Michael Schwarz’s research while affiliated with Yahoo and other places

We study the dynamics of multiround position auctions, considering both the case of exogenous click-through rates and the case in which click-through rates are determined by an endogenous consumer search process. In both contexts, we demonstrate that dynamic position auctions converge to their associated static, envy-free equilibria. Furthermore, convergence is efficient, and the entry of low-quality advertisers does not slow convergence. Because our approach predominantly relies on assumptions common in the sponsored search literature, our results suggest that dynamic position auctions converge more generally.

We consider market rules for the transfer of IP addresses, numeric identifiers required by all computers connected to the Internet. Excessive fragmentation of IP address blocks causes growth in the Internet's routing table, which is socially costly, so an IP address market should discourage subdividing IP address blocks more than necessary. Yet IP address transfer rules also need to facilitate purchase by the networks that need the addresses most, from the networks who value them least. We propose a market rule that avoids excessive fragmentation while almost achieving social efficiency, and we argue that implementation of this rule is feasible despite the limited powers of central authorities. We also offer a framework for the price trajectory of IP addresses. In a world without uncertainty, the unit price of IP addresses is constant until all addresses are in use and begins decreases at that time. With uncertainty, the price before that time is a martingale, and the price trajectory afterwards is a supermartingale. Finally, we explore the role of rental markets in sharing information about address value and assuring allocative efficiency.

In this appendix we explore some parallels between our results and some recent results on global games. Frankel, Morris, and Pauzner (2003) show that in global games, different equilibria may be pinned down by vanishingly small noise. They also show that a sufficient condition for an equilibrium in a global game to be robust to the structure of noise is to be a weighted potential maximizer, provided that the payoffs are own-action quasiconcave. These concepts are defined in Section 6 of FMP as follows. Definition A complete information game g is own-action quasiconcave if for all i and opposing action profiles a −i ∈ A −i and for all constants c, the set {a i : g i (a i , a −i) ≥ c} is convex.

We present the results of a large field experiment on setting reserve prices in auctions for online advertisements, guided by the theory of optimal auction design suitably adapted to the sponsored search setting. Consistent with the theory, following the introduction of new reserve prices revenues in these auctions have increased substantially.

We define the median stable matching for two sided matching markets with side payments and prove constructively that it exists.

We argue that the intrinsic inefficiency of proprietary software has historically created a space for alternative institutions that provide software as a public good. We discuss several sources of such inefficiency, focusing on one that has not been described in the literature: the underinvestment due to fear of hold-up. An inefficient hold-up occurs when a user of software must make complementary investments, when the return on such investments depends on future cooperation of the software vendor, and when contracting about a future relationship with the software vendor is not feasible. We also consider how the nature of the production function of software makes software cheaper to develop when the code is open to the end users. Our framework explains why open source dominates certain sectors of the software industry (e.g., programming languages), while being almost non existent in some other sectors (e.g., computer games). We then use our discussion of efficiency to examine the history of institutions for provision of public software from the early collaborative projects of the 1950s to the modern “open source” software institutions. We look at how such institutions have created a sustainable coalition for provision of software as a public good by organizing diverse individual incentives, both altruistic and profit-seeking, providing open source products of tremendous commercial importance, which have come to dominate certain segments of the software industry.

This paper explores information disclosure in matching markets. A school may suppress some information about students in order to improve their average job placement. We consider a setting with many schools, students, and jobs, and show that if early contracting is impossible, the same, "balanced" amount of information is disclosed in essentially all equilibria. When early contracting is allowed and information arrives gradually, if schools disclose the balanced amount of information, students and employers will not find it profitable to contract early. If they disclose more, some students and employers will prefer to sign contracts before all information is revealed. (JEL C78, D82, D83)