Evolution of cooperation driven by incremental learning

It has been shown that the details of microscopic rules in structured populations can have a crucial impact on the ultimate outcome in evolutionary games. So alternative formulations of strategies and their revision processes exploring how strategies are actually adopted and spread within the interaction network need to be studied. In the present work, we formulate the strategy update rule as an incremental learning process, wherein knowledge is refreshed according to one's own experience learned from the past (self-learning) and that gained from social interaction (social-learning). More precisely, we propose a continuous version of strategy update rules, by introducing the willingness to cooperate W, to better capture the flexibility of decision making behavior. Importantly, the newly gained knowledge including self-learning and social learning is weighted by the parameter ω, establishing a strategy update rule involving innovative element. Moreover, we quantify the macroscopic features of the emerging patterns to inspect the underlying mechanisms of the evolutionary process using six cluster characteristics. In order to further support our results, we examine the time evolution course for these characteristics. Our results might provide insights for understanding cooperative behaviors and have several important implications for understanding how individuals adjust their strategies under real-life conditions.