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Apology and forgiveness evolve to resolve failures in cooperative agreements - PubMed

  • ️Thu Jan 01 2015

Apology and forgiveness evolve to resolve failures in cooperative agreements

Luis A Martinez-Vaquero et al. Sci Rep. 2015.

Abstract

Making agreements on how to behave has been shown to be an evolutionarily viable strategy in one-shot social dilemmas. However, in many situations agreements aim to establish long-term mutually beneficial interactions. Our analytical and numerical results reveal for the first time under which conditions revenge, apology and forgiveness can evolve and deal with mistakes within ongoing agreements in the context of the Iterated Prisoners Dilemma. We show that, when the agreement fails, participants prefer to take revenge by defecting in the subsisting encounters. Incorporating costly apology and forgiveness reveals that, even when mistakes are frequent, there exists a sincerity threshold for which mistakes will not lead to the destruction of the agreement, inducing even higher levels of cooperation. In short, even when to err is human, revenge, apology and forgiveness are evolutionarily viable strategies which play an important role in inducing cooperation in repeated dilemmas.

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Conflict of interest statement

The authors declare no competing financial interests.

Figures

Figure 1
Figure 1

Success of commitments and revenge after commitments break. Stationary distribution of the most dominant strategies (proposers that cooperate within the commitment) relative to the stationary distribution of the pure defectors as a function of noise for PP, NP, PN and NN scenarios separately (a) and together (b). Different lines correspond to different Sout. We assumed ω = 0.9, b/c = 2, ε = 0.25, and δ = 4.

Figure 2
Figure 2

Commitments increase the level of cooperation. Levels of cooperation (a), defection (b) and non-playing (c) for the dominant strategies (proposers that cooperate within the commitment), as a function of the noise for the different scenarios. The black lines correspond to the situation where commitments cannot be made, serving as a baseline for the other approaches. We assumed ω = 0.9, b/c = 2, ε = 0.25, and δ = 4.

Figure 3
Figure 3

Forgiveness is evolutionary viable if apology is sincere. Stationary distribution of the main strategies with respect to the stationary distribution of the pure defectors as a function of the apology cost for the PP scenario and α = 0.01 (left) and α = 0.1 (right). Vertical dashed lines mark the values of c and δ. We assumed ω = 0.9, b/c = 2 (with c = 1), ε = 0.25, and δ = 4.

Figure 4
Figure 4

Sincere apology increases the level of cooperation. Levels of cooperation (a), defection (b) and non-playing (c) for the main strategies (proposers that cooperate within the commitment) as a function of the apology cost for the different scenarios. Vertical dashed lines mark the values of c and δ. We assumed ω = 0.9, b/c = 2, α = 0.1, ε = 0.25, and δ = 4.

Figure 5
Figure 5

Thresholds for conditional forgiveness. Stationary distribution of cooperative proposers as a function of the cost of their apologies γ and the threshold τγ they require to forgive a co-player for the PP scenario. We assumed ω = 0.9, ε = 0.25 and δ = 4.

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