![]() Such games with only two pure strategies are sometimes adequate when studying what Roughgarden calls the evolutionary tier. Noncooperative game theory is often explained to students of evolutionary biology using simple illustrative games like the Prisoners’ Dilemma, the Battle of the Sexes and the Hawk-Dove Game (which game theorists traditionally call Chicken). But even in economic applications, it is not always straightforward to relate the parameters of the model to an environment within which it is to be applied. Rubinstein’s bargaining model is perhaps the most promising starting point for a theory of bargaining in biology. There is no schism between cooperative game theory and noncooperative game theory to match the divide that Roughgarden sees between her own followers and the supposedly homophobic neo-Spencerians championed by Richard Dawkins. Orthodox bargaining theory is entirely compatible with the kind of methodological individualism that orthodox evolutionary biology takes for granted. When the theory of repeated games can be applied, the folk theorem implies that this requirement does not limit the attainable levels of fitness to any great extent. Implicit agreements among animals need to be self-policing, if they are to be honoured in practice. Roughgarden’s (2009) book will be used as a source of errors of interpretation that need to be avoided. A fuller introduction appears as chapters 16 and 17 in my book Playing for Real ( Binmore, 2007). This paper seeks to provide an introduction for biologists to the economic theory of bargaining. However, such an approach will fail if the basic theory has not been fully understood, as in Roughgarden’s (2009) study of bargaining between mated pairs in his recent Genial Gene. Each new species will require a new modification of the basic theory. The suggestion is not that bargaining models developed for use in economics can be taken down from the shelf and used straight from the package. Game theorists must shoulder some of the blame for failing to communicate their ideas adequately to the wider scientific community, but there seems no good reason for biologists to continue to reinvent game-theoretical wheels, especially when the reinvented wheels are sometimes square. Both ideas are similarly absent from Axelrod’s (1984) Evolution of Cooperation. Maynard Smith’s (1982) path-breaking Evolution and the Theory of Games never mentions the idea of a Nash equilibrium, even though Nash equilibrium is the fundamental concept in game theory. ![]() ![]() For example, Trivers (1971) was unaware of the folk theorem of repeated game theory when he reinvented the concept of reciprocal altruism, which had been around for 20 years or more at the time he wrote. However, it will be a pity if a full development of the approach has to wait until evolutionary theorists reinvent ideas that are standard in economic theory, as has been the case in previous biological applications of game theory. As one of the architects of the economic theory of bargaining ( Binmore et al., 1982 Binmore & Dasgupta, 1987), I am delighted at this initiative, which I believe to be an important development in evolutionary biology. ![]() (1999), Johnstone & Hinde (2006) and Periera et al. Such a bargaining game necessarily sits on top of the kind of evolutionary game that is a staple of the biological literature.Ī number of biologists have explored the possibility of using this approach to model the nurturing behaviour of animals from species in which parents jointly care for their offspring: for example, McNamara et al. The joint behaviour of mated pairs of animals who cooperate in raising their young can be seen as the successful resolution of what economists would call a bargaining game, in which the two parents negotiate over who contributes how much to their joint venture.
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