Control design to minimize the number of bankrupt players for networked evolutionary games with bankruptcy mechanism

This paper analyzed the strategy optimization problem of networked evolutionary games (NEGs) with bankruptcy mechanism. The main objective was to design a state-feedback control such that the number of bankrupt players is minimized. First, an algebraic expression was formulated for this type of NEGs by the semi-tensor product of matrices, based on which the sets of profiles with different numbers of bankrupt players are defined. Second, a desired profile set in which the number of bankrupt players is no higher than a given value was obtained, and the convergence region of this set was calculated. Third, for any profile in the convergence region of the desired set, we propose a controller design method to minimize the number of bankrupt players. Finally, an example is given to illustrate the validity of our results.