We study security-bid auctions in which bidders compete for an asset by bidding with securities whose payments are contingent on the asset's realized value. In formal security-bid auctions, the seller restricts the security design to an ordered set and uses a standard auction format (e.g., first-or second-price Auction theory and its applications have become increasingly important as an area of economic research over the last 20 years. As a result, we now have a better understanding of how the structure of an auction affects its outcome. Almost all the existing literature studies the case when bidders use cash payments, so that the value of a bid is not contingent on future events.In a few cases, such as art auctions, the realized value is subjective and cannot be used as a basis for payment; however, this is the exception. In many important applications, the realization of the future cash flow generated by the auctioned asset or project can be used in determining the actual payment. That is, the bids can be securities whose values are derived from the future cash flow. We call this setting a securitybid auction, and provide an extensive characterization of such auctions.Formal auctions of this type are commonly used in government sales of oil leases, wireless spectrum, highway building contracts, and leadplaintiff auctions. Informal auctions of this type (in the sense that formal auction rules are not set forth in advance) are common in the private sector. Examples include authors selling publishing rights, entrepreneurs selling their firm to an acquirer or soliciting venture capital, and sports associations selling broadcasting rights.
1The major difference between a formal and an informal mechanism is the level of commitment by the seller. In an informal mechanism, bidders choose which securities to offer, and the seller selects the most attractive offer ex post. In this case, the auction contains the elements of a signaling game because the seller may infer bidders' private information from their security choices when evaluating their offers. In a formal mechanism the seller restricts bidders to use
We show that it is impossible to achieve collusion in a duopoly when (a) goods are homogenous and firms compete in quantities; (b) new, noisy information arrives continuously, without sudden events; and (c) firms are able to respond to new information quickly. The result holds even if we allow for asymmetric equilibria or monetary transfers. The intuition is that the flexibility to respond quickly to new information unravels any collusive scheme. Our result applies to both a simple stationary model and a more complicated one, with prices following a mean-reverting Markov process, as well as to models of dynamic cooperation in many other settings. (JEL D43, L12, L13)
Motivated by recent cartel practices, a stable collusive agreement is characterized when firms' prices and quantities are private information. Conditions are derived whereby an equilibrium exists in which firms truthfully report their sales and then make transfers within the cartel based on these reports. The properties of this equilibrium fit well with the cartel agreements in a number of markets including citric acid, lysine, and vitamins. (JEL D43, D82, K21, L12, L61, L65)
A seller wishes to sell multiple goods by a deadline, for example, the end of a season. Potential buyers enter over time and can strategically time their purchases. Each period, the profit-maximizing mechanism awards units to the buyers with the highest valuations exceeding a sequence of cutoffs. We show that these cutoffs are deterministic, depending only on the inventory and time remaining; in the continuous-time limit, the optimal mechanism can be implemented by posting anonymous prices. When incoming demand decreases over time, the optimal cutoffs satisfy a one-period-look-ahead property and prices are defined by an intuitive differential equation.We are grateful to the editor, Jesse Shapiro, and the referees for many excellent comments. We thank
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