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Genetic Algorithms and Game Theory

This overview examines the intersection of genetic algorithms and game theory, particularly in the context of the Iterated Prisoner's Dilemma (IPD). Genetic algorithms, inspired by evolutionary theory, maintain a population of solutions that evolve over generations using selection, mutation, and crossover. The work discusses Axelrod's findings on successful strategies like TIT-FOR-TAT, emphasizing traits such as niceness, vengefulness, and forgiveness. Riechmann further analyzes genetic algorithms as evolutionary games, exploring the dynamics of agent interactions and the pursuit of Nash equilibrium in strategic scenarios.

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Genetic Algorithms and Game Theory

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  1. Genetic Algorithms and Game Theory Douglas King Department of General Engineering University of Illinois at Urbana-Champaign December 4, 2003

  2. Overview • What is a genetic algorithm? • Axelrod: Using the genetic algorithm to develop successful strategies in the iterated prisoners dilemma • Riechmann: Genetic algorithm as a game, itself

  3. What is a Genetic Algorithm? • Search/Optimization method inspired by genetic/evolutionary theory • Maintains a collection (population) of solutions rather than just one • These solutions (strategies) are represented as strings of bits (chromosomes) • Population evolves using three genetic operators: • Selection: “Survival of the fittest” • Mutation: Random bit-flip (probabilistic) • Crossover: Combine two chromosomes (probabilistic)

  4. Axelrod: Iterated Prisoner’s Dilemma (IPD) • Equilibrium when both defect, but both will do better if they cooperate • Background: Axelrod’s tournaments • TIT-FOR-TAT wins both tournaments • Desirable strategy characteristics: • Niceness • Vengefulness • Forgiveness Figure 1: Payoff Matrix

  5. Axelrod’s GA Approach • Strategies have three-turn memory • Strategies coded as strings of 70 bits • 64 for the possible three-turn combinations • 6 for the initial conditions • Fitness determined by performance against “Kingmakers” from second tournament • Population size of 20 • Experiments run for 50 generations

  6. GA Experiment Results • GA evolves TIT-FOR-TAT-like behavior over time • Niceness: Continue to cooperate after three rounds of mutual cooperation • Vengefulness: Defect when opponent breaks a sequence of mutual cooperation • Forgiveness: Cooperate when opponent appears to “apologize” for defection

  7. Some Concerns • Axelrod: Would these GA-strategies do as well in a different environment? • Is GA population size too small? • Note: Chromosome can only represent a small subset of strategies • Memory increases chromosome size exponentially • Nevertheless, these results show promise

  8. Riechmann’s Analysis of the GA • Genetic algorithm as an evolutionary game • Many agents who interact with each other • Fitness based on how well agents play the game • More advanced conditions… • Population as a group of agents trying to achieve Nash equilibrium • Agents play against all other agents • HOWEVER: Population does not represent every strategy

  9. Summary • The field of genetic algorithms is closely related to the field of game theory • Applications: Axelrod • Theoretical: Riechmann • Further examination of the links between these fields could provide a greater understanding

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