Game theory in biology: 50 years and onwards

Abstract

Game theory in biology gained prominence 50 years ago, when Maynard Smith & Price formulated the concept of an evolutionarily stable strategy (ESS). Their aim was to explain why conflicts between animals of the same species usually are of a ‘limited war’ type, not causing serious injury. They emphasized that game theory is an alternative to previous ideas about group selection, which were used by ethologists to explain limited aggression. Subsequently, the ESS concept was applied to many phenomena with frequency dependence in the evolutionary success of strategies, including sex allocation, alternative mating types, contest behaviour and signalling, cooperation, and parental care. Both the analyses of signalling and cooperation were inspired by similar problems in economics and attracted much attention in biology. Here we give a perspective on which of the ambitions in the field have been achieved, with a focus on contest behaviour and cooperation. We evaluate whether the game-theoretical study of the evolution of cooperation has measured up to expectations in explaining the behaviour of non-human animals. We also point to potentially fruitful directions for the field, and emphasize the importance of incorporating realistic behavioural mechanisms into models. This article is part of the theme issue ‘Half a century of evolutionary games: a synthesis of theory, application and future directions’.

Half a century of evolutionary games: a synthesis of theory, application and future directions

“…Published 50 years ago, ‘The logic of animal conflict’ by John Maynard Smith & George Price [ 4 ] is the paper that is typically considered the ‘birth’ of evolutionary game theory (though there were strong precedents, especially in the field of sex ratio theory [ 5 ]). Leimar & McNamara [ 6 ] and Grodwohl & Parker [ 7 ] provide a comprehensive discussion of the historic value of Maynard Smith & Price [ 4 ]. The article of Maynard Smith and Price was largely motivated by the prevalence of ‘limited war’ conflicts in nature.…”

“…Why do fights in nature not more commonly escalate far enough to result in serious injury or death? The computer simulations in the original work of Maynard Smith & Price [ 4 ] were later summarized and simplified into a simple toy model, called the Hawk-Dove game (see [ 6 ]). This game describes the interactions of two strategies in a population of players.…”

“…The ESS is analogous to (but slightly stricter than) a Nash equilibrium ([ 10 ] and box 1 in [ 6 ]). In the words of John Maynard Smith, an ESS (here denoted I ) ‘must have the property that, if almost all members of the population adopt I , then the fitness of these typical members is greater than that of any possible mutant; otherwise, the mutant could invade the population, and I would not be stable’ ([ 2 , p. 14]).…”

“…The ESS criterion tells us that once the population is at the ESS, other strategies cannot invade, but it says nothing about getting there in the first place, as noted by Eshel & Motro [ 14 ] (see also [ 15 – 17 ]). To ensure convergence towards the ESS, we also need the convergence stability criterion (eqn 5 in [ 11 ], box 1 in [ 6 ]). A less commonly used but related criterion is that of the neighbourhood invader strategy (NIS) [ 18 ].…”

“…Evolutionary game theory has come a long way since it was first hinted at in models of sex allocation [ 5 ] and since it was elevated to its status as a central part of evolutionary theory by Maynard Smith & Price [ 4 ] (see [ 6 , 7 ]). It has become an essential tool in the evolutionary modeller's toolkit [ 34 ] and has been tightly linked with a range of theoretical concepts and methods [ 11 ].…”