I came across this old post from Katja Grace where she provides an argument for smoking bans based on game theory. The basic story is that people like conformity, and there is a coordination problem that the government can fix:

Imagine everyone is doing A. Everyone likes doing B more than doing A, but not as much as they like conformity. There would be a huge gain to a coordinated shift to B, but nobody moves there alone. In some such situations those involved arrange coordination, but often it is impossible. If there are many equilibria like this, and no means to move to better ones, intervention by someone with the power to force a coordinated move could be a great thing.

She provides an example where everyone goes to the same crappy bar because that’s where everyone goes. If any individual person, in her example Roger, decides to go to a better bar, they are worse off since they prefer being around people. But if everyone went to a better bar, they would all be better off than the status quo. Here is the  normal form game she uses to model the situation:

Payoffs for Roger in choosing  a nightclub

Roger
Southpac Elsewhere
Everyone else Southpac 2 1
Elsewhere 0 3

In this game, Southpac is the crappy bar. If Roger, or any individual, goes elsewhere when anyone else is still at Soutpac, their payoff goes from 2 to a 1, so he is worse off. If everyone goes somewhere else though, then the payoff to Roger and everyone else is 3, so they are all better off.

She uses this game to argue that the government could sometimes make everyone better off, for instance in the event of a smoking ban. But I think this doesn’t work as a justification for smoking bans or any bans that attempt to fix coordination problems like this.

The failure of this model is obvious if you consider that once everyone is in the higher payoff equilibrium, there is no incentive to diverge, and the status quo becomes the dominant strategy for everyone. In her example, this means that once everyone goes elsewhere, they never go back to Southpac.

This means that a temporary smoking would suffice to fix the coordination problem. Anything more than that is unnecessary, and it runs the risk that this model is incorrect and you are holding people in a lower payout equilibrium. Thus this model can never justify permanent bans like we see.

This model also offers an easy empirical test which I think intuition suggests it would fail. If you enacted a temporary smoking ban and then removed it, would bars and restaurants revert to smoking or would they stay nonsmoking? If Katja is correct, they should stay nonsmoking. I would bet by and large though this would not be the case.