Exercises

 

1. Determine the evolution of the following game under replicator dynamics.

 

 

S

H

S

5,5

0,2

H

2,0

2,2

 

 

2. Determine the evolution of the following game under replicator dynamics.

 

 

A

B

A

3,3

1,4

B

4,1

0,0

 

3. Determine the evolution of Chicken under replicator dynamics.

 

4.

Determine the evolution of the following game under replicator dynamics:

 

 

A

B

A

1,1

1,3

B

3,1

2,2

 

Hint.  Before you launch into calculations, ask yourself whether the one-shot game above is strong dominance solvable.  Would you think that strongly dominated strategies survive replicator dynamics?

 

5.

Determine the evolution of the following game under replicator dynamics:

 

 

A

B

A

3,3

0,2

B

2,0

2,2

 

 

6. Consider the generic game in a finite but large population with low selection coefficient

 

 

A

B

A

a

b

B

c

d

 

Suppose A and B are best replies to themselves. 

a. What must be the relations between a, b, c, and d for for ρA > 1/N to obtain?

b.  What must be that relation be for ρA > ρB to obtain?

 

 

7. Consider the following Stag Hunt:

 

 

S

H

S

3

0

H

2

1

 

a game in which each strategy is a best reply to itself.  If played in a finite but large population with low selection coefficient, does ρS > ρH obtain?

 

 

 

Answers