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Using genetic programming (GP) to solve the Prisoner’s Dilemma is an interesting application of evolutionary algorithms to game theory. The objective would be to evolve strategies that play the Prisoner’s Dilemma and aim to find optimal or near-optimal solutions.
First, let’s recap the Prisoner’s Dilemma:
Two prisoners are given the option to betray each other (defect) or stay silent (cooperate). The possible outcomes are:
- Both prisoners cooperate: Each serves 1 year in prison.
- Both prisoners defect: Each serves 2 years in prison.
- One prisoner cooperates and the other defects: The defector is freed, and the cooperator serves 3 years.
The dilemma is that while it’s best for both to cooperate, individual self-interest leads them to defect.
Using GP to evolve strategies:
Representation: Each individual in the population represents a strategy for playing the Prisoner’s Dilemma. A simple approach is to use a decision tree where the nodes represent past actions of both players, and the leaves decide the next move.
Initialization: Start with a population of random strategies.
Fitness Function: The fitness of a strategy is determined by playing it against other strategies in the population (and possibly some standard strategies like “Always Defect” or “Always Cooperate”). The score from each game contributes to the fitness of the strategy. The total fitness might be the sum of scores from all games.
Selection: Strategies are selected for reproduction based on their fitness, with better-performing strategies more likely to be chosen.
Crossover and Mutation: Produce a new generation of strategies by combining parts of two parent strategies (crossover) and introducing small random changes (mutation).
Evaluation: Play the strategies in the new generation against each other and calculate their fitness.
Termination: Continue the evolution process for a set number of generations or until a certain level of performance is achieved.
Result: At the end of the evolution process, the most fit strategy (or…