MATH/MTHE 339: Evolutionary Game Theory Homework Assignment 4
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MATH/MTHE 339: Evolutionary Game Theory
Homework Assignment 4
2022
1. (7 marks total) Consider the following payoff matrix:
Π1 =
2 −1 0 .
a. (6 marks) Analyze the replicator equation for this payoff matrix by finding all of the equilibria and
characterizing their stability by linearizing.
b. (1 marks) Roughly sketch the phase portrait. You do not have to be exact in the placement of equi- libria. Simply show the qualitative nature of the equilibria.
2. (7 marks total) Consider the following payoff matrix:
Π2 =
−3 1 0 .
a. (6 marks) Analyze the replicator equation for this payoff matrix by finding all of the equilibria and
characterizing their stability by linearizing.
b. (1 marks) Roughly sketch the phase portrait. You do not have to be exact in the placement of equi- libria. Simply show the qualitative nature of the equilibria.
3. (7 marks total) Consider the following payoff matrix:
Π3 =
−3 −1 1 .
a. (6 marks) Analyze the replicator equation for this payoff matrix by finding all of the equilibria and
characterizing their stability by linearizing.
b. (1 marks) Roughly sketch the phase portrait. You do not have to be exact in the placement of equi- libria. Simply show the qualitative nature of the equilibria.
4. (4 marks total) Consider the following payoff matrix:
Π4 = ,
with parameter γ for the replicator equation. Draw a bifurcation diagram for γ ∈ [0, 3].
2022-04-23