Coevolution is considered as an effective means to optimize the conditions for the survival of cooperation. In this work, we propose a coevolution rule between individuals' node weights and aspiration, and then explore how this mechanism affects the evolution of cooperation in the spatial prisoner's dilemma game. We show that there is an optimistic amplitude of node weights that guarantees the survival of cooperation even when temptation to antisocial behavior is relatively large. An explanation is provided from a microscopic point of view by dividing nodes into four different types. What is interesting, our coevolution rule results in spontaneous emergence of cyclic dominance, where defectors with low weight become cooperators by imitating cooperators with high weight.

Understanding the learning dynamics in multiagent systems is an important and challenging task. Past research on multi-agent learning mostly focuses on two-agent settings. In this paper, we consider the scenario in which a population of infinitely many agents apply regret minimization in repeated symmetric games. We propose a new formal model based on the master equation approach in statistical physics to describe the evolutionary dynamics in the agent population. Our model takes the form of a partial differential equation, which describes how the probability distribution of regret evolves over time. Through experiments, we show that our theoretical results are consistent with the agent-based simulation results.

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