The equilibrium where everyone follows “set dial to equilibrium temperature” (i.e. “don’t violate the taboo, and punish taboo violators”) is only a weak Nash equilibrium.
If one person instead follows “set dial to 99” (i.e. “don’t violate the taboo unless someone else does, but don’t punish taboo violators”) then they will do just as well, because the equilibrium temp will still always be 99. That’s enough to show that it’s only a weak Nash equilibrium.
Note that this is also true if an arbitrary number of people deviate to this strategy.
If everyone follows this second strategy, then there’s no enforcement of the taboo, so there’s an active incentive for individuals to set the dial lower.
So a sequence of unilateral changes of strategy can get us to a good equilibrium without anyone having to change to a worse strategy at any point. This makes the fact of it being a (weak) Nash equilibrium not that compelling to me; people don’t seem trapped unless they have some extra laziness/inertia against switching strategies.
But (h/t Noa Nabeshima) you can strengthen the original, bad equilibrium to a strong Nash equilibrium by tweaking the scenario so that people occasionally accidentally set their dials to random values. Now there’s an actual reason to punish taboo violators, because taboo violations can happen even if everyone is following the original strategy.
Correct me if I’m wrong:
The equilibrium where everyone follows “set dial to equilibrium temperature” (i.e. “don’t violate the taboo, and punish taboo violators”) is only a weak Nash equilibrium.
If one person instead follows “set dial to 99” (i.e. “don’t violate the taboo unless someone else does, but don’t punish taboo violators”) then they will do just as well, because the equilibrium temp will still always be 99. That’s enough to show that it’s only a weak Nash equilibrium.
Note that this is also true if an arbitrary number of people deviate to this strategy.
If everyone follows this second strategy, then there’s no enforcement of the taboo, so there’s an active incentive for individuals to set the dial lower.
So a sequence of unilateral changes of strategy can get us to a good equilibrium without anyone having to change to a worse strategy at any point. This makes the fact of it being a (weak) Nash equilibrium not that compelling to me; people don’t seem trapped unless they have some extra laziness/inertia against switching strategies.
But (h/t Noa Nabeshima) you can strengthen the original, bad equilibrium to a strong Nash equilibrium by tweaking the scenario so that people occasionally accidentally set their dials to random values. Now there’s an actual reason to punish taboo violators, because taboo violations can happen even if everyone is following the original strategy.