Zero-Determinant Strategies in Winner Takes All Game

A player taking zero-determinant (ZD) strategies could enforce a linear relationship between his payoff and opponents’ payoff, thereby control the total excepted payoff of opponents. On the other hand, the winner-take-all (WTA) behaviors are universal in society. This paper focuses on the evolution dynamics of ZD strategies in WTA game, where we explore how the focused player controls the sum of the opponent’s payoff under the dynamic rule of WTA. Numerical simulations also illustrate the effect of parameters on total payoff.