Transcript 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
• Riechmann: Genetic algorithm as a game,
itself
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)
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
C
D
C 3,3 0,5
D 5,0 1,1
Figure 1: Payoff Matrix
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
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
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
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
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