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We have studied evolutionary ultimatum game with spatially arranged players, who have choice between the two kinds of strategies (named greedy and altruist). The strategies in the ultimatum game here are described by p ( i ) and a ( i ) , that is, the probability of offering i to himself and the accepting probability when receiving i . By using computer simulations with C++ builder, we have provided the dynamics of the greedy and altruistic strategies and found that the proportion evolution of the “greedy” strategy for different initial cases is approximately 60%. Furthermore, the explanations for the interesting phenomenon are presented from different aspects. In addition, we illustrate that the factor of the expectation level (aspiration level) in the updating rule plays an important role in the promotion of altruistic behaviors.

The Dynamics of the Discrete Ultimatum Game and the Role of the Expectation Level