The logic of divisively asymmetric contests : respect for ownership and the desperado effect

It is current orthodoxy in biological game theory that in animal contests with easily recognized asymmetries between the contestants, an asymmetry will be used to settle the dispute. Here it is argued that, if the winning of contests plays a major part in gaining reproductive success, an individual will not be selected to respect an asymmetry which will place it always in the losing role. Asymmetries that create consistent losers of this sort are termed divisive asymmetries. Divisive asymmetries cannot be used to settle important contests in an evolutionarily stable way because the consistent losers will have no incentive to respect them. WHEN BOURGEOIS MAY NOT BE AN ESS One of the most widely accepted successes of the Evolutionarily Stable Strategy (ESS; Maynard Smith & Price 1973; Maynard Smith 1982) approach to our understanding of animal behaviour is the explanation it provides of the observation that in fights between territory holders and intruders, the territory holders generally win. The explanation is that ownership is used as an asymmetry to settle the dispute in favour of the owner. The main result from ESS theory supporting this explanation is that even in the unlikely case that ownership was uncorrelated with fighting ability and with the value of the territory to an individual, ownership could still be used as an arbitrary asymmetry to settle disputes in favour of the owner. How much more likely it is, then, that ownership will be used to settle the dispute without real fighting when it is, in fact, correlated with fighting ability or with the value of the territory to an individual. This is the argument advanced by Maynard Smith & Parker (1976). My main purpose here is to argue that in an important class of cases, which can be roughly characterized as those involving long term territories, ownership cannot be used as an arbitrary asymmetry, or even, to an extent, as a correlated asymmetry. The argument will apply more generally to all ‘divisive asymmetries’, a term I shall define later. So far as territorial disputes are concerned, this will leave us with the simpler argument that if owners do win fights against intruders, then it is because the owners are bigger and better fighters. Various comments that follow naturally will be made after the argument has been given. Maynard Smith & Parker (1976) model a territorial dispute as an asymmetric hawk-dove game. That is, each contestant knows its role (owner or intruder), and has a choice of two strategies called H and D. The sense in which a contestant knows its role is that it is allowed to make its choice of strategy depend on its role, permitting for example a strategy that Maynard Smith & Parker call ‘Bourgeois’: if owner play H, if intruder play D. They showed that Bourgeois is an ESS when V, the value of winning the fight, is less than C, the cost of losing the fight. The standard payoffs for the hawkdove game are represented as: to H, ( V C ) / 2 against H, and V against D; to D. 0 against H, and V/2 against D. While the logic of Maynard Smith & Parker’s argument is not disputed here. they neglect an interesting property of V and C that is highly relevant to the likelihood of the condition V < C being fulfilled. The benefits of winning and costs of losing are likely to depend on the fighting rules adopted by the population, for the following reasons. In a population that respects ownership, the winner of a fight is likely to retain the territory for a long time: while in a population in which territories change hands frequently, the winner of a fight is likely to lose it again soon. The value of winning is therefore higher in a population that