The first talk that I ever gave, to the Animal Behaviour Society conference in Snowbird, Utah, 2006.

1. Evolution’s strategies
Genetic algorithms and game theory models
Steven Hamblin and Peter L. Hurd
Department of Psychology, University of Alberta

2. What I’ll be discussing…
1.
Extensive form games and
alternatives to ESS.
2.
Solving game theory models using
genetic algorithms.

3. ESS - Evolutionarily stable strategy
! An
uninvadable strategy: if every
member of a population plays that one
strategy, then no mutant can invade.
(Maynard Smith, 1982)
! An
ESS is a mathematical description of
a population equilibrium.

4. Extensive form game - usually
Payoff matrix (normal form)
better for biological games.

5. A common - all information sets reached with
Pervasive problem with more complex games
is strategies that are not pervasive.
non-zero probability.
Here, it never pays for player 1 to choose the
last branch, so player 2’s choice at that branch
is moot.

6. ES set
! A
set of strategies that would,
individually, be ESSs except that they
all invade each other. (Thomas, 1985;
Cressman, 1992)

7. The ESS formalism is not enough for
games with realistic complexity.

8. Solving them another way…

9. An alternative tool: Genetic algorithms.
!
Algorithms that simulate evolution to solve
optimization problems.
!
Heuristic search as opposed to analytical
solutions.
!
Scales more effectively to larger games
(greater biological realism).

10. The e85 model (Enquist, 1985)
If we add another state variable or signal, we
can end up with over ten million strategies!
324 pure strategies with a
pervasive ESS.

11. Strategies split into two halves: when ego
strong and when ego weak.
Graph shows strategy evolution over time.
18 colours for each half: 18 * 18 = 324 total
0
500

12. As the mutation rate goes higher, it becomes harder and
harder (or impossible) for the GA to find the ESS.

13. Pink/Red - A previously unknown ES set
The ESS goes extinct very quickly.
solution to the e85 game.
0
500

14. Results
! A
set of strategies whose end move is
always “attack”, is a previously
unknown ES set solution to the e85
game.
! The
ES set has much greater attractive
power than the ESS.

15. Take home message…
!
ESS is useful intuitively, but
limited practically.
!
Most games with temporal
sequence / underlying state / etc.,
won’t have an ESS.
!
Even more useful solution tools
(e.g. ES sets) are too complicated
to calculate for larger, more
realistic games.
!
Genetic algorithms are a sensible
choice to solve complex game
theory models.

16. Acknowledgements
!
Pete Hurd, for … well, just about everything.
!
Eldridge Adams, for valuable discussion on the
inability of GAs to find the e85 ESS.
!
The members of the Hurd lab for feedback and
advice.
!
Brandy Williams, for design input.