The Evolutionary Games
We Play
Psychology 3107
Introduction
Animals tend to behave in ways that
maximize their inclusive fitness
Usually pretty straightforward
But, sometimes we must know what others
are doing before we adopt a strategy
What if your mating call is drowned out by
others’ calls, what to do, ahh what to do…
Fitness and Strategies
In certain cases payoffs, and hence fitness
maximization, depend on what other populations
are doing
When the payoff to one individual depends on
the behaviour of others we cannot use the
principle of fitness maximization until we know:



What the alternatives are
P(encountering alternatives)
Consequences of encounter
Game Theory
Think of it like a game
Each individual’s behaviour is its strategy,
payoffs are in units of fitness
Players produce more players (offspring)
Changes in fitness are directly proportional
to payoffs
An evolutionary Stable Strategy is one
that, when adopted by enough individuals,
maximizes payoff
Pure Strategy
One that cannot be replaced
Food storing
Recover your own seeds (Anderssen and
Krebs, 1978)
If they recovered communally, a selfish
hoarder would replace the communals
damned quckly
Mixed Strategies
Hawks and Doves

Not real hawks or doves, strategies
Always fight, or always give up
Look at the payoffs
Look at the costs
Determine what proportion should be
hawks and should be doves
Hawks and Doves
Say its all Doves
Hawk shows up, wins resource
Spreads genes
Now more hawks
Oh oh, now you are fighting, P(injury) = .5
Now being a dove pays
Either strategy good when rare, bad when
common
Doves and Hawks
V =V alue of resource for winner
W = cost of a wound
T = cost of display (no fighting)
(John Maynard Smith, 1978)
Whoa, I know Kung Fu
Set up a payoff Matrix
Opponent in the contest
Hawk
Dove
Hawk
½(V-W)
V
Payoff
Received
By
Dove
0
½V-T
ESS as easy as 123
If W > V then there can be no pure ESS

In a population of hawks, a small number of
doves do better than hawks
E(dove,hawk) > E(hawk, hawk)
E(dove, hawk) = 0
E(hawk, hawk) = ½(V-W)

W > V, therefore ½(V-W) < 0
Pure Doves don’t do it either
Payoff to Hawk is V
Payoff to doves is less than that

(½W – T)
Hmmm
So, what proportion of hawks and doves
balances it out?
What is theoretical population
biologist to do?
Find the proportion (p) of hawks of hawks
such that the following equation balances:
p ½(V-W) = (1-p) V = p (0) + (1-p) (½V– T)
Simply (?) solve for p
p = (V+2T) / (W+ 2T)
Apply it, sort of
Say V = 10
W = 20
T=3
Opponent in the contest
Hawk
Dove
Hawk
-5
10
Payoff
Received
By
Dove
0
2
Now, sub that back into the formula
P = 16/26 or 8/13
8/13ths of the population, with these payoff
values, must be hawks
The values are not that important really, the
point is that you can determine the point at
which a strategy can coexist with another
strategy as an ESS
Could be percentage of population, or
percentage of time each animal adopts a given
strategy
So?
It is actually
applicable that’s so
Toads looking for
breeding grounds
(Davies and
Hallaway, 1979)
Payoffs determined
Another so
Dungflies
Should a male hang around poo as it gets older?
Conclusions
This is a very brief intro to game theory
This stuff is way powerful
You have to sit and think some about the
payoffs and costs
Dynamic programming models are
becoming more popular