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

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  • Hashimoto Koh
    Department of Complexity Science and Engineering, The Graduate School of Frontier Sciences, University of Tokyo, 7-3-1 Hongo, Bunkyou-ku,Tokyo 113-8656
  • Ikegami Takashi
    Department of General Systems Sciences, The Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8904

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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.

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