Mixed Strategy Nash Equilibria

In mixed strategy Nash equilibria, players randomize to make opponents indifferent. Replicator dynamics in evolutionary game theory tracks strategy frequencies, converging to NE or cycling in rock-paper-scissors.

Payoff Matrix (Row player)

a=3

b=0

c=5

d=1

a (C,C)3

b (C,D)0

c (D,C)5

d (D,D)1

Nash Equilibrium & Dynamics

Computing...

Indifference condition:
EU_C(p*) = EU_D(p*)
p* = (d−b)/((a−c)+(d−b))

Replicator:
ṗ = p(1−p)[f_C−f_D]

RPS: neutrally stable
cycle → mixed NE center