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Evolution and the Theory of Games (Smith, 1982, 2012)

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John Maynard Smith

JLJ - game theory yes, but the work could be subtitled 'an analysis of mating strategies of insects and animals'. Show me a contest in nature and I will show you a developed strategy to win at the contest.

p.1 This book is about a method of modelling evolution, rather than about any specific problem to which the method can be applied.

p.10 This chapter aims to make clear the assumptions lying behind evolutionary game theory. I will be surprised if it is fully successful.

p.10 In this chapter, I introduce the concept of an 'evolutionary stable strategy', or ESS. A 'strategy' is a behavioral phenotype, i.e. it is a specification of what an individual will do in any situation in which it may find itself.

p.110 A number of authors have pointed out that organs used in fighting are displayed prior to fighting, and that such displays may settle contests without escalation.

p.176 It often turns out that to find the ESS, or to find an optimal strategy, requires formidable mathematical efforts.

p.177 The optimal growth pattern for a plant depends on what nearby plants are doing.

p.178 The work of Axelrod (1981) has shown how fruitful it can be to look for an ESS when repeated contests occur between the same two opponents.

p.178 In this book I have considered only games which can be represented in matrix form, and games whose strategy set can be defined by one or more continuous variables. More complex games can be represented in extended form, as a tree whose nodes are choice points for one or other contestant. It may prove helpful to use such a representation in an evolutionary context.