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: "In the way in which the success of a chosen sex ratio depends on choices made by the co-parasitizing females, this problem resembles certain problems discussed in the "theory of games." In the foregoing analysis a gamelike element, of a kind, was present and made necessary the use of the word ''unbeatable'' to describe the ratio finally established. This word was applied in just the same sense in which it could be applied to the "minimax" strategy of a zero-sum two-person game. Such a strategy should not, without qualification, becalled optimum because it is not optimum against -although unbeaten by- any strategy differing from itself. This is exactly the case with the "unbeatable" sex ratios referred to." Hamilton (1967).

  • ; the value of x which gives its player the greatest possible advantage over the player playing x_0, is found to be given by the relationship x^---=(2x_0)^{1/2} -x_0 and shows 1/2 to be the unbeatable play." Hamilton (1967).


The concept can be traced through Ronald Fisher (1930) to Darwin (1859); see Edwards (1998). George R. Price generalised the verbal argument, which was then formalised by mathematically by John Maynard Smith , into the Evolutionarily Stable Strategy (ESS). An unbeatable strategy is always an ESS, though an ESS is not necessarily unbeatable, as it may be beaten by large migrations into the population.


REFERENCES




  • http://www.people.fas.harvard.edu/~kojima/unbeatable02.pdf

  • http://www.iiasa.ac.at/Publications/Documents/IR-02-019.pdf