Gradual learning supports cooperation in spatial prisoner's dilemma game

TL;DR

This paper investigates how gradual learning protocols, as opposed to standard or exaggerated imitation, influence cooperation levels in spatial prisoner's dilemma games, finding that gradual learning significantly promotes cooperation.

Contribution

It introduces and analyzes the effects of exaggerated and gradual learning rules on strategy evolution, highlighting the importance of cautious updating in fostering cooperation.

Findings

Gradual learning significantly supports cooperation.

Exaggerated learning has no notable effect on final states.

Gradual learning slows invasion speeds of strategies, especially reducing defector success.

Abstract

According to the standard imitation protocol, a less successful player adopts the strategy of the more successful one faithfully for future success. This is the cornerstone of evolutionary game theory that explores the vitality of competing strategies in different social dilemma situations. In our present work we explore the possible consequences of two slightly modified imitation protocols that are exaggerated and gradual learning rules. In the former case a learner does not only adopt, but also enlarges the strategy change for the hope of a higher income. Similarly, in the latter case a cautious learner does not adopt the alternative behavior precisely, but takes only a smaller step towards the other's strategy during the updating process. Evidently, both scenarios assume that the players' propensity to cooperate may vary gradually between zero (always defect) and one (always cooperate) where these extreme states represent the traditional two-strategy social dilemma. We have observed that while the usage of exaggerated learning has no particular consequence on the final state, but gradual learning can support cooperation significantly. The latter protocol mitigates the invasion speeds of both main strategies, but the decline of successful defector invasion is more significant, hence the biased impact of the modified microscopic rule on invasion processes explains our observations.