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Genetic Algorithms and Game Theory

Genetic Algorithms and Game Theory. Douglas King Department of General Engineering University of Illinois at Urbana-Champaign December 4, 2003. Overview. What is a genetic algorithm? Axelrod: Using the genetic algorithm to develop successful strategies in the iterated prisoners dilemma

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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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