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Evolving continuous behaviors in the Iterated Prisoner's Dilemma

P G Harrald¹, D B Fogel

¹Manchester School of Management, UMIST, UK.

|January 1, 1996

Summary

Cooperation can evolve in a complex Iterated Prisoner's Dilemma, but requires a minimum strategy complexity. However, this cooperative outcome is not stable under evolutionary dynamics.

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Area of Science:

Evolutionary computation
Game theory
Artificial intelligence

Background:

The Iterated Prisoner's Dilemma (IPD) is a foundational model in game theory and evolutionary biology.
Traditional IPD assumes discrete strategies (cooperate/defect), limiting realistic applications.

Purpose of the Study:

To investigate the evolution of cooperation in a continuous strategy space variant of the IPD.
To determine the role of strategy complexity in the emergence of cooperation.

Main Methods:

Evolutionary programming simulations were performed on a modified IPD.
Player strategies were modeled using feed-forward perceptrons with a single hidden layer.
Population size and hidden layer complexity were systematically varied.

Main Results:

A minimum level of strategic complexity was found necessary for cooperation to emerge.
Cooperation did not emerge as a stable equilibrium under the simulated evolutionary dynamics.
Increased complexity in player strategies influenced the evolutionary trajectory.

Conclusions:

Complex strategies are essential for cooperation to evolve in this continuous IPD model.
Cooperation is an unstable outcome, suggesting ongoing evolutionary pressures.
The findings highlight the importance of strategy representation in evolutionary game theory simulations.

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