Information Design and Asymmetric Auction


This dissertation contains two topics. The first topic focuses on how to use information design to minimize costs of implementing a policy that guarantees 100% passing rate of all participants by providing enough compensation for the their effort. The second topic explores an auction setting which involves financially distressed business insider and deep-pocketed investor. Chapter 1 studies the design of a feedback system that encourages a group of agents with different ability levels to complete a task, given that they are sufficiently compensated for their effort. The goal is to design the feedback system in such a way that guarantees all agents finish the task regardless of their ability and at the same time minimizes the compensation required. In the model, a group of agents faces a task that requires costly effort to complete. An agent’s progress toward task-completion is determined by both his ability and effort. The agent does not know his ability nor his progress toward task-completion, but the effort is his private information. A principal can monitor each agent’s progress, but she has no information about an agent’s ability nor effort. The principal’s job is to provide enough compensation for the agents so that they all complete the task in the end. Meanwhile, the principal wants to keep the total compensation to a minimum. An optimal feedback system balances the trade-off between revealing too much information and letting the agents enjoy the information-rent from their privately known effort, versus revealing too little information and resulting in some agents over-exerting effort. The first-best outcome is one in which the principal’s expenditure exactly equals the aggregate amount of effort that is required so that all agents successfully finish the task. I first show under what conditions a feedback system can be designed to achieve the first-best outcome, and when the first-best outcome is not attainable, what the optimal feedback system should be. I then demonstrate that once more flexibility is allowed in designing such system, the first-best outcome is always attainable. Chapter 2 studies an auction model with business insiders who are potentially budget-constrained and a deep-pocketed investor who is only constrained by his lack of insider knowledge but not his budget. I show that the outsider status sometimes puts the deep-pocketed investor in danger of the winner’s curse. As a result, when the probability of business insiders being budget-constrained is low, the outsider bids more conservatively. Consequently, the auction’s allocation efficiency is higher when insiders are less likely to be constrained by their budget. However, the seller does not necessarily benefit from this increase in allocation efficiency, as the expected revenue can decrease as a result of the deep-pocketed investor shading his bid. The presence of more business insiders helps alleviate the winner’s curse and increase the seller’s expected revenue in some situations. But in certain cases, for example, when the outsider’s valuation depends on the average of the insiders’ valuations, having many insiders in the auction only makes the outsider more cautious in his bidding. Therefore, aside from insiders’ budget, the relationship between the outsider’s valuation and those of the insiders’ is equally if not more important from the seller’s perspective. In addition, I also demonstrate that a reservation price has different implications for the allocation efficiency and the seller’s expected revenue. In particular, a reservation price always hurt the former – the higher the reservation price, the lower the allocation efficiency. However, a moderate reservation price can improve the seller’s revenue.

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