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6 - Mixed strategies – I. A classification of mechanisms

Published online by Cambridge University Press:  05 June 2012

John Maynard Smith
Affiliation:
University of Sussex
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Summary

One of the clearest predictions of evolutionary game theory is that, in symmetric games, mixed ESS's are often to be expected whenever the potential costs of a contest are large compared to the advantages of winning. Is this expectation borne out? Equally important, what must we know about any particular case before it can reasonably be interpreted as a mixed ESS? These questions are by no means easy to answer, in particular because there are a number of different ways in which the processes of genetic evolution and individual learning can interact in producing stable mixed strategies.

In this chapter, I discuss, with the aid of concrete examples, some of the different ways in which a population may come to show variable behaviour. This discussion leads up to a classification of the mechanisms which underlie such behaviour; the classification is given in Table 10 on p. 78.

The first distinction which must be made is between a mixed strategy, in which the payoffs to the different actions are equal, and a pure strategy of the form ‘In situation 1, do A; in situation 2, do B’, in which some individuals are forced to make the best of a bad job. The distinction is best explained by an example. Rohwer (1977) has shown that in winter flocks of the Harris sparrow, individuals vary in the colour of their plumage from dark to pale, and that this variation is correlated with aggressiveness and dominance rank within flocks, the darker birds being more dominant.

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Publisher: Cambridge University Press
Print publication year: 1982

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