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lecture20 - BioNB 221 Lecture 20 Oct 15 2008 Lecture 20...

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BioNB 221: Lecture 20 Oct. 15, 2008 Page 1 Lecture 20: Game Theory and Evolution of Conflict Professor H. Kern Reeve 1. The mysterious case of the speckled wood butterfly: 2. The Hawk-Dove Game: Hawk Dove Hawk (1/2)(V-C) V Dove 0 V/2 In this payoff matrix , V = value of resource; C = cost of injury. 3. ESS's in the Hawk-Dove Game Dove is an ESS if V/2 > V (never for V > 0!) Hawk is an ESS if (1/2)(V - C) > 0, i.e., V > C What happens if C > V (i.e., injury is very costly)? Neither Hawk nor Dove is an ESS. Selection favors a "mixed" strategy, i.e., individuals should play Hawk with probability P*, Dove with probability 1-P*. But how do we find P*? In a mixed ESS, the average payoffs for the component strategies are equal. That is, P* is such that when two individuals playing the mixed ESS meet each other, the average payoffs for playing Hawk and playing Dove are the same. (This makes sense, because if the average payoff for playing Hawk [for example] were greater than that for playing Dove, then Hawk should be played with higher probability.) Thus, let's set up the equation:
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