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In his book "The Selfish Gene", Richard Dawkins says that retaliator emerges as an evolutionary stable strategy. But I think dove is also a kind of retaliator and so if dove increases, the hawks and others can exploit them.

Is retaliator an ESS? If not, which strategy is ESS?


  • hawk : They always fight hard and retreat only when injured.

  • doves : They merely threaten in a dignified way and never hurt anyone.

If a hawk fights a dove, dove runs away. If dove meets dove they go on posturing until one of them is tired and retreats. If a hawk meets hawk they fight until someone gets seriously injured or dies.

  • retaliators : A retaliator plays dove at the beginning of every fight. If opponent attacks, he attacks , if opponent behave like a dove he behaves like a dove. When 2 retaliators meet they behave like doves.

  • bully : A bully behave like a hawk until someone hits back. Then, he runs away.

  • prober retaliator : He is like a retaliator but he tries a brief escalation of the contest. He is hawk like if opponent doesn't strike back. If opponent strikes back he behave like a dove. If he is attacked he retaliates.

The pay offs: 50 for winning, 0 for losing, -100 for being seriously injured. and -10 for wasting time in a long contest.

Source: The Selfish Gene

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closed as too broad by fileunderwater, Chris, Nandor Poka, cagliari2005, WYSIWYG Apr 16 at 11:25

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Why would you label the dove a kind of retaliator? – fileunderwater Oct 25 '13 at 8:05
Could you please describe the kind of payoff matrix in play and the definition of the different strategies (dove, hawk, retaliator)? – Remi.b Oct 25 '13 at 8:20
@fileunderwater As retaliators play like doves at the beginning of every fight and 2 doves do exactly the same thing as 2 retaliators will do when they meet. – biogirl Oct 25 '13 at 8:22
@remi.b Sure. Will edit the question---- – biogirl Oct 25 '13 at 8:23
@biogirl But that is the whole point of the retaliator - that they behave as dove initially, but then retaliates. Doves don't retaliate (they always back down if challanged) so I dont see the point of labelling them as "...a kind of retaliator". – fileunderwater Oct 25 '13 at 9:04

2 Answers 2

A strategy is an ESS against a certain strategy. That is, a strategy is not an ESS in itself. In principle, any pure strategy can be destabilized depending on the other strategies in the game.

Retaliators are an ESS against Hawks. The reason is that the payoff of Retaliators against other Retaliators is higher than the payoff of a rare Hawk in a population of Retaliators.

Retaliators are not an ESS agaist Doves though. This is because the payoff of a Retaliator against a Dove is the same as the payoff of a Retaliator against another Retaliator (i.e., Doves and Retaliators have the same fitness). For example, drift could increase the frequency of Doves in a population dominated by Retaliators. Depending on the increase of Doves by drift, a rare Hawk could then invade (depending on your payoff matrix).

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This is incorrect, for a strategy to be an ESS it must be stable against any alternate strategy. – augurar Jan 6 at 4:04
@augurar I don't think so. If you open a book on evolutionary game theory, it's a common place to say that an strategy A is a stable strategy against B but not against C. It's true that books/articles say that an ESS cannot be bettered by another strategy, but it's assumed that you're talking about the strategies that are available in your model -- as opposed to any possible strategy (e.g., in the typical Hawk-Dove game you're only considering two strategies). – falsum Jan 6 at 15:40

I think Dawkins answers this in the book as well.

The point was that most strategies are not stable because the "random" introduction/mutation/evolution of some alternate strategies will disrupt a population of the first strategy.

The example was a group of doves being invaded by a single hawk (the conspiracy of doves). Because the hawk does relatively better (by winning every conflict against a dove), than even after generations of entirely doves, the random addition of a hawk (say by mutation) will take hold because the hawk always wins against a dove. Whatever feature/gene that created a hawk in the pool of doves will be passed to some offspring.

If I remember correctly, the only stable case was prober-retaliator, since all others get invaded by someone else.

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Yeah he has answered it in the newer editions.... – biogirl Jan 17 at 6:08

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