Month: October 2007

Win the Nobel Prize in Economics.  That’s funny, because this is precisely the kind of work which is going out of style in the broader profession.  These guys are smart, smart, smart, and Hurwicz is probably the best known of the three.  They are all high-powered theorists, doing incentives, mechanism design, and social choice theory.  None of them are easy to explain to your grandmother. 

Here is the scientific overview.

No doubt mechanism design, and the general problem of inducing truth-telling, will be with us forever.  But how practical are these general results?  Or have the theorists simply provided us with cautionary notes and left the real applications to the context-specific world of practice?  Did these guys get at the real reasons why we don’t organize the entire economy as a second-price auction?

Part of me thinks: "Hey, let’s say Natasha wants Yana to tell her the truth about when she will clean her room.  This stuff isn’t useful!"

Another part of me thinks: "It is most important to get theory right.  These guys are brilliant.  Only the philistines demand that all scientific contributions have immediate applications."

Some of you might argue: "These guys have already had a big impact on real world auctions and incentive schemes."  In terms of the induced improvement in human welfare, I find that a difficult case to make.  The important progress has come from recognizing much simpler truths about incentives.

Ok, Grandma may still have some difficulty but in honor of today’s Nobelists, Hurwicz, Maskin and Myerson let’s give it a go.  Suppose that you are selling a rare painting for which you want to raise the maximum revenue.  There are two potential buyers, Tyler, who values the painting at $100,000, and Alex who values it at $20,000.  The problem would be simple if you knew this information – you would then set the price at $99,999 and Tyler would buy maximizing your revenue.  But how much Tyler and Alex value the painting is their own private information.  How then should sell the painting?

One possibility that springs quickly to mind is an auction.  In a standard English open-cry auction Alex and Tyler will bid for the painting and the bids will keep rising until Alex is forced to drop out at $20,001.  Thus the auction earns you $20,001.  Not bad but is this the maximum revenue possible?  Remember that Tyler values the painting at $100,000 so you could be leaving a lot of money on the table.

What else can you do?  Well, how about an auction with a reserve price, say $50,000 – think of a reserve price as a secret bidder who calls in his bids on the phone.  A reserve price of $50,000 works well in this case as Tyler will pay $50,001.  But note that you just got lucky, if Tyler had valued the good at $30,000 you would have earned nothing at all.  Thus you would like to know whether a reserve is always optimal and how to set it.  (Riley and Samuelson, and much more generally Myerson both show that a reserve price is always optimal and how to set it).

But why stop at a reserve price?  How about a reserve price and an entry fee?  But why stop at reserve prices and entry fees?  You can add any kind of requirement to the auction that you want but will these requirements help you to raise revenue?  Lets boil the problem down to its essence.  Think about an auction as a mechanism – bidders put information into the mechanism, their bids, and the mechanism tells them the outcome.  (Hurwicz was the first to really start thinking about mechanisms in these very general terms.)

You want to design the mechanism to achieve a certain outcome.  The mechanism can be as complicated as you want but it must satisfy certain conditions.  First, the bidders must participate voluntarily – you can’t boil them in oil – so there is a participation constraint.  At the end of the day the bidders must expect to be at least as well off as if they did not play the mechanism game (at least on average).

Second, there is an incentive compatability constraint.  You don’t know how much Alex and Tyler truly value the painting so suppose that Tyler mimics whatever Alex does – Tyler can do this since he values the painting at least as much as Alex does.  It follows that whatever outcome the mechanism assigns to Alex, Tyler must get at least as much.  This is a significant constraint because it means that if you want Tyler to do something different than Alex, and you do, you want Tyler to bid more, then you must give Tyler something in return.  Thus, even in the optimal mechanism you, the seller, are not going to get everything.  Tyler is going to walk away with some surplus.

We still haven’t solved for optimal mechanism, however.  And here is where the magic comes.  Not magic as in something wonderful but magic as in hand-waving.  Maskin and Myerson proved something very useful about mechanisms with these types of constraints.  It turns out that if you follow the constraints then you can restrict attention to mechanisms in which Tyler and Alex always tell the truth about their values, this is called the revelation principle.  (In a sense, this is obvious for imagine that we find the optimal mechanism given that Tyler and Alex submit whatever bids/information they want.  Then you tell Tyler and Alex – next time why don’t you tell the truth about your values and we promise to give you exactly the outcome that we would have given you under the previous mechanism.)

In the case of auctions the direct mechanism is well known, a second price auction.  In a second price auction the high bidder wins but pays the second highest-bid.  In this auction it makes sense for every bidder to bid his true value – see if you can work out why – and it turns out that as the revelation principle says, revenues in this direct auction are the same as in say a regular English auction (under certain conditions, of course).

Ok, I have gone on for a while.  Here’s the bottom line.  The basic set-up of agents with private information submitting "bids" which are then fed into a mechanism resulting in outcomes is very general.  How to raise taxes, regulate a monopolist, fund a public good (here’s my own contribution to mechanism design), allocate organs, assign interns to hospitals, split common costs, allocate electricity across a grid – all can be thought of as mechanism design problems.   The tools that Hurwicz, Maskin and Myerson developed and their methods of paying attention to participation and incentive compatability constraints and using the revelation principle helps us to design, at least in principle, the best solutions to all of these problems.

Here is Wikipedia on Hurwicz.  He is the granddaddy of the group, and the Nobel Committee sums it up nicely:

The seminal work of Leonid Hurwicz (1960,1972) marks the birth of mechanism design theory.  In Hurwicz’s formulation, a mechanism is a communication system in which participants exchange messages with each other, messages that jointly determine the outcome.  These messages may contain private information, such as an individual’s (true or pretended) willingness to pay for a public good.  The mechanism is like a machine that compiles and processes the received messages, thereby aggregating (true or false) private information provided by many agents.  Each agent strives to maximize his or her expected payoff (utility or profit), and may decide to withhold disadvantageous information or send false information (hoping to pay less for a public good, say).  This leads to the notion of “implementing” outcomes as equilibria of message games, where the mechanism defines the “rules” of the message game.  The comparison of alternative mechanisms is then cast as a comparison of the equilibria of the associated message games…

Hurwicz’s (1972) notion of incentive-compatibility can now be expressed as follows: the mechanism is incentive-compatible if it is a dominant strategy for each participant to report his private information truthfully.

In other words, no incentive scheme, no matter how clever, can get people to tell the truth.  Grove, Clarke, Tideman, and Tullock lurk in the hallways.  Note that a second price auction (let everyone bid and the winner pays the price of the next highest bid) fails in terms of Paretian optimality.  The government takes the second price bid from the winner, but what should it do with the money?  Either the government wastes resources by destroying wealth, or it redistributes that wealth in some way but then the resulting redistribution in turn feeds back into bids and we can no longer derive truth-telling as optimal (but is this really a practical problem?; my fear is that the entire incentive-compatibility literature has never gotten at the real reason why we don’t run the entire economy as a second-price auction.) 

Here is Roger Myerson’s very nice piece on Hurwicz.  Myerson ties Hurwicz to the socialist calculation debate of Mises and Hayek and also to the later work of Jean Tirole.  It is sometimes said that moral hazard problems favor capitalism, adverse selection problems favor socialism.

Hurwicz also wrote a very important paper with Kenneth Arrow on the stability of general equilibrium theory, as well as other notable theory pieces, not all on mechanism design.  Here is a list of major works, some of the early ones have pdfs attached.

The Nobel Scientific Background paper is the best introduction to all of these people, and a good introduction to mechanism design in general.

As for Myerson, here is his home page.  Here is his CV.  Here is one overview.  Here is Myerson in Google Scholar.

His most cited paper is on auction design.  He laid out basic results for how to use auctions to extract revenue and elicit information about the value of the good.  These results have informed numerous privatizations and auction schemes in the last twenty-five years.

Here is a very important paper, with David Baron, on how to regulate a monopolist with unknown costs.  Strict marginal cost pricing is no longer possible.  Under some assumptions, allow the monopolist to charge a relatively high price, but design penalties to elicit an honest reporting of costs.  The key point of course is that monopolists won’t always report their costs truthfully.  This is one of the most important papers in regulatory economics in the last thirty years and it has helped disillusion many economists with a narrow ideal of marginal cost pricing.

Myerson also has important papers on how social choice theory is linked to bargaining theory, and which social choice procedures are most likely to elicit truthtelling.

I think of his "Mechanism Design with An Informed Principal" as one of his most important papers, though Google Scholar does not concur.  Let’s say that a principal knows something an agent does not and wishes to maintain that information asymmetry.  How can a principal construct the best incentive scheme for the agent?  The problem is, choosing the scheme itself may reveal information to the agent and thus eliminate the principal’s advantage.  Myerson showed what solutions to this problem have to look like.  This is a very clever problem and a very elegant paper.

Among the current research papers you will notice a strong interest in public choice and institutions, though Myerson is not usually thought of as applied, nor is that where his influence has come.  Electoral rules, corruption, and political institutions all are commanding his attention.

Here is an interview with Myerson on game theory.  Here is Myerson’s take on the core problems of social choice theory, a summary of the theoretical side of the field.

Here is Myerson on Hurwicz, which is also a very good introduction to Hurwicz.

Off the beaten track, here is Roger Myerson on Thomas Schelling’s Strategy of Conflict.  Here is Myerson’s Op-Ed draft on why America should accept limits on its military power, namely to limit deadly rivalries.  Here Myerson recommends federalism for Iraq.

In view of these difficulties, it is desirable to design mechanisms in which all equilibrium outcomes are optimal for the given goal function. The quest for this property is known as the implementation problem. Groves and Ledyard (1977) and Hurwicz and Schmeidler (1978) showed that, in certain situations, it is possible to construct mechanisms in which all Nash equilibria are Pareto optimal, while Eric Maskin (1977) gave a general characterization of Nash implementable social-choice functions. He showed that Nash implementation requires a condition now known as Maskin monotonicity (see Section 3.3 for an illustration of this property). Maskin (1977) also showed that if Maskin monotonicity and a condition called no-veto-power are both satisfied, and if there are at least three agents, then implementation in Nash equilibrium is possible.

Maskin considered Nash equilibria in games of complete information, but his results have been generalized to Bayesian Nash equilibria in games of incomplete information (see Postlewaite and Schmeidler, 1986, Palfrey and Srivastava, 1989, Mookherjee and Reichelstein, 1990, and Jackson, 1991). For example, Palfrey and Srivastava (1991) show how the double auction can be modified so as to render all equilibria incentive efficient.

Maskin’s results have also been extended in many other directions, such as virtual (or approximate) implementation (Matsushima, 1988, Abreu and Sen, 1991), implementation in renegotiation-proof equilibria (Maskin and Moore, 1999) and by way of sequential mechanisms (Moore and Repullo, 1988).  Implementation theory has played, and continues to play, an important role in several areas of economic theory, such as social choice theory (Moulin, 1994) and the theory of incomplete contracts (Maskin and Tirole, 1999).

Giuseppe Bertola writes:

Just as the Eurozone countries began to enjoy full and irreversible
economic integration, inequality increased very sharply in the EU15 and
more sharply in the 12 Eurozone countries, bringing its previous
decline to an end and reverting to the 1996 level by 2004…one finds that EMU does appear to improve economic performance (both in
terms of per capita income and in terms of unemployment) and the
intensity of international transactions (especially as regards foreign
direct investment flows).  But it also appears to be associated with
higher inequality, and with lower social spending.  Interestingly, the
inequality variation associated with EMU is fully accounted for by
changes in social policy expenditure (excluding pensions) as a share of
GDP, and in GDP and unemployment (both of which are of course likely to
be influenced by integration policies, as well as by global cyclical
and technological development).

We will of course see how far this trend goes, but it is consistent with my view that Europe will, in economic terms, become like the United States more rapidly than vice versa. 

Brad DeLong writes:

I don’t understand how any professional economist can disagree with the fact that more technology-driven inequality should call forth more social insurance in response.

I do think taxation should be progressive, but the comparative statics are tricky.  If absolute standards of living are rising, and credit constraints are being relaxed, economic failure often means no cable TV rather than starvation.  That militates in favor of less social insurance, noting on the other hand that we can afford it more as well. 

Furthermore greater productivity for the high earners can mean greater deadweight loss from the taxes and in the longer run less innovation and lower living standards (a prize to the first person who in the comments shouts "trickle down!" and accuses me of believing in discredited supply side notions; I’ll also recognize that well-spent government revenue can raise rather than lower the living standard). 

Whether "the rich would have worked virtually as hard for less" will depend on social norms.  I personally think that "shop at Barney’s slurp my sushi run a hedge fund psycho norms" — at least concentrated in a few percent of the human race — may be better for humanity than the sanity promoted by Bob Frank and Montaigne.  The thing is, part of the craziness of these people might include them not wanting to give away half or more of what they earn. 

Of course we could calm these people down altogether (or maybe not, or maybe letting them run a hedge fun is calming them down), but I’m not sure we want to. 

What about me?  I could read Epictetus all day long for free, listening to my already-purchased Indian classical music CDs and blogging for you all.  But at fifty percent marginal rates of taxation or higher, I would work considerably less at the margin.  I don’t look at a budget, to me the extra work "just don’t seem right."  Maybe it’s because I don’t play the ultimatum game like a chimpanzee.  But in any case for many people I think there is a significant notch effect at about 45-50 percent and up for the tax rate.

I might add that serious egalitarian-oriented health care reform — if indeed it succeeded — would significantly lower the case for greater progressivity of taxation.

Dani Rodrik tells us.  My whirlwind summary is pro-trade, pro-safety net, multilateral not bilateral, better procedures, pro-immigration, progressive toward poor countries, letting poor countries determine their own economic policies, and giving democracies more trade rights than non-democracies. 

I might well accept that if it were truly a package deal and truly the deal we would get.  But I don’t think multilateral institutions — a thin reed as they are — can stand that much stress or take on that much responsibility.  I also shudder to think who gets to define what a democracy is and what deals are cut to grant the higher status and how the excluded non-democracies take such a scolding.  Boosting safety nets and boosting immigration are not in every way congruent.  Most of all I wonder which of these goals are priorities.  I’ll put all of the procedural issues on the low side, as people aren’t happy with procedures no matter how good they are.  I want to start with more trade and immigration — unilaterally or bilaterally if need be — and see how much social spending we can afford without moving to European-level rates of taxation.  Most of the progressives I suspect want to start with more social spending and see how much open trade the public will then accept.  Viewed in these terms, we’re probably going to end up in very different places.