Alokacijski mehanizmi i Leonid Hurwicz

autora/ice cronomy

Puzz je već prenio vijest da je prošlogodišnji Nobelovac iz ekonomije, Leonid Hurwicz (90) preminuo. Ja sam nakon proglašenja dobitnika preveo kratki članak prof. Peter Boettkea o Nobelovoj za 2007. Laska mi kad kaže da znam puno više o tome zašto je dobio Nobelovu. Nisam znao baš, i trebao sam se više informirati. Jednostavna činjenica je da, za razliku od mnogih drugih predmeta Nobelove nagrade u ekonomiji, “mechanisam design theory” i Leonid Hurwicz nisu dio standardnog curriculuma, unatoč tome da je dio aktivnog istraživanja u ekonomiji već više od 20 godina sa sve više aplikacija. U New Palgrave Dictionary of Economics, unos pod “mechanism design” je napisao Roger Myersen, koji je dobio Nobelovu zajedno sa Hurwiczom, no ime Leonid Hurwicz se, čudno, pojavljuje samo jednom i to u bibliografiji. Sigurno se iz toga ne može zaključiti tko je Leonid Hurwicz. Ovako WSJ opisuje “mechanism desig theory”:

Regarded as the father of the field known as “mechanism design theory,” Mr. Hurwicz tackled a problem that the field of economics didn’t traditionally consider: When markets don’t allocate resources efficiently, or at all, what sort of allocation mechanisms can be created that will do so?

In textbooks, Adam Smith’s invisible hand matches buyers with sellers equally. A million potato farmers will find a million potato eaters and will sell their goods for the maximum that buyers are willing to pay. In the real world, buyers and sellers can’t find each other, or one buyer tries to corner the market, or the government grows the potatoes. Mechanism design theory addresses what happens when buyers and sellers keep private information about how they value a good or service.

Mr. Hurwicz, born in Moscow, began developing theories that show when markets aren’t capable of operating efficiently — and to measure what type of mechanism would work best. “Leo Hurwicz made the breakthrough that the key part of the problem is that people don’t have incentives to share information” about the price at which they are willing to buy or sell, said Roger B. Myerson, who studied Mr. Hurwicz’s work as a Harvard graduate student and shared his Nobel Prize along with Eric S. Maskin.

Ni na naprednom levelu se o toj teoriji ne uči/raspravlja pretjerano. “Mechanism design” se ne nalazi u standardnim (naprednijim) knjigama, recimo iz mikroekonomije. Hal Varian, autor jednog od najpoznatijih udžbenika iz mikroekonomije, je pisao radove o “economic mechanism design”, ali nije temu uključio u svoj udžbenik za studente. Vjerojatno zato jer je “mechanism design” vrlo matematički orijentirana metodologija analize rezultata ekonomske efikasnosti, ali je ipak sub-disciplina mikroekonomije i teorije igara. “Mechanism Design Theory” se obično pojavi oko diskusija o dizajnu aukcija (zbog potreba privatizacije primjerice) ili teoriji igara. Za sve više od toga treba tražiti specijalne izvore, poput Hurwiczove knjige Designing Economic Mechanisms objavljene tek 2006. Za jednog prosječnog studenta da se upozna sa predmetom “mechanisam design theory”, po mom mišljenju, je slučajnost. Možda će to Nobel promjeniti i “mechanism design” će polako uči u udžbenike. Do onda pročitajte ispod više o teoriji iz New Palgrave Dictionary of Economics (nema matematičkih formula!).

Abstract

A mechanism is a specification of how economic decisions are determined as a function of the information that is known by the individuals in the economy. Mechanism theory shows that incentive constraints should be considered coequally with resource constraints in the formulation of the economic problem. Where individuals’ private information and actions are difficult to monitor, the need to give people an incentive to share information and exert efforts may impose constraints on economic systems just as much as the limited availability of raw materials. Mechanism design is the fundamental mathematical methodology for analysing economic efficiency subject to incentive constraints.

Overview

A mechanism is a specification of how economic decisions are determined as a function of the information that is known by the individuals in the economy. In this sense, almost any kind of market institution or economic organization can be viewed, in principle, as a mechanism. Thus mechanism theory can offer a unifying conceptual structure in which a wide range of institutions can be compared, and optimal institutions can be identified.

The basic insight of mechanism theory is that incentive constraints should be considered coequally with resource constraints in the formulation of the economic problem. In situations where individuals’ private information and actions are difficult to monitor, the need to give people an incentive to share information and exert efforts may impose constraints on economic systems just as much as the limited availability of raw materials. The theory of mechanism design is the fundamental mathematical methodology for analysing these constraints.

The study of mechanisms begins with a special class of mechanisms called direct-revelation mechanisms, which operate as follows. There is assumed to be a mediator who can communicate separately and confidentially with every individual in the economy. This mediator may be thought of as a trustworthy person, or as a computer tied into a telephone network. At each stage of the economic process, each individual is asked to report all of his private information (that is, everything that he knows that other individuals in the economy might not know) to the mediator. After receiving these reports confidentially from every individual, the mediator may then confidentially recommend some action or move to each individual. A direct-revelation mechanism is any rule for specifying how the mediator’s recommendations are determined, as a function of the reports received.

A direct-revelation mechanism is said to be incentive compatible if, when each individual expects that the others will be honest and obedient to the mediator, then no individual could ever expect to do better (given the information available to him) by reporting dishonestly to the mediator or by disobeying the mediator’s recommendations. That is, if honesty and obedience is an equilibrium (in the game-theoretic sense), then the mechanism is incentive compatible.

The analysis of such incentive-compatible direct-revelation mechanisms might at first seem to be of rather narrow interest, because such fully centralized mediation of economic systems is rare, and incentives for dishonesty and disobedience are commonly observed in real economic institutions. The importance of studying such mechanisms is derived from two key insights: (i) for any equilibrium of any general mechanism, there is an incentive-compatible direct-revelation mechanism that is essentially equivalent; and (ii) the set of incentive-compatible direct-revelation mechanisms has simple mathematical properties that often make it easy to characterize, because it can be defined by a set of linear inequalities. Thus, by analysing incentive-compatible direct-revelation mechanisms, we can characterize what can be accomplished in all possible equilibria of all possible mechanisms, for a given economic situation.

Insight (i) above is known as the revelation principle. It was first recognized by Gibbard (1973), but for a somewhat narrower solution concept (dominant strategies, instead of Bayesian equilibrium) and for the case where only informational honesty is problematic (no moral hazard). The formulation of the revelation principle for the broader solution concept of Bayesian equilibrium, but still in the case of purely informational problems, was recognized independently by many authors around 1978 (see Dasgupta, Hammond and Maskin, 1979; Harris and Townsend, 1981; Holmstrom, 1977; Myerson, 1979; Rosenthal, 1978). Aumann’s (1974; 1987) concept of correlated equilibrium gave the first expression to the revelation principle in the case where only obedient choice of actions is problematic (pure moral hazard, no adverse selection). The synthesis of the revelation principle for general Bayesian games with incomplete information, where both honesty and obedience are problematic, was given by Myerson (1982). A generalization of the revelation principle to multistage games was stated by Myerson (1986).

The intuition behind the revelation principle is as follows. First, a central mediator who has collected all relevant information known by all individuals in the economy could issue recommendations to the individuals so as to simulate the outcome of any organizational or market system, centralized or decentralized. After the individuals have revealed all of their information to the mediator, he can simply tell them to do whatever they would have done in the other system. Second, the more information that an individual has, the harder it may be to prevent him from finding ways to gain by disobeying the mediator. So the incentive constraints will be least binding when the mediator reveals to each individual only the minimal information needed to identify his own recommended action, and nothing else about the reports or recommendations of other individuals. So, if we assume that the mediator is a discrete and trustworthy information-processing device, with no costs of processing information, then there is no loss of generality in assuming that each individual will confidentially reveal all of his information to the mediator (maximal revelation to the trustworthy mediator), and the mediator in return will reveal to each individual only his own recommended action (minimal revelation to the individuals whose behaviour is subject to incentive constraints).

The formal proof of the revelation principle is difficult only because it is cumbersome to develop the notation for defining, in full generality, the set of all general mechanisms, and for defining equilibrium behaviour by the individuals in any given mechanism. Once all of this notation is in place, the construction of the equivalent incentive-compatible direct-revelation mechanism is straightforward. Given any mechanism and any equilibrium of the mechanism, we simply specify that the mediator’s recommended actions are those that would result in the given mechanism if everyone behaved as specified in the given equilibrium when his actual private information was as reported to the mediator. To check that this constructed direct-revelation mechanism is incentive compatible, notice that any player who could gain by disobeying the mediator could also gain by similarly disobeying his own strategy in the given equilibrium of the given mechanism, which is impossible (by definition of equilibrium).

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