Evolutionary Stability of Behavioural Rules

Abstract

I develop the notion of evolutionary stability of behavioural rules in a game-theoretic setting. Each individual chooses a strategy, possibly taking into account the game's history, and the manner in which he chooses his strategy is encapsulated by a behavioural rule. The payoffs obtained by individuals following a particular behavioural rule determine that rule's fitness. A population is stable if whenever some individuals from an incumbent behavioural rule mutate and follow another behavioural rule, the fitness of each incumbent behavioural rule exceeds that of the mutant behavioural rule. I show that any population comprised of more than one behavioural rule is not stable, and present necessary and sufficient conditions for stability of a population comprised of a single behavioural rule.