An optimal strategy to solve the Prisoner's Dilemma

Area of Science:

• Evolutionary biology
• Game theory
• Theoretical ecology

Background:

• Cooperation is crucial for evolution but seemingly contradicts natural selection's focus on selfish competition.
• Explaining the origin of cooperation under natural selection, particularly in the Prisoner's Dilemma (PD), remains a significant challenge.

Purpose of the Study:

• To introduce a novel model, the Optimal Replicator Equation (ORE), extending the Replicator Equation (RE).
• To demonstrate how this ORE model can explain the emergence of cooperation in the Prisoner's Dilemma.

Main Methods:

• Developed an extension of the Replicator Equation (RE) to the Optimal Replicator Equation (ORE).
• Incorporated the concept of competing populations alongside individual-level selection.
• Applied the ORE to the basic Prisoner's Dilemma (PD) model.

Main Results:

• The ORE model provides a simple, natural rule for the emergence of cooperation.
• Cooperation can arise from selfishness when the societal reward is sufficiently attractive.
• Contrary to prevailing notions, selfish individuals can spontaneously cooperate under specific conditions.

Conclusions:

• The Optimal Replicator Equation (ORE) offers a new framework for understanding cooperation's evolution.
• Selfishness itself can drive cooperation if the benefits of social participation are high enough.
• This finding challenges traditional views on the evolution of cooperation in competitive environments.