# Genetic Algorithms and Game Theory - University of Illinois at ...

AI and Robotics

Oct 23, 2013 (4 years and 8 months ago)

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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

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