This is a simulation of particular situation described in the book The Selfish Gene by Richard Dawkins

From the "Selfish Gene" by Richard Dawkins

Suppose a species of bird is parasitized by a particularly nasty kind of tick which carries a dangerous disease. It is very important that these ticks shouldbe removed as soon as possible. Normally an individual bird can pull off itsowns ticks when preening itself. There is one place, however-the top of the head-which it cannot reach with its own bill. The solution to the problem quicklyoccurs to any human. An individual may not be able to reach his own head,but nothing is easier than for a friend to do it for him. Later, when the friendis parasitized himself, the good deed can be paid back. Mutual grooming is infact very common in both birds and mammals.This makes immediate intuitive sense. Anybody with conscious foresight cansee that it is sensible to enter into mutual back-scratching arrangements. But we have learnt to beware of what seems intuitively sensible. The gene has noforesight. Can the theory of selfish genes account for mutual back-scratching, or ’reciprocal altruism’, where there is a delay between good deed and repayment? Williams briefly discussed the problem in his 1966 book, to which I have alreadyreferred. He concluded, as had Darwin, that delayed reciprocal altruism canevolve in species that are capable of recognizing and remembering each other asindividuals. Trivers, in 1971, took the matter further. When he wrote, he didnot have available to him Maynard Smith’s concept of the evolutionarily stablestrategy. If he had, my guess is that he would have made use of it, for it providesa natural way to express his ideas. His reference to the ’Prisoner’s Dilemma’-afavourite puzzle in game theory- shows that he was already thinking along thesame lines. Suppose B has a parasite on the top of his head. A pulls it off him. Later, thetime comes when A has a parasite on his head. He naturally seeks out B in order that B may pay back his good deed. B simply turns up his nose and walks off. Bis a cheat, an individual who accepts the benefit of other individuals’ altruism,but who does not pay it back, or who pays it back insufficiently. Cheats do betterthan indiscriminate altruists because they gain the benefits without paying the costs. To be sure, the cost of grooming another individual’s head seems smallcompared with the benefit of having a dangerous parasite removed, but it is notnegligible. Some valuable energy and time has to be spent.Let the population consist of individuals who adopt one of two strategies.As in Maynard Smith’s analyses, we are not talking about conscious strategies, but about unconscious behaviour programs laid down by genes. Call the two strategies Sucker and Cheat. Suckers groom anybody who needs it, indiscrim-inately. Cheats accept altruism from suckers, but they never groom anybodyelse, not even somebody who has previously groomed them. As in the case of1 the hawks and doves, we arbitrarily assign pay-off points. It does not matterwhat the exact values are, so long as the benefit of being groomed exceeds the cost of grooming. If the incidence of parasites is high, any individual sucker in apopulation of suckers can reckon on being groomed about as often as he grooms.The average pay-off for a sucker among suckers is therefore positive. They all doquite nicely in fact, and the word sucker seems inappropriate. But now supposea cheat arises in the population. Being the only cheat, he can count on beinggroomed by everybody else, but he pays nothing in return. His average pay-offis better than the average for a sucker.Cheat genes will therefore start to spread through the population. Suckergenes will soon be driven to extinction. This is because, no matter what theratio in the population, cheats will always do better than suckers. For instance,consider the case when the population consists of 50 per cent suckers and 50 percent cheats. The average pay-off for both suckers and cheats will be less thanthat for any individual in a population of 100 per cent suckers. But still, cheatswill be doing better than suckers because they are getting all the benefits-suchas they are-and paying nothing back. When the proportion of cheats reaches90 per cent, the average pay-off for all individuals will be very low: many ofboth types may by now be dying of the infection carried by the ticks. But stillthe cheats will be doing better than the suckers. Even if the whole populationdeclines toward extinction, there will never be any time when suckers do betterthan cheats. Therefore, as long as we consider only these two strategies, nothingcan stop the extinction of the suckers and, very probably, the extinction of thewhole population too.But now, suppose there is a third strategy called Grudger. Grudgers groomstrangers and individuals who have previously groomed them. However, if anyindividual cheats them, they remember the incident and bear a grudge: theyrefuse to groom that individual in the future. In a population of grudgers andsuckers it is impossible to tell which is which. Both types behave altruisticallytowards everybody else, and both earn an equal and high average pay-off. Ina population consisting largely of cheats, a single grudger would not be verysuccessful. He would expend a great deal of energy grooming most of the indi-viduals he met- for it would take time for him to build up grudges against allof them. On the other hand, nobody would groom him in return. If grudgersare rare in comparison with cheats, the grudger gene will go extinct. Once thegrudgers manage to build up in numbers so that they reach a critical propor-tion, however, their chance of meeting each other becomes sufficiently great tooff-set their wasted effort in grooming cheats. When this critical proportion isreached they will start to average a higher pay- off than cheats, and the cheatswill be driven at an accelerating rate towards extinction. When the cheats arenearly extinct their rate of decline will become slower, and they may survive asa minority for quite a long time. This is because for any one rare cheat there isonly a small chance of his encountering the same grudger twice: therefore theproportion of individuals in the population who bear a grudge against any givencheat will be small...............