Emergence of a New Attracting Set by a Mixed Strategy in Game Dynamics

抄録

Game dynamics with a mixed strategy player is studied. A new attracting set emerges under a certain condition by introducing a mixed strategy into a system with a pure strategies system. In terms of a replicator system, introducing a mixed strategy means to increase the number of rows and columns of the interaction matrix by 1 without changing its rank size. As a result, a system has a neutral dimension and a new attracting set emerges on the center manifold of a fixed point. A possible scenario of evolution via a mixed strategy is briefly discussed.