Evolutionary game dynamics with three strategies in finite populations
نویسندگان
چکیده
We propose a model for evolutionary game dynamics with three strategies A, B and C in the framework of Moran process in finite populations. The model can be described as a stochastic process which can be numerically computed from a system of linear equations. Furthermore, to capture the feature of the evolutionary process, we define two essential variables, the global and the local fixation probability. If the global fixation probability of strategy A exceeds the neutral fixation probability, the selection favors A replacing B or C no matter what the initial ratio of B to C is. Similarly, if the local fixation probability of A exceeds the neutral one, the selection favors A replacing B or C only in some appropriate initial ratios of B to C. Besides, using our model, the famous game with AllC, AllD and TFT is analyzed. Meanwhile, we find that a single individual TFT could invade the entire population under proper conditions.
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