Mechanism Theory

Matthew O. Jackson

Stanford University – Department of Economics; Santa Fe Institute; Canadian Institute for Advanced Research (CIFAR)

Abstract:

Some of the basic results and insights of the literature on mechanism design are presented. In that literature game theoretic reasoning is used to model social institutions as varied as voting systems, auctions, bargaining protocols, and methods for deciding on public projects. A theme that comes out of the literature is the difficulty of finding mechanisms compatible with individual incentives that simultaneously result in efficient decisions (maximizing total welfare), the voluntary participation of the individuals, and balanced transfers (taxes and subsidies that net to zero across individuals). This is explored in the context of various incentive compatibility requirements, public and private goods settings, small and large societies, and forms of private information held by individuals.

How Mechanism Design Theory Affect The Outcomes Of Interactions – Introduction

The design of the institutions through which individuals interact can have a profound impact on the results of that interaction. For instance, whether an auction is conducted with sealed bids versus oral ascending bids can have an impact on what bidders learn about each other’s valuations and ultimately how they bid. Different methods of queuing jobs and charging users for computer time can affect which jobs they submit and when they are submitted. The way in which costs of a public project are spread across a society can affect the decision of whether or not the project is undertaken.

The theory of mechanism design takes a systematic look at the design of institutions and how these affect the outcomes of interactions. The main focus of mechanism design is on on the design of institutions that satisfy certain objectives, assuming that the individuals interacting through the institution will act strategically and may hold private information that is relevant to the decision at hand. In bargaining between a buyer and a seller, the seller would like to act as if the item is very costly thus raising the price, and the buyer would like to pretend to have a low value for the object to keep the price down. One question is whether one can design a mechanism through which the bargaining occurs (in this application, a bargaining protocol) to induce efficient trade of the good – so that successful trade occurs whenever the buyer’s valuation exceeds that of the seller. Another question is whether there exists such a mechanism so that the buyer and seller voluntarily participate in the mechanism.

The mechanism design literature models the interaction of the individuals using game theoretic tools, where the institutions governing interaction are modeled as mechanisms. In a mechanism each individual has a message (or strategy) space and decisions result as a function of the messages chosen. For instance, in an auction setting the message space would be the possible bids that can be submitted and the outcome function would specify who gets the object and how much each bidder pays as a function of the bids submitted. Different sorts of assumptions can be examined concerning how individuals choose messages as a function of their private information, and the analysis can be applied to a wide variety of contexts. The analysis also allows for transfers to be made among the individuals, so that some might be taxed and others subsidized (as a function of their private information) to bring their incentives into alignment.

A theme that comes out of the literature is that it is often impossible to find mechanisms compatible with individual incentives that simultaneously result in efficient decisions (maximizing total welfare), the voluntary participation of the individuals, and balanced transfers (taxes and subsidies that always net out across individuals).

Nevertheless, there are some important settings where incentives and efficiency are compatible and in other settings a \second-best” analysis is still possible. This is described in detail in what follows in the context of different incentive compatibility requirements, public and private goods settings, small and large societies, and forms of private information held by individuals.

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How Mechanism Design Theory Affect The Outcomes Of Interactions