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No Strategy Can Win in the Repeated Prisoner's Dilemma: Linking Game Theory and Computer Simulations
Julián García1, Matthijs van Veelen2
1Faculty of Information Technology, Monash University, Melbourne, VIC, Australia.
Frontiers in Robotics and AI
|January 27, 2021
Summary
Computer simulations of strategy evolution in games often overlook game theory. Our algorithms demonstrate simulations align with evolutionary game theory, highlighting mutation
Area of Science:
- Evolutionary Game Theory
- Computational Game Theory
- Agent-Based Modeling
Background:
- Computer simulations are common for studying strategy evolution in repeated games.
- These simulations often neglect insights from game theory for analysis and questioning.
- Evolutionary game theory suggests Nash equilibria are unstable due to potential mutants.
Purpose of the Study:
- To reconcile computer simulations of strategy evolution with established game theory.
- To investigate the impact of Nash equilibrium instability on simulation outcomes.
- To explore the influence of mutations and exploration on cooperation levels in simulated populations.
Main Methods:
- Development of algorithms to demonstrate agreement between simulations and game theory.
- Analysis of simulation data in the context of evolutionary game theory principles.
- Examination of strategy dynamics in populations with potentially infinite strategy sets.
Main Results:
- Simulations were shown to align with theoretical predictions from evolutionary game theory.
- The inherent instability of Nash equilibria was confirmed in simulation dynamics.
- Populations were observed to cycle between different equilibria, indicating inescapable dynamics.
- Cognition appeared to have limited influence on the observed cycling dynamics.
Conclusions:
- Simulations can effectively model the cyclical dynamics predicted by evolutionary game theory.
- The role of mutations and exploration is crucial in determining cooperation levels.
- Cognitive factors may play a lesser role in strategy evolution dynamics than previously assumed.
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