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Evolution is based on the assumption that competing players update theirstrategies to increase their individual payoffs. However, while the appliedupdating method can be different, most of previous works proposed uniformmodels where players use identical way to revise their strategies. In this workwe explore how imitation-based or learning attitude and innovation-based ormyopic best response attitude compete for space in a complex model where bothattitudes are available. In the absence of additional cost the best responsetrait practically dominates the whole snow-drift game parameter space which isin agreement with the average payoff difference of basic models. Whenadditional cost is involved then the imitation attitude can gradually invadethe whole parameter space but this transition happens in a highly nontrivialway. However, the role of competing attitudes is reversed in the stag-huntparameter space where imitation is more successful in general. Interestingly, afour-state solution can be observed for the latter game which is a consequenceof an emerging cyclic dominance between possible states. These phenomena can beunderstood by analyzing the microscopic invasion processes, which reveals theunequal propagation velocities of strategies and attitudes.

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