Strategy regulation of networked snowdrift games based on incentive mechanism

Abstract This paper investigates the strategy regulation problem of networked snowdrift games (SGs) with incentive mechanism and presents some new results. First, the dynamics of the networked SGs with periodic incentives are converted into an algebraic form using semi‐tensor product of matrices, and a periodic switching system is constructed to describe the dynamics of this kind of games. Second, the target profiles under which the total payoff of all players is not less than a given threshold are calculated, and a method to determine all the initial profiles that can converge to these target profiles under periodic incentives is given. Moreover, the range of incentive values for both optimal and ineffective incentives is obtained when each player has the same number of neighbors. Third, a state feedback switching scheme is proposed, which ensures that the total payoff of the game can meet the threshold condition under a finite number of incentives, thereby reducing the incentive cost. Finally, an example is given to validate the effectiveness of our theoretical results.