Mechanism Design
Mechanism Design
Mechanism design deals with the problem of how to design a “mechanism” or a game that has an equilibrium whose outcome maximizes some objective function, such as the maximization of social welfare, subject to certain constraints that depend on the specific problem.
Mechanism design begins with the assumption that each one of the agents for whom the mechanism is designed has access to a different piece of private information, and that elicitation of this information is important for achieving the desired objective. Mechanism design is thus all about incentives: about how to provide the agents with incentives to reveal their private information, and to act in accordance with the designer’s objectives. Accordingly, the most important constraint in mechanism design is called “incentive compatibility,” or IC. The IC constraint obliges the designer to take into account the fact that the agents will try to manipulate the mechanism to their advantage. For example, in one famous mechanism design problem the challenge is how to design an auction that maximizes the expected revenue to the seller under the assumption that the willingness of the potential buyers’ to pay for the auctioned object is their private information.
The roots of the question of how to collect decentralized information for the purpose of allocating resources can be found in economists’ early debates regarding the feasibility of a centralized socialist economy. These early discussions emphasized the complexity of the systems involved, but it soon became evident that any system for making decisions over the allocation of resources might be open to manipulation. One of the first to recognize the importance of incentives in this context was Leonid Hurwicz (b. 1917), who coined the term incentive compatibility in 1959.
Mechanism design was established as a field of study in the early 1970s as a result of Hurwicz’s work on the possibility of attaining efficient outcomes in dominant strategy equilibria in “economic environments”; the investigation by James Mirrlees into optimal income taxation schemes; and the studies by Edward H. Clarke and Theodore Groves of efficient dominant strategy mechanisms for the provision of public goods, which are known as “Vickrey-Clarke-Groves,” or VCG, mechanisms (William Vickrey studied such mechanisms in the 1960s in the context of his work on auctions). In the late 1970s Kenneth Arrow and Claude d’Aspremont and Louis-André Gerard-Varet showed that it was possible to obtain incentive compatible, efficient, and budget-balanced mechanisms. However, in 1983, in their research into optimal mechanisms for bilateral trade, Roger Myerson and Mark Satterthwaite showed that these earlier possibility results might break down if the agents were permitted to refrain from participation in the mechanism if it does not give them an expected utility that is larger than their reservation utility. In 1982 Myerson published a paper on optimal auctions that to this day serves as the model for implementing mechanism design. The literature on mechanism design continued to expand, and presently encompasses price discrimination, regulation, public-good provision, taxation, auction design, procurement, the organization of markets and trade, and more.
Mechanism design has not had the effect on policy anticipated by its early practitioners. This is probably because many of its main results are not robust against changes in the details of the underlying environment (as argued by Robert Wilson in the so-called Wilson Critique). It still remains to be seen whether the current work on “robust mechanism design” would make the theory more practicable.
SEE ALSO Game Theory; Mixed Strategy; Multiple Equilibria; Nash Equilibrium
BIBLIOGRAPHY
Arrow, Kenneth J. 1979. The Property Rights Doctrine and Demand Revelation Under Incomplete Information. In Economics and Human Welfare, ed. Michael J. Boskin, 23, 29–31. New York: Academic Press.
Clarke, Edward H. 1971. Multipart Pricing of Public Goods. Public Choice 8: 19–33.
D’Aspremont, Claude, and Louis-André Gerard-Varet. 1979. Incentives and Incomplete Information. Journal of Public Economics 11: 25–45.
Groves, Theodore. 1973. Incentives in Teams. Econometrica 41: 617–631.
Hurwicz, Leonid. 1959. Optimality and Informational Efficiency in Resource Allocation Processes. In Mathematical Methods in the Social Sciences, ed. Kenneth Arrow et al., 27–46. Stanford, CA: Stanford University Press.
Hurwicz, Leonid. 1972. On Informationally Decentralized Systems. In Decision and Organization, ed. Charles B. McGuire and Roy Radner, 297–333. Amsterdam: North-Holland.
Mirrlees, James. 1971. An Exploration in the Theory of Optimum Income Taxation. Review of Economic Studies 38: 175–208.
Myerson, Roger B. 1981. Optimal Auction Design. Mathematics of Operations Research 6: 58–73. Myerson, Roger B., and Mark A. Satterthwaite. 1983. Efficient Mechanisms for Bilateral Trading. Journal of Economic Theory 28: 265–281.
Vickrey, William. 1961. Counterspeculation, Auctions, and Competitive Sealed Tenders. Journal of Finance 16: 8–37.
Wilson, Robert. 1987. Game-Theoretic Analyses of Trading Processes. In Advances in Economic Theory: Fifth World Congress, ed. Truman Bewley, 33–77. Cambridge, U.K.: Cambridge University Press.
Zvika Neeman