Weighted Nash equilibrium of incomplete-profile networked evolutionary games with multiple payoffs

This paper investigates the existence and convergence of weighted Nash equilibrium for incomplete-profile networked evolutionary games with multiple payoffs. First, the incomplete-profile networked evolutionary game under probabilistic myopic best response adjustment rule is transformed into an algebraic form based on the semi-tensor product of matrices. Second, a method for calculating weighted Nash equilibrium is presented, and the relationship between weighted Nash equilibrium and positive-probability fixed point is derived. Furthermore, a criterion is provided to verify whether the profiles in the feasible profile set can converge to the set of weighted Nash equilibriums with probability one. Finally, an illustrative example is given to support the new results obtained in this paper.