algebraic form is established for NEGs with attackers and forbidden profiles. Secondly, based on the algebraic form, a necessary and sufficient condition is presented for the robust constrained reachability of NEGs. Thirdly, a series of robust reachable sets is constructed by using the robust constrained reachability, based on which a constructive procedure is proposed to design state feedback controls for the robust consensus of NEGs with attackers and forbidden profiles. Finally, an illustrative example is given to show that the main results are effective.

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“…Liu et al applied the evolutionary game theory to analyze the stability for pool selection dynamics by investigating the evolutionarily stable strategy [30]. In [31], Li et al investigated the robust constrained reachability of networked evolutionary game (NEG) which is effective in dealing with attackers and forbidden profiles. They established a constructive procedure for the robust consensus of NEGs based on algebraic representation.…”

Optimal Control of Networked Evolutionary Games With Bankruptcy Risk

“…Using this new technique, one can convert the dynamics of an NEG into a discrete-time dynamic system, which establishes a bridge between NEGs and classic control theory. Up to now, the STP method has been successfully applied to NEGs, and many essential results have been presented [21]- [25].…”