Transcript The Complexity of Cooperation

Evolving New
Strategies
The Evolution of Strategies in
the Prisoner’s Dilemma
-By Robert Axelrod
Why’s and What’s of
Evolution
Agents are not always fully
aware of there situations.
Instead, they must adapt to
them.
Methods for adapation in
nature are a combination of
natural selection and
mutation.
The Steps in a Model of
Evolution
 Specify the Environment in which
the evolutionary process can
operate.
 A method for simulating genetics.
 A test to discovery whether
strategies diverge or converge in
similar situations.
 Statisical Analysis of the computer
simulation
The Simulated
Environment
An iterated prisoner’s dilemma
of known length.
A determined number of
generations.
 Adaptive agents that play
against eight successful rules of
Axelrod’s tournament.
The Genetic Algorithm
Each Agent has it’s own
‘Chromosome’.
The Strategies are deterministic
and based on a three turn
memory.
64 Corps Genes + 6 Additional
Genes to deal with the start of
the game.
There are 10 to the 21st
combinations of C’s and D’s.
The Genetic Algorithm
Cont’d
An initial random population is
selected and run.
The more successful individuals
are chosen to mate at random.
Crossover and mutation
determine the child’s genes.
The new generation replaces the
old one.
Results
A constant population of twenty
individuals meeting 151 times
with each of the eight rules ~
24,000 moves per generation.
The median adaptive agent was
as successful as the best rule in
Axelrod’s tournament
The adaptive agents act similar
to TFT.
A Surprising Result
In 11 of 50 generations the
Agents learned to exploit
there opponents.
In this case defecting first
payed.
These new strategies are
not robust.
Five Important traits for
each agent
“Don’t Rock the boat (C after
RRR).”
“Be provocable (D after RRS).”
“Acccept an apology (C after
TSR).”
“Forget (C after SRR).”
“Accept a rut (D after PPP).”
Where can we go from
here?
Dock our model with Axelrod’s
as a litmus test for its
usefulness.
Increasingly use our program to
run experiments.
Data analysis and
documentation will be
increasingly important
Some of Axelrod’s Ideas
for Expanding the Model
Adaptive Mutation Rates.
Several vs. Individual
Chromosomes (Coadapation).
Dominant and recessive genes.
Gradual vs. Rapid Evolution.
Population viscosity and mating.
Speciation and ecological
niches.