I think there may also be a Nash equilibrium with a mix of all 4 Bots, for a fairly small band of possible epsilon values.
d = 1 − 3e
f = 1⁄2
c = e
p = 2e − 1⁄2,
( ¼ < e < 1⁄3)
I haven’t proved this is a Nash equilibrium vs any modal agent, maybe you can.
This is unstable but I expect an evolution sim would obtain an oscillating pattern similar to the c,f,p equilibrium you find. In fact, when e = 1⁄3 this new equilibrium is the same as your original one.
Expected utility is 1+2e and so is less good than c,f,p for allowed epsilon values.
Very interesting.
I think there may also be a Nash equilibrium with a mix of all 4 Bots, for a fairly small band of possible epsilon values.
d = 1 − 3e
f = 1⁄2
c = e
p = 2e − 1⁄2,
( ¼ < e < 1⁄3)
I haven’t proved this is a Nash equilibrium vs any modal agent, maybe you can.
This is unstable but I expect an evolution sim would obtain an oscillating pattern similar to the c,f,p equilibrium you find. In fact, when e = 1⁄3 this new equilibrium is the same as your original one.
Expected utility is 1+2e and so is less good than c,f,p for allowed epsilon values.