Lecture 13: Game Theory

Game Theory

models in which the optimum strategy is contingent on the frequency of behavior of others. Individuals ‘play’ against each other and “winning” is equated to fitness

Game Theory in Crickets

Two types of crickets: callers (produces signalling sound to attract mates) and satellites (hover around callers and intercept females). Callers have a higher success in mating but a higher risk of predation, while satellites have a lower success in mating but a lower risk of predation → strategies will reach equilibrium

Evolutionary Stable Strategy (ESS)

a set of strategies that, once adopted by a critical proportion of the population, cannot be replaced by other strategies

Nash Equilibrium

a stable state in a game where no player can improve their outcome by changing their own strategy if all other players' strategies remain the same

Origin of an Evolutionary Stable Strategy

each individual consistently plays one of the possible strategists so that the relative proportion of pure strategists in the population remain stable. Then each individual varies its strategy, playing each with a certain frequency.

ESS in Male Side-blotched lizzards

3 genetically determined colour polymorphs that each display a different reproductive strategy with same fitness payoff. The predominant colour fluctuates annually (Orange, then blue, then yellow then back to orange)

payoff matrix

formally states fitness payoffs to individuals playing all possible strategies

Hawks versus Doves

Hawks are aggressive; continue to fight until seriously injured or opponent retreats

Doves show aggressive displays, but always retreat rather than fight

Payoff Matrix Equations (A + B payoff relationship)

Payoff Matrix: A vs. B

	A (Opponent)	B (Opponent)
A	(Resource value - injury cost) / 2	Resource cost (if A wins)
B	0 (if B loses)	(Resource value / 2) - Display cost

• then tally from left to right row for fitness payoff

Payoff Matrix Equations (Proportion of A and B)

• A → p[(resource value - injury cost)/2] + (1-p)[resource value]

• B → p[0] + (1-p)[(resource value / 2) - display cost)

Where p is the proportion of A in a population

Asymmetries in Game Theory Models

1. Resource Hoarding Potential

2. Value of the resource

3. Arbitrary Asymmetries

Resource Hoarding Potential

an animal's inherent ability to win a physical fight if one were to occur

Game Theory Model Asymmetry in Funnel-Web spiders

females engage in territorial battles over productive web sites and employs conditional strategy: if an intruder is larger than the resident, the resident will exhibit aggressive displays but never fight. If the intruder is smaller, then the resident will be aggressive

Winner Effect

where wining a fight increases the probability of future wins

Loser Effect

Where losing a fight decreases the probability of future wins

Game Theory Asymmetry in Resource Value

One player has private information about the resource's value that the other lacks

Game Theory Asymmetry in Bowl and Doily Spider

A virgin female lays 40 eggs after fertilization, after 5 minutes there are 10 unfertilized eggs so the occupying male aggressivley defends against rivals. After 7 minutes there are only 4 unfertilized eggs so the male switches to a dove strategy (aggressive displays but not fighting)

→ shows Asymmetry in resource value

Game Theory: Arbitrary Asymmetries

asymmetries that are not connected to RHP or resource value. Rules or social conventions for setting disputes amoung conspecifics. Eg: prior ownership

Prior Ownership as an Arbitrary Asymmetry in Hamadryas Baboons

In mating: a male is perceived as “owner” of female if allowed prior association. This is respected even if intruding male in dominant.

In feeding: if no prior ownership of item is given dominant wins, if prior access is given the dominant does not challenge

Value of refined game theory models

• enhance understanding of behaviour

• organize empirical findings

• generate testable hypothesis