Lecture 13: Game Theory

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11 Terms

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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

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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

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Evolutionary Stable Strategy (ESS)

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

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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

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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.

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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)

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payoff matrix

formally states fitness payoffs to individuals playing all possible strategies

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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

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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

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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

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