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yonski

Member

Registered: 2005-12-14

Posts: 67

Evolutionary Game Theory question

1. The problem statement, all variables and given/known data

Quite a long intro to the question so I thought it easier to include it as an image:

2. The attempt at a solution

I can do Q2.3 and get the payoff matrix given when V=4 and C=6.

For Q2.4a I get

.

For Q2.4b I normalize the payoff matrix to get

Now comes the problems.

For an ESS we must have

     (*)

By using the normalized matrix we can rewrite these as

.

Let x = (h,d,b) be our interior ESS, then by (*) we have

2d - 0.5b = 0.5h + d    and    h - b = 0.5h + d .

The first of these can be rearranged to give h=2d-b while the second can be rearranged to give h=2d+2b. Clearly these can only both be satisfied when b=0. But this contradicts the fact that x = (h,d,b) is an interior ESS. Hence there can be no interior ESS's.

Now that seemed correct to me, but it doesn't tie-in with Q2.4c. This question claims that the only ESS is the pure strategy B. By considering the H-D subgame I get an ESS at (2/3,1/3,0).

Assuming the question is written correctly, where am I going wrong?

Thanks for any help!!

Last edited by yonski (2010-01-06 00:22:51)

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Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."