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

grandgoatAI and Robotics

Oct 23, 2013 (3 years and 9 months ago)

75 views

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