Modeling and optimization for networked evolutionary games with player exit mechanism: Semi-tensor product of matrices method

摘要

This study investigates a class of networked evolutionary games (NEGs) with player exit mechanisms through the matrices semi-tensor product (STP) method for the first time. In these NEGs, the behavior of players changing strategies at the same time is similar to cellular automata. Firstly, the player's exit is identified as a "virtual" strategy. This strategy will be chosen by players whose payoff is below a threshold and will not be changed. Based on this identification, a new strategy updating rule is proposed. Secondly, by using the method of STP, the NEGs with player exit mechanisms are formulated as an iterative matrix equation. Furthermore, a control sequence is designed to minimize the number of exiting players by analyzing the structure of the iterative matrix. Finally, the validity of our new results is illustrated by an example of the opinion evolution.

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