We analyze optimal auction mechanisms when bidders base costly entry decisions on their valuations, and bidders pay with a fixed royalty rate plus cash. With sufficient valuation uncertainty relative to entry costs, the optimal mechanism features asymmetry so that bidders enter with strictly positive but different (ex-ante) probabilities. When bidders are ex-ante identical, higher royalty rates—which tie payments more closely to bidder valuations—increase the optimal degree of asymmetry in auction design, further raising revenues. When bidders differ ex-ante in entry costs, the seller favors the low cost entrant; whereas when bidders have different valuation distributions, the seller favors the weaker bidder if entry costs are low, but not if they are high. Higher royalty rates cause the seller to favor the weaker bidder by less, and the strong bidder by more.
Academic & Professional Qualification
- Ph.D., Carnegie Mellon University
- Ph.D., University of Virginia
- B.S., Peking University
Prof. Tingjun Liu received his Ph.D. in Financial Economics from Carnegie Mellon University in 2007. He also holds a B.S. in Physics from Peking University, and a Ph.D. in Physics from the University of Virginia. Prior to joining The University of Hong Kong, Tingjun taught at Renmin University of China and Cheung Kong Graduate School of Business.
Tingjun's research interests include theoretical corporate finance, mergers and acquisitions, and auction theory. His work on mergers and acquisitions shows that if an acquiring firm does not have enough cash to pay for the acquisition — and hence needs to obtain financing after winning, the acquirer will offer a premium to the target firm. Such a premium signals a high quality of the acquirer and facilitates the post-acquisition financing, the benefit of which outweighs the cost of a higher acquisition price. His research on auction theory focuses on security-bid auctions — auctions in which bidders pay with securities that are claims to project revenues. Security-bid auctions are more complicated than cash auctions because the value of securities depends on the bidder’s private information. Tingjun explores how a seller can overcome such complications to best design security-bid auctions. He also studies the strategic nondisclosure in management buyout, showing how nondisclosure can create a winner’s curse, and via this channel increased competition can reduce shareholder payoffs. Externally, he serves on the program committees of leading international conferences including Western Finance Association meetings, European Finance Association meetings, and Midwest Finance Association conferences.
- Theoretical Corporate Finance
- Mergers and Acquisitions
- Auction Theory
- “Costly Auction Entry, Royalty Payments, and the Optimality of Asymmetric Designs,”
(with Dan Bernhardt and Takeharu Sogo), Journal of Economic Theory, 2020, 188, 105041.
- “Optimal Equity Auctions with Two-dimensional Types,”
(with Dan Bernhardt), Journal of Economic Theory, 2019, 184, 104913.
- “Targeting Target Shareholders,”
(with Dan Bernhardt and Robert Marquez), Management Science, 2018, 64(4): 1489-1509.
- “Endogenous Entry to Security-Bid Auctions,”
(with Dan Bernhardt and Takeharu Sogo), American Economic Review, 2016, 106(11): pp. 3577-89.
- “Optimal Equity Auctions with Heterogeneous Bidders,”
Journal of Economic Theory, 2016, 166, pp. 94-123.
- “Takeover Bidding with Signaling Incentives”,
The Review of Financial Studies, 2012, 25(2), pp. 522-556.
- “Hedging and Competition,”
(with Christine Parlour), Journal of Financial Economics, 2009, 94(3), pp. 492-507.
Awards and Honours
- General Research Fund awards (PI) for three consecutive years, Research Grants Council of Hong Kong, 2017-2019
- UG Teaching Reward, Faculty of Business and Economics, Hong Kong University, 2018
- Featured article, Targeting Target Shareholders, Management Science, 2018
- Research Output Prize, Faculty of Business and Economics, Hong Kong University, 2017
We analyze the design and performance of equity auctions when bidder's valuations and opportunity costs are private information, distributed according to an arbitrary joint density that can differ across bidders. We identify, for any incentive compatible mechanism, an equivalent single-dimensional representation for uncertainty. We then characterize the revenue-maximizing and surplus-maximizing equity mechanisms, and compare revenues in optimal equity and cash auctions. Unlike in cash auctions, the adverse selection arising from bidders' two-dimensional types in equity auctions can lead to a global violation of the regularity condition, which represents a maximal mismatch between incentive compatibility and maximization of revenue or surplus. Such mismatch can lead a seller to exclude bidders and demand a bidder-specific stake from a non-excluded bidder, providing insights into when a firm should employ an auction and when it should just negotiate with a single bidder.