We study a novel mechanism design model in which agents each arrive sequentially and choose one action from a set of actions with unknown rewards. The information revealed by the principal affects the incentives of the agents to explore and generate new information. We characterize the optimal disclosure policy of a planner whose goal is to maximize social welfare. One interpretation of our result is the implementation of what is known as the "wisdom of the crowd." This topic has become increasingly relevant with the rapid spread of the Internet over the past decade.

We present several results regarding randomized one-round communication complexity. Our results include a connection to the VCdimension, a study of the problem of computing the inner product of two real valued vectors, and a relation between "simultaneous" protocols and one-round protocols. We study very simple types of protocols which include only one round of communication. These protocols were introduced by Yao (1979) and were later studied by several authors (cf.

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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