I think that evidential equilibria are equivalent to a much simpler property.
If (a,b) is a joint strategy such that for each a′≠a there exists b′ such that U(a′,b′)≤U(a,b), then (a,b) is an evidential equilibrium. (Construct the probability distributions which assign δ mass to each (a′,b′) and the rest to (a,b), and let δ→0.) And the converse is trivial too.
Yeah, it seems pretty likely that the definition I gave is wrong. Here’s an alternative:
A totally mixed evidential equilibrium must (a) assign nonzero probability to each outcome and (b) have each player maximize evidential expected utility. An evidential equilibrium is a totally mixed evidential equilibrium or a limit of them.
I’m pretty sure you can still have mutual cooperation on the prisoner’s dilemma, by iteratively changing probabilities assigned to C/C C/D D/C D/D so that players are indifferent between C and D in each totally mixed equilibrium.
EDIT: this one also seems wrong. It might be possible to create something similar to trembling hand perfect equilibria, where we have a sequence of perturbed games with people maximizing evidential utility on each perturbed game.
I think that evidential equilibria are equivalent to a much simpler property.
If (a,b) is a joint strategy such that for each a′≠a there exists b′ such that U(a′,b′)≤U(a,b), then (a,b) is an evidential equilibrium. (Construct the probability distributions which assign δ mass to each (a′,b′) and the rest to (a,b), and let δ→0.) And the converse is trivial too.
Am I missing something here?
Yeah, it seems pretty likely that the definition I gave is wrong. Here’s an alternative:
A totally mixed evidential equilibrium must (a) assign nonzero probability to each outcome and (b) have each player maximize evidential expected utility. An evidential equilibrium is a totally mixed evidential equilibrium or a limit of them.
I’m pretty sure you can still have mutual cooperation on the prisoner’s dilemma, by iteratively changing probabilities assigned to C/C C/D D/C D/D so that players are indifferent between C and D in each totally mixed equilibrium.
EDIT: this one also seems wrong. It might be possible to create something similar to trembling hand perfect equilibria, where we have a sequence of perturbed games with people maximizing evidential utility on each perturbed game.