Heterogeneous negotiation undermines cooperation in prisoner’s dilemma game

Contradictory findings have been reached on the effect of heterogeneous social ties and heterogeneous payoffs fostering cooperation, in which the former is positive while the latter is negative, due to the neglect of a common fact that both social ties and payoffs may be strongly impacted by individuals’ negotiation status. Thus, we here examine how the heterogeneity of negotiation status influences cooperation by acting jointly on both aspects. To this end, we design a two-stage model. In the first stage, the network dynamics and payoff structure are defined by a heterogeneous negotiation edge game, in which the share of payoff redistribution is associated with the negotiation status. The cooperative strategy dynamics of the second stage are contingent on the network and payoff structure established in the first. The Nash Equilibrium of the heterogeneous negotiation edge game reveals how the network and payoff are changed by the heterogeneous negotiation status. More specifically, the stronger the negotiation status of the relationship destroyer, the more payoffs are distributed to cooperators. Investing excessive negotiation status with the relationship destroyer, however, potentially disconnect links between cooperators. Furthermore, the simulation shows that the efficiency of fostering cooperation reduces as heterogeneity in negotiation status grows greater. In other words, we demonstrate equal negotiation status is the most effective for promoting cooperation. We claim that this work has proposed a potentially persuasive approach to explain why contradictory results were produced by relative studies and it contributes to a further understanding of the relationship between heterogeneity and cooperation.