Evolution of cooperation in the negotiation game with behavioral error
Although the cooperation is vulnerable to invasions of selfish free-riders, cooperation is widely observed in various taxonomic groups. In order to explain maintenance of cooperative interaction, various mechanisms have been proposed. One of such a mechanism is “negotiation” among individuals. It is often observed that organisms choose their own behavior based on their partner’s behavior. In this case, individuals determine their action as a solution after the recursive reciprocal-observation, which may prevent invasions of selfish free-riders. The evolution of cooperation with negotiation process has been theoretically investigated by using “negotiation game,” in which we consider the evolution of a response pattern to the attitude of partners called reaction norm. However, previous studies failed to reveal the general properties of the evolution the reaction norm because the evolutionary stable reaction norm becomes infinite number. In the present study, we try to overcome this difficulty with focusing on a behavioral error. The assumption of error may be sufficiently realistic because a realized behavior of individual could differ from its original decision by noise. We assumed that individuals linearly response to the cooperation level of the partner, and investigated the evolution of the liner reaction norm in the negotiation game with behavioral error.
According to the analysis based on adaptive dynamics, the existence of behavioral error makes number of ESS reaction norm finite, which allow us to investigate the general properties of cooperation level in the negotiation game. In the result of the simulation, we found that the curvature of the benefit function is an important factor for the evolution of reaction norm. When the benefit function is convex (concave), the slope of the reaction norm always becomes positive (negative). By comparing the evolution in the negotiation game to a usual cooperation game without negotiation, we also found that when the benefit function is convex (concave) shape, the cooperation level in the negotiation game is higher (lower) than that in the usual cooperation game. Moreover, oscillation of cooperation level was observed in the negotiation game, while such oscillation never occurs in the usual cooperation game. The large behavioral error prevents the occurrence of such oscillation and makes singular cooperation level more stable. Our results show that the negotiation can be a factor promoting evolution of cooperation depending on the shape of benefit function in the presence of behavioral error.