game theory explains perplexing evolutionary stable strategy erin n. bodine math 188: social choice...

Game Theory Explains Perplexing Evolutionary

Stable Strategy

Erin N. Bodine

Math 188: Social Choice & Decision Making 22 – April - 2003

Side Blotch Lizards (Uta stanburiana)

Observations of Morph Frequency and Fitness

Male Type Years of Highest Frequency

blue/less aggressive 1991, 1995

orange/aggressive 1992

yellow/sneaker 1993-94

YearFitness

Orange Blue Yellow

1991 4.73 1.00 1.61

1992 1.28 1.00 1.45

1994 0.90 1.26 1.00

Morph FrequencySinervo and Lively find a cycle in which

morph has the highest frequency.

Morph FitnessSinervo and Lively find that the cycle of

morph frequency relates to the fitness of each male type.

Relative Morph Fitness

Rock-Paper-Scissors

R S P

r 0 1 -1

s -1 0 1

p 1 -1 0

Game Matrix for Rock-Paper-Scissors

Payoffs shown are for player I

The model of rock-paper-scissors typically used by game theorists.

1 = win

0 = draw

-1 = loss

for player I

Let nature randomly pick two side-blotched lizards to inhabit the same territory for mating. Depending on what male morph they are, the lizard with the greater fitness in that territory will play out like a game of rock-paper-scissors.