Mechanism Design: Theory and Applications

Transcription

1 Mechanism Design: Theory and Applications Project leaders: Efthymios Athanasiou and Sergei Izmalkov Markets facilitate economic transactions, so do contractual agreements, auction and bargaining procedures. This ongoing project is devoted to the analysis and design of these trading processes as well as design of economic and social mechanisms in other applications. Several suggested areas of focus are listed below. Students are welcome to do theoretical or empirical projects as well as develop own ideas in the broad fields of game theory, mechanism design, and applied microeconomics. Strategy-Proof Mechanism Design and Computer Science A mechanism design problem typically concerns a well-formulated, yet incompletely specified problem. Each instantiation of the optimization problem can be ascertained only after the agents involved reveal information they hold privately. For instance, to appeal to a celebrated example, the optimal level of provision of a public good cannot be computed before the individuals who will benefit from its procurement reveal their valuation for the good. The implementation exercise concerns the attainment of such information. A mechanism assigns to each instantiation of the problem (in the case of public good provision that is simply a profile of individual valuations) a solution and a system of transfers. A mechanism is optimal, if it always select an optimal solution. It is Strategy-Proof if it always induces each agent to disclose the information he holds private, independently of how other agents may act. Lately, Strategy-Proof Mechanism Design has found a prominence in Computer Science. Agents (organizations, people, computers, software) sharing bandwidth on a network cannot be expected to follow the rules of a protocol truthfully and faithfully especially if deviating from the protocol is beneficial to them. Thus, unlike traditional distributed computing protocols, a protocol for these new settings must be designed explicitly to account for willing manipulation by the users. Hershberger and Suri (Vickrey Pricing in Network Routing. Fast Payment Computation) describe why the current standard on the Internet suffers from agent manipulation that yields congestion and even crashes: One of the most famous distributed protocols on the Internet is the Transmission Control Protocol (TCP), implemented on each host (computer) on the Internet. An important feature of this protocol is its congestion control mechanism. The New Economic School: AY

2 protocol uses packet loss as an indication of network congestion and is designed to reduce the sending host s transmission rate (using a fairly aggressive exponential back). It then gradually increases the transmission rate until another sign of congestion is detected. This cycle of increasing and then decreasing the transmission rate allows the protocol to discover and utilize whatever bandwidth is available between two communicating hosts while at the same time sharing the overall resource among many such pairs. TCP is self-regulating meaning that it assumes that individual hosts will respond to congestion exactly as the designers of the protocol intended. But a self-interested host has motivation not to decrease its sending rate in the hope that others will reduce their rate, eliminating the congestion, while he can continue to enjoy the higher rate. In one extreme case no one follows the TCP congestion rules and the system crashes. In another extreme case a few misbehaving users enjoy an unfair share of the network resources. Because a protocol like TCP is easily manipulated many researchers have proposed game-theoretic and pricing-based mechanisms to share bandwidth and other network resources. The general problem of sharing bandwidth along a network can addressed by resorting to the economic literature on the abstract problem of assigning a number of indivisible objects to a lesser number of potential claimants. Two recent references where one may find both a survey of the economic literature, as well as the computer scientist s perspective on it, are: Algorithmic Game Theory, 2007, edited by Nisan et al., Cambridge University Press, Internet and Network Economics, 2008, edited by Papadimitriou and Zhang, Springer Social Choice with applications to Income Taxation, Health Insurance Provision and Education Social Choice is the branch of economics that deals with collective decision making. It stems from Arrow s impossibility theorem concerning the problem of aggregating individual preferences and it infiltrates most other areas of economic analysis. Typically, policy recommendations involve the optimization of an objective function that constitutes a measure of social well-being under constraints. A particular instance of Social Choice concerns the construction of such measures. Recently, attempts have been made to incorporate into the analysis of income taxation a model of the individual that accommodates differences across a multitude of characteristics. Those characteristics warrant a different treatment. This augmentation of the standard Mirrlees model allows for interesting fairness questions to be raised. In particular, one may treat the measure of the social well-being as encompassing a variety of competing ethical principles that may, inter alia, influence policy. In addition, the incentive problem becomes more pronounced. In the case of income taxation individuals may vary with respect to both their productivities and disposition towards labor. In the case of health individuals may vary over their genetic predisposition and their habits. In the case of education individuals may vary with respect to their innate abilities and their effort choices. These pieces of information are typically unknown to the policy maker and usually crucial for the design of policy. 2

3 The Social Planner is then faced with the following problem. What values and ethical principals does he wish to promote? What measure of social welfare encompasses his values? How to optimize his objective subject to incentive constraints? What concrete policies are derived from the solution to the optimization program? This approach along with applications is presented in: A Theory of Fairness and Social Welfare, 2001, Fleurbaey and Maniquet, Cambridge UP. The book surveys the latest results on the topic and outlines a general methodology for tackling these general problem. Although, the book places greater emphasis on income taxation the literature has followed up with results concerning health insurance and education. Auctions and markets in Russia Goods and services, licenses, advertising slots are allocated via auctions, as they are simple, fast, and efficient mechanisms to find the prices and determine the allocation. Auctions appear essentially everywhere, from selling antiques to privatization of state enterprises. Auction theory, design and analysis of auctions in practice attract lots of attention from the economists. Possible areas of research are abundant and include design of efficient (and optimal) auctions for specific circumstances of sale and analysis of bidding (in particular, collusive) practices. The following are a few examples of possible auctions and markets to consider. Russian governments of different levels are obliged to purchase most of what they need via electronic marketplaces, data on which is publicly available. Rosimushestvo is privatizing various firms it controls or has a stake in. Yandex and Google conduct sponsored search auctions every time a user searches for something over the net. These auctions are of particular interests as Yandex and Google serve as market makers, with an opportunity to adjust the rules of the auction as they see fit. New paradigms in Mechanism Design (coming from Economics and Computer Science) Enhanced-Privacy Mechanism Design Privacy of information is clearly a human desideratum, stemming from possible effects of any information revealed by current actions on future interactions. Somewhat surprisingly, it has received virtually no attention in Microeconomic Theory literature. In part this can be explained by the fact that most of mechanisms obtained as solutions (to a variety of problems in auctions, contract theory, bargaining, market design, voting, etc.) are idealistic in relying on assistance of a mediator. Such a mediator collects reports from the players and selects an outcome. In essence, when private information does matter, privacy is substituted by the trust in mediator, often by an explicit assumption on the ability of the mediator to commit to the mechanism. As long as the mediator is trusted with correctly processing collected reports so as to obtain and reveal the outcome and nothing more, the mechanism 3

4 obtains the perfect privacy: only the minimal unavoidable information is revealed by the outcome. But, can we really trust the mediators? Are trusted mediators readily available? In a series of papers, Izmalkov, Lepinski & Micali demonstrate that any finite mediated normal-form mechanism can be (perfectly) implemented by an unmediated extensive-form mechanism with a public mediator so that: (1) the two mechanisms are strategy equivalent: their normal forms are isomorphic, and thus solutions of the games generated by these mechanisms are the same; (2) the two mechanisms are privacy equivalent: the players learn exactly the same information during and after the play of each mechanism provided they use equivalent strategies; and (3) the public mediator only performs the public actions, so that everyone can verify that he is acting properly, and never learns any information that should remain private. Yet, many practical issues related to notions of privacy, trust, and commitment remain unresolved. To what extent do theoretical properties of common auctions suffer from the lack of trust in the auctioneer, or lack of privacy in the auction procedure? What are effects of privacy concerns in dynamic transactions, e.g. online transactions in a large market-place such as amazon.com. How to design practical mechanisms that respect privacy of their participants? Minimal Knowledge, Belief-Leveraging Mechanism Design In a stock market, one may buy a stock for a high price not because he personally values it very high, but because he believes that others may value it even higher, or because he believes that someone believes that someone else values very high. Beliefs and high-order believes indeed influence our strategic behavior in many settings. However, auctions and other classical economic mechanisms do not leverage such beliefs to say generate higher revenue. (Indeed, dominant-strategy mechanisms leverage solely the players knowledge of their own valuations, not their beliefs about the valuations of their opponents. Bayesian mechanisms with a common prior leverage at most the players first-order beliefs, because their higher-order ones are forced to coincide with their first-order ones.) On the other side, in the design of optimal mechanisms (unlike the classic mechanism design) it is assumed that the seller also has beliefs about knowledge of the others, and acts depending on them. An open research area is how to design mechanisms that leverage higher order beliefs (or anything beyond first order believes), require minimal knowledge by the seller, and are optimal (or at least good in some sense). There is a very recent research on these topics, see in particular, works of Silvio Micali with coauthors. No Commitment- and Commitment-Providing Mechanism Design Commitment is the ability to follow a specific plan of action even if it is not rational to do so at any moment a player makes a decision. It can be profit-enhancing as it forces other rational players to adjust their behavior. Ability to commit is particularly crucial for the party that proposes a mechanism to play by others. The famous Coase conjecture states that the monopolist selling a durable good in large supply would have to sell it at a price 4

5 of zero if he is not able to commit not to lower prices tomorrow. The best mechanism for the monopolist would be to set a price and stick to it even if a customer refuses to buy it. In mechanism design, it is often assumed that the designer can commit to the mechanism it offers. Crucially, the need for commitment often comes at a point when the designer learns some new information about the players it interacts with (such as monopolist learning that a customer refused its offer). Among the open questions are identification of the minimally required commitment for achieving specific (classic) goals of mechanism design and design of mechanism that achieve these goals with the minimally required commitment. Reduced-Complexity Mechanism Design Classically, when designing an economic mechanism (e.g., a combinatorial auction) one disregards computational issues. As a result, classical mechanisms often run in time that is exponential in the number of players or other parameters, such as the number of goods in the case of an auction. In practice, therefore, one cannot live long enough to see the outcomes generated by these mechanisms. This problem becomes particularly acute for internet transactions, such as those involved in tomorrow s secure exchanges, because the number of participants in such games is typically large. They definitely are not 2- or 3-player games. It becomes thus imperative to seek new economic mechanisms that can perform well with bounded computational resources. Social networks and Media If one would be asked a question what is the most visible development in the world in the last 10 years, a definite candidate is the explosion of the online communities and social networks. Think Facebook, netflix, twitter, livejournal, imhonet. This is largely an uncharted territory, and so both exciting and challenging at the same time. There are plenty of papers on these and related topics, so search effectively for them (using google scholar and appropriate keywords). 5