On the Concentration of Allocations and Comparisons of Auctions in Large Economies

We analyze competitive pressures in a sequence of auctions with a growing number of bidders, in a model that includes private and common valuations as special cases. We show that the key determinant of bidders' surplus (and implicitly auction revenue) is how the goods are distributed. In any setting and sequence of auctions where the allocation of good(s) is concentrated among a shrinking proportion of the population, the winning bidders enjoy no surplus in the limit. If instead the good(s) are allocated in a dispersed manner so that a non- vanishing proportion of the bidders obtain objects, then in any of a wide class of auctions bidders enjoy a surplus that is bounded away from zero. Moreover, under dispersed allocations, the format of the auction matters. If bidders have constant marginal utilities for objects up to some limit, then uniform price auctions lead to higher revenue than discriminatory auctions. If agents have decreasing marginal utilities for objects, then uniform price auctions are asymptotically efficient, while discriminatory auctions are asymptotically {\sl in}efficient. Finally, we show that in some cases where dispersed allocations are efficient, revenue may increase by bundling goods at the expense of efficiency.Auction, Competition, Mechanism, Asymptotic Efficiency, Revenue Equivalence

Bidding With Securities: Auctions and Security Design

We study security-bid auctions in which bidders compete by bidding with securities whose payments are contingent on the realized value of the asset being sold. Such auctions are commonly used, both formally and informally. In formal auctions, the seller restricts bids to an ordered set, such as an equity share or royalty rate, and commits to a format, such as first or second-price. In informal settings with competing buyers, the seller does not commit to a mechanism upfront. Rather, bidders offer securities and the seller chooses the most attractive bid, based on his beliefs, ex-post. We characterize equilibrium payoffs and bidding strategies for formal and informal auctions. For formal auctions, we examine the impact of both the security design and the auction format. We define a notion of the steepness of a set of securities, and show that steeper securities lead to higher revenues. We also show that the revenue equivalence principle holds for equity and cash auctions, but that it fails for debt (second-price auctions are superior) and for options (a first-price auction yields higher revenues). We then show that an informal auction yields the lowest possible revenues across all possible formal mechanisms. Finally, we extend our analysis to consider the effects of liquidity constraints, different information assumptions, and aspects of moral hazard.

On the Concentration of Allocations and Comparisons of Auctions in Large Economies

We analyze competitive pressures in a sequence of auctions with a growing number of bidders, in a model that includes private and common valuations as special cases. We show that the key determinant of bidders' surplus (and implicitly auction revenue) is how the goods are distributed. In any setting and sequence of auctions where the allocation of good(s) is concentrated among a shrinking proportion of the population, the winning bidders enjoy no surplus in the limit. If instead the good(s) are allocated in a dispersed manner so that a non-vanishing proportion of the bidders obtain objects, then in any of a wide class of auctions bidders enjoy a surplus that is bounded away from zero. Moreover, under dispersed allocations, the format of the auction matters. If bidders have constant marginal utilities for objects up to some limit, then uniform price auctions lead to higher revenue than discriminatory auctions. If agents have decreasing marginal utilities for objects, then uniform price auctions are asymptotically efficient, while discriminatory auctions are asymptotically inefficient. Finally, we show that in some cases where dispersed allocations are efficient, revenue may increase by bundling goods at the expense of efficiency

The Relevance of a Choice of Auction Format in a Competitive Environment

We examine the relevance of an auction format in a competitive environment by analyzing and comparing uniform and discriminatory price auctions with many bidders. We show that if the number of objects for sale is small relative to the number of bidders, then all equilibria of both auctions are approximately efficient and lead to approximately the same revenue. When the number of objects for sale is proportional to the number of bidders, then the particulars of the auction format matter. All equilibria of the uniform auction are efficient while all of the equilibria of the discriminatory auction are inefficient. The relative revenue rankings of the auction formats can go in either direction, depending on the specifics of the environment

Endogenous Information Flows and the Clustering of Announcements

We consider the release of information by a firm when the manager has discretion regarding the timing of its release. While it is well known that firms appear to delay the release of bad news, we examine how external information about the state of the economy (or the industry) affects this decision. We develop a dynamic model of strategic disclosure in which a firm may privately receive information at a time that is random (and independent of the state of the economy). Because investors are uncertain regarding whether and when the firm has received information, the firm will not necessarily disclose the information immediately. We show that bad news about the economy can trigger the immediate release of information by firms. Conversely, good news about the economy can slow the release of information by firms. As a result, the release of negative information tends to be clustered. Surprisingly, this result holds only when firms can preempt the arrival of external information by disclosing their own information first. These results have implications for conditional variance and skewness of stock and market returns

The wisdom of the crowd when acquiring information is costly

We consider a sequential investment process that is characteristic of crowdfunding platforms, among other contexts. Investors wish to avoid the cost of information acquisition and thus prefer to rely on information acquired by previous investors. This may lead to a phenomenon similar to an information cascade. We characterize the optimal policy that balances between the incentive to acquire information and the optimal investment decision. The policy is based on time-varying transparency levels such that it may be worthwhile to conceal some information in some periods

Raising Capital from Heterogeneous Investors

A firm raises capital from multiple investors to fund a project. The project succeeds only if the capital raised exceeds a stochastic threshold, and the firm offers payments contingent on success. We study the firm's optimal unique-implementation scheme, namely the scheme that guarantees the firm the maximum payoff. This scheme treats investors differently based on size. We show that if the distribution of the investment threshold is log-concave, larger investors receive higher net returns than smaller investors. Moreover, higher dispersion in investor size increases the firm's payoff. Our analysis highlights strategic risk as an important potential driver of inequality

Evidence games : truth and commitment

An evidence game is a strategic disclosure game in which an informed agent who has some pieces of verifiable evidence decides which ones to disclose to an uninformed principal who chooses a reward. The agent, regardless of his information, prefers the reward to be as high as possible. We compare the setup where the principal chooses the reward after the evidence is disclosed to the mechanism-design setup where he can commit in advance to a reward policy. The main result is that under natural conditions on the truth structure of the evidence, the two setups yield the same equilibrium outcome

Test design and minimum standards

We analyze test design and certification standards when an uninformed seller has the option to generate and disclose costly information regarding asset quality. We characterize equilibria by a minimum principle: the test and disclosure policy are chosen to minimize the asset’s value conditional on nondisclosure. Thus, when sellers choose the information provided, simple pass/fail certification tests are likely to dominate the market. A social planner could raise informational and allocative efficiency, and lower deadweight testing costs, by raising the certification standard. Monopolist certifiers also satisfy the minimum principle but set a higher standard and reduce testing rates to maximize revenue

Endogenous Information Flows and the Clustering of Announcements

We consider the strategic timing of information releases in a dynamic disclosure model. Because investors don’t know whether or when the firm is informed, the firm will not necessarily disclose immediately. We show that bad market news can trigger the immediate release of information by firms. Conversely, good market news slows the release of information by firms. Thus, our model generates clustering of negative announcements. Surprisingly, this result holds only when firms can preemptively disclose their own information prior to the arrival of external information. These results have implications for conditional variance and skewness of stock returns.