Incorporating rules for responding into evolutionary games

Abstract

Evolutionary game theory is concerned with the evolutionarily stable outcomes of the process of natural selection. The theory is especially relevant when the fitness of an organism depends on the behaviour of other members of its population. Here we focus on the interaction between two organisms that have a conflict of interest. The standard approach to such two-player games is to assume that each player chooses a single action and that the evolutionarily stable action of each player is the best given the action of its opponent. We argue that, instead, most two-player games should be modelled as involving a series of interactions in which opponents negotiate the final outcome. Thus we should be concerned with evolutionarily stable negotiation rules rather than evolutionarily stable actions. The evolutionarily stable negotiation rule of each player is the best rule given the rule of its opponent. As we show, the action chosen as a result of the negotiation is not the best action given the action of the opponent. This conclusion necessitates a fundamental change in the way that evolutionary games are modelled.

Conflict between parents over care

“…In seeking endpoints, game theoretic models should look for solutions that are both ESSs and continuously stable. interactions between the male and the female, rather than a single decision by each parent, and models should take this into account [12,30].…”

“…One negotiation rule (the best response rule) that has been suggested is for each parent to always adopt the best effort given the current effort of its partner [35]. If a parent followed this rule, it would increase its effort in response to a decrease in effort by its partner, but not by enough to compensate fully [29,30]. Although this rule appears plausible, it is not a stable outcome of evolution: suppose that most members of a population adopted this rule, and consider an individual following a mutant strategy with a low level of effort.…”

“…The result is that, although the young are slightly worse off, the mutant individual is better off overall, because of its reduced effort. Thus, by exploiting the willingness of its partner to compensate, a lazy mutant individual will do better than will other population members, and the mutant strategy will invade [30].…”

“…The female rule will evolve so that it is the best negotiation rule given the male rule, and vice versa [30]. McNamara et al [30] find the pair of negotiation rules that will evolve when individuals differ in quality.…”

“…The female rule will evolve so that it is the best negotiation rule given the male rule, and vice versa [30]. McNamara et al [30] find the pair of negotiation rules that will evolve when individuals differ in quality. Individuals using these rules compensate less strongly than they do under the best response rule when raising their own effort in response to a reduction in the effort of their partner.…”