1 Stag Hunt with Easily Spooked Hares (Schecter/Gintis) Two hunters can kill a s

Question

1 Stag Hunt with Easily Spooked Hares (Schecter/Gintis) Two hunters can kill a stag, with is worth 8. One hunter alone cannot kill a stag. One hunter alone can kil four hares, each worth 1. However, if two hunters go after the hares, the hares will run away and each hul only kill one hare. If two hunters are hunting together, each has two possible strategies, hunt stag (s) or hunt hares (h). The payoffs are as follows: Hunter 2 Hunter4,4 0,4 h4,0 11 1. Use best responses to find the pure strategy Nash equilibria 2. Let ? = (p, 1-P) be a mixed strategy. Use ? and Theorem 8.1 in Chapter 8 of Game Theory in Action to decide which of the pure strategy Nash equilibria correspond to an evolutionarily stable state (show that your results satify or fail to satify the conditions of Theorem 8.1)

Explanation / Answer

1) From given payoffs matrix we see that their is 2 Pure strategy Nash equilibria as (s,s) and (h,h) of Hunter 1 and 2.

2) Let we use mixed strategy t=(p , 1-p) on payoff matrix as

Let calculate firm 1's expected utility from firm 2's mixed strategy

EU1(s) = p*4 + (1-p)*0 = 4p

EU1(h) = p*4 + (1-p)*1 = 4p + 1 - p = 1 + 3p

Let calculate firm 2's expected utility from firm 1's mixed strategy

EU2(s) = q*4 + (1-q)*0 = 4q

EU2(h) = q*4 + (1-q)*1 = 4q + 1 - q = 1 + 3q

In Equilibrium :

EU1(s) = EU1(h)

4p = 1 + 3p

p = 1

and 1-p = 0

Simillarly,

q = 1

and 1-q = 0

Then equilibrium in mixed strategy is as

Probability p 1-p probabiity Hunter1 2 s h q s 4,4 0,4 1-q h 4,0 1,1

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