We investigate the “generalized second-price ” (GSP) auction, a new mechanism used by search engines to sell online advertising. Although GSP looks similar to the Vickrey-Clarke-Groves (VCG) mechanism, its properties are very different. Unlike the VCG mechanism, GSP generally does not have an equilibrium in dominant strategies, and truth-telling is not an equilibrium of GSP. To analyze the properties of GSP, we describe the generalized English auction that corresponds to GSP and show that it has a unique equilibrium. This is an ex post equilibrium, with the same payoffs to all players as the dominant strategy equilibrium of VCG. (JEL D44, L81, M37) This paper investigates a new auction mechanism, which we call the “generalized secondprice” auction, or GSP. GSP is tailored to the unique environment of the market for online ads, and neither the environment nor the mechanism has previously been studied in the mechanism design literature. While studying the properties of a novel mechanism is often fascinating in itself, our interest is also motivated by the spectacular commercial success of GSP. It is the dominant transaction mechanism in a large and rapidly growing industry. For example, Google’s total revenue in 2005 was $6.14 billion. Over 98 percent of its revenue came from GSP auctions. Yahoo!’s total revenue in 2005 was $5.26 billion. A large share of Yahoo!’s revenue is derived from sales via GSP auctions. It is believed that over half of Yahoo!’s revenue is derived from sales via GSP auctions. As of May 2006, the combined market capitalization of these companies exceeded $150 billion. Let us briefly describe how these auctions work. When an Internet user enters a search

We characterize ex post incentive compatible public decision rules, and apply this characterization to (i) bilateral trade and (ii) public good provision. 1

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Wilson (1987) criticizes the existing literature of game theory as relying too much on common-knowledge assumptions. In reaction to Wilson’s critique, the recent literature of mechanism design has started employing simpler mechanisms such as dominant strategy mechanisms. However, there has been little theory behind this approach. In particular, it has not been made clear why, when a mechanism designer is not willing to make strong common-knowledge assumptions, she would respond by using simpler mechanisms instead of even more complicated ones. This paper tries to fill the void and investigates some foundations for using simpler mechanisms such as dominant strategy mechanisms.

We design a Generalized Position Auction for players with private values and private budget constraints. Our mechanism is a careful modification of the Generalized English Auction of Edelman, Ostrovsky and Schwarz (2007). By enabling multiple price trajectories that ascent concurrently we are able to retrieve all the desired properties of the Generalized English Auction, that was not originally designed for players with budgets. In particular, the unique ex-post equilibrium outcome of our auction is Pareto-efficient and envy-free. Moreover, we show that any other position auction that satisfies these properties and does not make positive transfers must obtain in ex-post equilibrium the same outcome of our mechanism, for every tuple of distinct types. This uniqueness result holds even if the players ’ values are fixed and known to the seller, and only the budgets are private. JEL Classification Numbers:

This paper considers infinite repetition of a simple trade game with bilateral hidden values. We analyze the extent to which efficient trade is possible in an ongoing relationship between impatient agents, and how the answer depends on the institutional environment. Myerson and Satterthwaite (1983) showed that there is no budget balanced, incentive compatible, and individually rational mechanism that achieves efficiency in a static trade setting. We demonstrate that in repeated trade settings with discount factors significantly less than one, there exist stationary dynamic mechanisms that achieve (I) ex post incentive compatibility, ex post individual rationality, ex ante budget balance, and efficiency; or (II) interim incentive compatibility, ex post individual rationality, ex post budget balance, and efficiency. We provide some analysis and examples of secondbest, inefficient mechanisms that satisfy (III) ex post incentive compatibility, ex post individual rationality, and ex post budget balance. We then expand the model to allow agents to make deposits and withdrawals from a joint savings account. We then construct non-stationary recursive mechanisms utilizing such accounts that achieve (IV) ex post incentive compatibility, ex post individual rationality, and approximate efficiency, using a joint savings account whose balance cannot become negative. The alternative settings we study correspond to different institutional environments and assumptions on the agents ’ knowledge of underlying probability distributions. We are grateful to participants in the Stanford theory lunch for helpful comments.

We survey the recent literature on the role of information in mechanism design. First, we discuss an emerging literature on the role of endogenous payo and strategic information for the design and the efficiency of the mechanism. We speci cally consider information management in the form of acquisition of new information or disclosure of existing information. Second, we argue that in the presence of endogenous information, the robustness of the mechanism to the type space and higher order beliefs becomes a natural desideratum. We discuss recent approaches to robust mechanism design and robust implementation.

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and- in economic environments-sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is sufficient. Ex post monotonicity is satis…ed in all single crossing environments with strict ex post incentive constraints. In many economically signi…cant environments, ex post implementation can be achieved in the direct mechanism. We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity (necessary and almost sufficient for complete information implementation). The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. Ex post implementation in the direct mechanism is also possible in this case. We describe an example where the Pareto correspondence

This paper surveys the recent literature concerning the structure of optimal taxes in dynamic economies in which agents are privately informed about skills and effort.

In an environment with dynamic arrivals of players who wish to purchase only one of multiple identical objects for which they have a private value, we analyze a sequential auction mechanism with an activity rule. If the players play undominated strategies then we are able to bound the efficiency loss compared to an optimal mechanism that maximizes the total welfare. We have no assumptions on the underlying distribution from which the players ’ arrival times and valuations for the object are drawn. Moreover we have no assumption of a common prior on this distribution. JEL Classification Numbers: