I’m a fair way out of my comfortable depth here, so take this with a larger grain of salt than usual. And I make no claims whatsoever about originality – for all I know this could have been covered fifteen times over in the relevant literature. (As might most things I write.) But I thought it was interesting enough to write up.

The question at issue concerns some points that came up because I happened to be simultaneously reading Michael Strevens’s work on explanation and idealisation (not online) alongside John Sutton’s book on models in economics. I might post something later about how one of Sutton’s cases appears to raise a difficulty for Strevens’s theory, but let’s start on a friendlier note: one of the cases he discusses seems really good news for Strevens’s theory.

We start with the biased auction game – one I’ll call __Bias__. (This game is discussed in detail by Sutton.)

bq. There are two players – Wise and Unwise. An amount of money __v__ is picked from [0,1] at random and placed in an envelope. Wise is told how much money is in the envelope, and Unwise is not. The two players are then invited to bid on the envelope. This will be a ‘single-shot’ auction – each player gets to make one bid, and the higher bid wins. Neither player must bid, and there is no reserve price. What does/should each player do?

The Nash equilibrium for __Bias__ is a little surprising. Wise should bid __v__/2, and Unwise should bid an amount chosen at random from [0,{1/2}]. Wise’s expected gain is, as you can tell, __v__/2, and Unwise’s expected gain is 0. Still, if Unwise does not bid the game cannot go into equilibrium, because then Wise can bid an arbitrarily small amount. So she must bid, even though this has no expected benefit for her.

Now assume that an instance of __Bias__ is played, with each player knowing they will not play again, and Wise and Unwise do just as expected. (Assume we are shown not just Unwise’s bid, but her procedure for generating the bid.) We ask:

bq. Why did Unwise bid?

Allegedly explanatory answer:

bq. Because the only Nash equilibrium for the game includes a bid by her.

Is this a good explanation? I’d say, as it stands, no.

Is this a causal explanation? Well, no. If Unwise did not bid, then Wise could have bid an arbitrarily low amount, then Unwise count have made an expected profit by bidding. So there’s a chain of reasoning that leads to Unwise bidding. But it isn’t a __causal__ explanation unless we are told this is what Unwise thought, and that simply isn’t in evidence.

Is this a unifying explanation? Not as it stands, but it easily could be. Many aspects of game behaviour can be unified under the assumption that the players select options that make Nash equilibria possible. But that doesn’t seem to make it a good explanation, unless we have specific evidence that players were motivated by a desire to move towards Nash equilibria.

__Prima facie__ this looks like bad news for unificationist theories of explanation. But turning that into a full objection might take actual, er, research about what actual unificationists say, which has never been TAR’s strongest feature.

Just in case it isn’t obvious, note that the question asked here is not __Why did Unwise maximise her expected utility?__ I think Bayesian answers to that question are easy. The question is why she chose one particular utility maximising strategy (bidding with the bid value chosen probabilistically) rather than not bid, which has just as high an expected utility.

(I should have mentioned when I first wrote this up that the ideas here owe quite a bit to comments made in my philosophy of economics seminar, especially by Alyssa Ney.)