Choice screen auctions have been recently deployed in 31 European countries, allowing consumers to choose their preferred search engine on Google's Android platform instead of being automatically defaulted to Google's own search engine. I show that a seemingly minor detail in the design of these auctions---whether they are conducted on a "per appearance" or a "per install" basis---plays a major role in the mix and characteristics of auction winners, and, consequently, in their expected overall market share. I also show that "per install" auctions distort the incentives of alternative search engines toward extracting as much revenue as possible from each user who installs them, at the expense of lowering the expected number of such users. The distortion becomes worse as the auction gets more competitive and the number of bidders increases. Empirical evidence from Android choice screen auctions conducted in 2020 is consistent with my theoretical results.

We consider general trading networks with bilateral contracts. We show that a suitably adapted chain stability concept is equivalent to stability if all agents' preferences are jointly fully substitutable and satisfy the Laws of Aggregate Supply and Demand (a condition we call monotone - substitutability). We also present three examples to show that are results are sharp, demonstrating that: If preferences of some agents do not satisfy the Laws of Aggregate Supply and Demand, then chain stable outcomes may not be stable. " If preferences of some agents are not fully substitutable, then chain stable outcomes may likewise not be stable. " If blocking sets are restricted to chains that do not "cross" themselves (i.e., chains that involve each agent in at most two contracts), then an outcome that is robust to such blocks may not be robust to richer blocks. Our results imply that in trading networks with transferable utility, an outcome is consistent with competitive equilibrium if and only if it is not blocked by any chain of contracts. We show moreover that, from a computational perspective, checking whether an outcome is chain stable is substantially easier than checking whether that outcome is stable directly. Indeed, we show that as the size of the economy grows, the number of chains of trades (corresponding to possible blocking chains) becomes infinitely smaller than the number of general sets of trades (corresponding to possible blocking sets).

Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. In this paper, we extend earlier models' canonical definitions of substitutability to a setting in which an agent can be a buyer in some transactions and a seller in others, and show that all the different substitutability concepts are equivalent. Next, we introduce a new class of fully substitutable preferences that models the preferences of intermediaries with production capacity. We then prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability. We show that full substitutability can be recast in terms of submodularity of the indirect utility function, the single improvement property, a "no complementarities" condition, and a condition from discrete convex analysis called M♮-concavity. Finally, we show that substitutability implies two key monotonicity conditions known as the Laws of Aggregate Supply and Demand. All of our results explicitly incorporate economically important features such as indifferences, non-monotonicities, and unbounded utility functions that were not fully addressed in prior work.

We study trading behavior and the properties of prices in informationally complex markets. Our model is based on the single-period version of the linear-normal framework of [Kyle 1985]. We allow for essentially arbitrary correlations among the random variables involved in the model: the true value of the traded asset, the signals of strategic traders, the signals of competitive market makers, and the demand coming from liquidity traders. We first show that there always exists a unique linear equilibrium, characterize it analytically, and illustrate its properties in a series of examples. We then use this equilibrium characterization to study the informational efficiency of prices as the number of strategic traders becomes large. If the demand from liquidity traders is uncorrelated with the true value of the asset or is positively correlated with it (conditional on other signals), then prices in large markets aggregate all available information. If, however, the demand from liquidity traders is negatively correlated with the true value of the asset, then prices in large markets aggregate all available information except that contained in liquidity demand.

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.

This paper studies information aggregation in dynamic markets with a finite number of partially informed strategic traders. It shows that for a broad class of securities, information in such markets always gets aggregated. Trading takes place in a bounded time interval, and in every equilibrium, as time approaches the end of the interval, the market price of a "separable" security converges in probability to its expected value based on the traders' pooled information.