biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...

, the idea of an unbeatable strategy was proposed by

W.D. Hamilton William Donald Hamilton (1 August 1936 – 7 March 2000) was a British evolutionary biologist, recognised as one of the most significant evolutionary theorists of the 20th century. Hamilton became known for his theoretical work expounding a ...

in his 1967 paper on

sex ratio The sex ratio (or gender ratio) is usually defined as the ratio of males to females in a population. As explained by Fisher's principle, for evolutionary reasons this is typically about 1:1 in species which reproduce sexually. Many species d ...

s in ''

Science Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...

''. In this paper Hamilton discusses sex ratios as

strategies Strategy (from Greek στρατηγία ''stratēgia'', "art of troop leader; office of general, command, generalship") is a general plan to achieve one or more long-term or overall goals under conditions of uncertainty. In the sense of the " ar ...

in a game, and cites Verner as using this language in his 1965 paper which "claims to show that, given factors causing fluctuations of the population's primary sex ratio, a 1:1 sex-ratio production proves the best overall genotypic strategy". : "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 game-like 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, be called 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). : " ..But if, on the contrary, players of such a game were motivated to outscore, they would find that

1/4,

is beaten by a higher ratio,

x^*

; 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)^ -x_0

and shows

1/2

to be the unbeatable play." Hamilton (1967). The concept can be traced through

R.A. Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who ...

(1930) to Darwin (1859); see Edwards (1998). Hamilton did not explicitly define the term "unbeatable strategy" or apply the concept beyond the evolution of sex-ratios, but the idea was very influential.

George R. Price George Robert Price (October 6, 1922 – January 6, 1975) was an American population geneticist. Price is often noted for his formulation of the Price equation in 1967. Originally a physical chemist and later a science journalist, he moved ...

generalised the verbal argument, which was then formalised mathematically by

John Maynard Smith John Maynard Smith (6 January 1920 – 19 April 2004) was a British theoretical and mathematical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics un ...

, into the

evolutionarily stable strategy An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) that is ''impermeable'' when adopted by a population in adaptation to a specific environment, that is to say it cannot be displaced by an alternative strategy (or set o ...

(ESS).

References

External links

* http://www.iiasa.ac.at/Publications/Documents/IR-02-019.pdf {{DEFAULTSORT:Unbeatable Strategy Game theory