Bilateral negotiation facilitates stable coexistence of cooperation with defection in Prisoner's Dilemma game

Abstract

We explore the effect of bilateral negotiation, a common means to resolve conflicts, on the stable coexistence of cooperation with defection, a phenomenon that occurs frequently in nature and human society but lacks a scientific explanation so far. To model how individuals negotiate, we define two negotiable strategies: the negotiable cooperation strategy and the negotiable defection strategy. By investigating the replicator dynamics of the Prisoner's Dilemma game with these negotiable strategies in infinite populations, cooperators and defectors may coexist stably only in a bilaterally-negotiating Prisoner's Dilemma game that includes all negotiable strategies. Moreover, we define the defection temptation as individuals' willingness to gamble for higher payoffs in a game and show that bilateral negotiation can diminish the defection temptation. Importantly, the bilaterally-negotiating Prisoner's Dilemma game's defection temptation being positive is the necessary and sufficient condition for stable coexistence, implying that bilateral negotiation can help cooperators coexist with defectors even when defection is tempting in the current game. In the stable coexistence equilibrium, the frequency of negotiable cooperators increases with their relative negotiation ability.