I am currently reading 'The Selfish Gene' by Richard Dawkins, which I am sure many here have read. The topic are evolutionary stable strategies (ESS) regarding cooperation.
I apologise for the long question. If you are already familiar with the topic and Dawkins' model of Cheat, Sucker and Grudger: my question is, how can Grudger be an ESS if it could be invaded both by Suckers (because they have no disadvantage against Grudger) and Cheats (because a Cheat minority is unlikely to meet the same Grudger twice, turning Grudger into Sucker effectively)?
Near the end of chapter 10 (p 185 in my version), Dawkins uses a model of birds who clean each other of parasites, therefore helping in survival (as cleaning themselves they cannot reach every spot of their body). He defines three different behaviours for the model:
- Sucker - birds who indiscriminately help and clean other birds
- Cheat - birds who let others help them but never do so themselves
- Grudger - birds who help others and remember who they helped. If the same bird does not help them later (reciprocate), they will not help that bird again.
Claim: Cheat and Grudger are ESS
He claims that both Cheat and Grudger in themselves are ESS - that is, if all birds behave this way, none of the other behaviours can develop because they will be immediately penalised by lower chances of reproducing.
The part that makes sense: Suckers is not an ESS, Cheat is
Sucker is of course not an ESS. If all birds were Suckers, any Cheat that developed would have a huge reproductive advantage and Cheat genes would overtake the population.
Being an ESS makes sense for Cheat. If all birds cheat, nobody will ever be helping each other. A minority of Suckers would be spending all their time helping and not getting anything in return, Cheats have the advantage and Suckers die out again. Grudger would be unlikely to meet a Cheat who they helped before again, so they too will spend all their time helping and die out again.
The part that confuses: Grudger is an ESS?
But Dawkins also claims that Grudger is an ESS, and he seems very confident in that. Now I don't consider myself enough of a smartypants to claim that he's wrong, but I don't understand how Grudger can be an ESS. If all birds behave in this way, and for any reason some Sucker developed - the Sucker would have no disadvantage. All birds would still always be helping each other, so nothing would stop the Suckers from propagating equally well as the Grudgers, invading the gene pool. That's already the ESS broken, but even further, the presence of Suckers would mean that if Cheats came up, they would have a realistic chance of surviving - Grudgers would shun them after having helped once, but if the number of Suckers is large enough, Cheats will have an advantage.
Moreover, back to the initial setting of Grudgers only - if a Cheat developed, he would be unlikely to meet the same Grudger twice, receiving the benefit all the time but never paying the cost. He would have an advantage and spread Cheat genes.
I'm not familiar enough with how these kinds of models are calculated in order to state chances that Cheats will take over completely, but however I think of it Grudger does not seem to be an ESS to me.
Does anyone have an explanation why Dawkins is so sure that it is? Seeing as in nature we do see patterns like Sucker and Grudger all the time, I must be missing something important here.