Download Assignment 5

Assignment 5
Due 10/02/2012
1. Find the evolutionary strategies (if any exist!) for one of the following games. All of the games are
symmetric so I’ve written only one payoff for each pair of strategies.
(a)
A
B
A
4
2
B
1
2
A
B
A
5
8
B
2
3
(b)
(c)
A
B
A
7/2
0
B
5
4
A
B
A
−1
1
B
12
0
(d)
(e)
S
D
S
−1/2
3
D
−1
−4
2. Answer both of the following.
(a) Are all Nash equlibria in 2-player, symmetric games necessarily evolutionary stable strategies in
the corresponding evolutionary game? How do you know?
(b) Are all evolutionary stable strategies in 2-player evolutionary games necessarily Nash equlibria in
the corresponding 2-player, symmetric game? How do you know?
3. I think it worthwhile to finish the game that we started in class today. I’ve done most of the leg-work
already, but try deriving the result without looking at your notes. It turns out to be very easy to solve,
but excellent practice for developing your “modelling” skills.
The game is as follows. Three people are playing a guess-a-number game. The winner is the person
who guesses the highest number that no one else guesses. Each player can choose numbers 1 to 3,
inclusive. The game is repeated. What is the mixed strategy Nash equilibrium?
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