Imitate or innovate: competition of strategy updating attitudes in spatial social dilemma games

TL;DR

This paper investigates how imitation and innovation strategies compete in spatial social dilemma games, revealing complex invasion dynamics and phase transitions influenced by costs and game types.

Contribution

It introduces a model allowing simultaneous competition between imitation and innovation attitudes, analyzing their effects across different social dilemma scenarios.

Findings

Best response dominates without additional cost in snow-drift games.

Imitation can invade when costs are added, showing complex transition dynamics.

In stag-hunt games, imitation is generally more successful, leading to cyclic dominance.

Abstract

Evolution is based on the assumption that competing players update their strategies to increase their individual payoffs. However, while the applied updating method can be different, most of previous works proposed uniform models where players use identical way to revise their strategies. In this work we explore how imitation-based or learning attitude and innovation-based or myopic best response attitude compete for space in a complex model where both attitudes are available. In the absence of additional cost the best response trait practically dominates the whole snow-drift game parameter space which is in agreement with the average payoff difference of basic models. When additional cost is involved then the imitation attitude can gradually invade the whole parameter space but this transition happens in a highly nontrivial way. However, the role of competing attitudes is reversed in the stag-hunt parameter space where imitation is more successful in general. Interestingly, a four-state solution can be observed for the latter game which is a consequence of an emerging cyclic dominance between possible states. These phenomena can be understood by analyzing the microscopic invasion processes, which reveals the unequal propagation velocities of strategies and attitudes.