I don’t like jeff’s version because it goes without saying that if you can administer a truth serum then you can get efficiency and budget balance (and individual rationality doesn’t even make sense anymore).

When you say “the double auction is not efficient” what you are really saying is “when the players play a Bayesian Nash Equilibrium of a double auction, they will shade their bids and the result is inefficient.” This is equivalent to saying that the mechanism I described (which is the direct-revelation counterpart of the double auction) is not incentive compatible.

To repeat, the Myerson Satterthwaite theorem says: Any direct revelation mechanism which is IR, IC, and BB is necessarily inefficient. Dropping any of the three (IR, IC, BB) enables an efficient direct revelation mechanism.

@Economix: One problem with that is there could be idiosyncratic reasons justifying deviations from the market average — renovations, for example.

@Dave: Good point, yes, I’m not sure how much the story changes in a repeated setting.

@David Reiley: I love that credit card story (and hate credit card companies!). I may have been too glib in my comparison of Coase and Myerson-Satterthwaite. Thanks for the clarifications!

@Ben McCann: Smart! I had a similar thought involving a conditionally-refundable deposit with a moving company, ie, prove to the landlord that if they gouge us on rent then the moving expenses will become a sunk cost.

@jeff: No, your mechanism (a sealed double auction) is not efficient. I agree completely with your statement of the revelation principle though. That’s actually what I meant by “IC is WLOG”: By the revelation principle we can, WLOG, consider only IC mechanisms. Thus, IC is not needed in M-S. With or without an IC restriction, you can’t have BB+IR+EFF.

I think you need to clarify what you mean about incentive compatibility. There are direct mechanisms that satisfy budget-balance, efficiency, and individual rationality. Here is one. If the seller’s cost is less than the buyer’s value then they trade at a price equal to the midpoint. (any price between value and cost will do.)

Of course that mechanism is not incentive compatible becuase either party would have an incentive to misreport their value/cost in order to get a more favorable price. So incentive compatibility is required for the Myerson-Satterthwaite theorem.

On the revelation principle. It does not say that incentive compatibility is without loss of generality. It says “if there is any mechanism at all that achieves your ends (under the solution concept of Bayesian Nash equilibrium) then there is a direct mechanism that is incentive compatible and achieves your ends.” The practical implication of this is that whatever impossibility result you obtain by restricting to direct, incentive-compatible mechanisms, obtains also in the more general class of mechanisms (under the solution concept of BNE.)

It’s clearly inefficient to have this happen. Her existing credit-card company knows how valuable a customer she is, more so that competing companies who might issue her a new card. In particular, her existing company knows her complete history of on-time payments, whereas other card companies might be scared to make her a new loan right now when many people seem at risk of defaulting on debt. She did end up finding a new card, but they didn’t give her a big enough credit limit to transfer the old debt. In the end it was OK for her – she has her old debt at the old price, and she has a new card that lets her make payments when she wants to make a new credit-card payment. But there was a lot of hassle in the meantime. She had to shop for a new card, she had to remember to convert her recurring payments to the new card, etc. And the previous credit-card company lost her as a good customer who would continue to make payments with them.

This is just one example of many recent claims of card companies “gouging” their existing customers by jacking up the price, just as Dan and his family experienced with their landlord.

I found it a bit puzzling that such things would start happening so much more frequently this year. I mean, if jacking up rates on existing customers is a profitable price-discrimination strategy, why didn’t they jack up to 24% on existing customers a year or two ago? The answer seems to be that competition in the credit-card market has gotten softer during the financial crisis. Usually, the threat that an existing customer would switch cards would be high enough that a company couldn’t jack up rates too much without losing the customer. But during the current credit crunch, it’s much harder for customers to switch, because so few new loans are being approved. This gives firms more market power over their existing customers than they usually do. Or so I hypothesize (thanks to Robin Lee for clarifying my thinking on this).

As an aside, Coase never assumed that the parties would have perfect information about each other’s values for trading with each other. He wrote in the days before noncooperative game theory was used much, and he just made a reasonable assumption that if people had clear property rights and no transaction costs), then they would reach an efficient outcome. After his work, Rubinstein and Stahl showed that if two parties bargain over a publicly known amount of surplus in an alternating-offers game, and both agents are rational players, we should expect an efficient trade to happen right away. But Myerson and Satterthwaite showed that such efficiency couldn’t happen in the presence of private information about how much surplus might be generated for each party.

(Coase contrasted property rights and low transaction costs with the opposite situation, where it’s too costly to trade. For example, think about millions of individual car drivers trying to compensate thousands of asthmatics for the reductions in air quality that they suffer as a result of the car exhaust. Conducting those billions of individual transactions is infeasible, so it doesn’t happen, and we end up with an inefficiently high level of pollution. Cap-and-trade systems are a policy attempt to assign clear property rights for pollution – or its absence – and thereby get more efficient levels of pollution.)

You alluded to one reason why the story differs a bit from the theory: your landlord is worried about his reputation in a repeated game. The theory assumes a one-shot auction where the universe ends thereafter, right?

What about contracts that are contingent on something like citywide vacancy rates? Such a contract would protect landlords from underpaying tenants in periods of high demand, protect tenants from overpaying in buyers’ markets, and protect both sides from unnecessary moving costs and unwanted periods of vacancy.