Replicator-Mutator Dynamics with Three Strategies

payoffs

a

11

2

a

12

1

a

13

1

a

21

1

a

22

1

a

23

2

a

31

1

a

32

0

a

33

3

mutation rates

μ

0.0001

m

1

1

m

2

1

m

3

1

critical points

x 1	x 2	x 3
0.333333	0.333333	0.333333
0.000100013	0.49995	0.49995
0.999867	0.0000666733	0.0000666733
0.0000500038	0.000100005	0.99985
0.666528	0.000166675	0.333306

λ 1	λ 2
0.333167	0.333167
0.4998	-0.499733
-0.9997	-0.999567
-1.99933	-0.999583
0.666341	-0.333113

This Demonstration shows the phase portrait in an equilateral triangle of the replicator-mutator dynamics with three strategies. The parameters

a

ij

≥0

denote the payoff that an

i

-strategist obtains in an interaction with a

j

-strategist. The parameter

μ

denotes the total fraction of mutants or entrants in the population. The parameters

m

i

≥0

denote the weights given by mutants to strategy

i

, so

m

i



3

∑

k=1

m

k

is the fraction of mutants that adopt strategy

i

. This Demonstration also calculates the critical points of the system and their corresponding eigenvalues, which are helpful in assessing the dynamic stability of the critical point.