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?