Jingfeng Lu

Optimal auctions with asymmetric financial externalities

This paper studies optimal auction design with asymmetric linear financial externalities among bidders. When the matrix Γ that relates biddersʼ payoffs to their payments is nonsingular, the payment-related component in the design objective must equal a unique linear combination of its counterparts in bidderʼs payoffs. If all multipliers of the linear combination are nonnegative, a modified Myerson procedure is discovered for deriving the optimal design. If any multiplier is negative, an arbitrarily high value can be achieved for design objective by setting proper fixed transfers to bidders. When the matrix Γ is singular, the unbounded optimum result typically prevails. We applied our method to auctions with cross shareholdings and charity auctions for revenue-maximizing and efficient designs.

Efficient and optimal mechanisms with private information acquisition costs

In auctions with private information acquisition costs, we completely characterize (socially) efficient and (revenue) optimal two-stage mechanisms, with the first stage being an entry right allocation mechanism and the second stage being a traditional private good provision mechanism. Both efficiency and revenue optimality require that the second-stage selling mechanism be ex post efficient and the number of entry slots be endogenously determined. We show that both efficient and optimal entry can be truthfully implemented in dominant strategies, and can also be implemented via all-pay, though not uniform-price or discriminatory-price, auctions.

Auctions with selective entry

We consider auctions with entry based on a general analytical framework we call the Arbitrarily Selective (AS) model. We characterize symmetric equilibrium in a broad class of standard auctions within this framework, in the process extending the classic revenue equivalence results of Myerson (1981), Riley and Samuelson (1981) and Levin and Smith (1994) to environments with endogenous and arbitrarily selective entry. We also explore the relationship between revenue maximization and efficiency, showing that a revenue maximizing seller will typically employ both higher-than-efficient reservation prices and higher-than-efficient entry fees.

Disclosure Policy in Tullock Contests with Asymmetric Stochastic Entry

We examine how disclosure policy can be optimally designed to incentivize contestants when their participation is exogenously stochastic. In a generalized Tullock contest setting with two players who are asymmetric in both their values and entry probabilities, we fully characterize the necessary and sufficient conditions under which no disclosure dominates full disclosure. We find that the comparison depends solely on a balance effect exercised by entry probabilities on the expected total effort. The optimal disclosure policy must better balance the competition. These conditions continue to hold when the precision r of Tullock contests is endogenously chosen by the designer.

Contests with endogenous entry

This paper studies the effort-maximizing design of a complete-information contest with endogenous entry. A fixed pool of homogenous potential players with identical marginal bidding cost must incur an entry cost to enter the contest before they bid for prize(s). The designer can flexibly adjust the impact function of a generalized nested lottery contest and use a fixed budget to fund single or multiple prizes. Applying Dasgupta and Maskin (Rev Econ Stud 53(1):1–26, 1986), we establish the existence of symmetric equilibrium for all contest mechanisms concerned. A uniform upper bound for expected overall bids is identified for any eligible contest, assuming that potential bidders play symmetric equilibria. We show that the upper bound can be achieved through a Tullock contest with a single contingent prize, which adopts compatible bundles of success function and entry fees/subsidies. In particular, we identify the conditions under which the optimum can be achieved by solely setting the right discriminatory power in a Tullock contest with a single fixed prize. Finally, our analysis characterizes the optimal shortlisting rule, which reveals that the contest designer generally should exclude potential bidders to elicit higher bids.

Pairing provision price and default remedy: optimal two-stage procurement with private R&D efficiency

This article studies cost‐minimizing two‐stage procurement with Research and Development (R&D). The principal wishes to procure a product from an agent. At the first stage, the agent can conduct R&D to discover a more cost‐efficient production technology. First‐stage R&D efficiency and effort and the realized second‐stage production cost are the agents private information. The optimal two‐stage mechanism is implemented by a menu of single‐stage contracts, each specifying a fixed provision price and remedy paid by a defaulting agent. A higher delivery price is paired with a higher default remedy, and a more efficient type opts for a higher price and higher remedy.

Optimal prize allocation in contests: The role of negative prizes

In this paper, we analyze the role of negative prizes in contest design with a fixed budget, risk-neutral contestants, and independent private abilities. The effort-maximizing prize allocation rule features a threshold. When the highest effort is above the threshold, all contestants with lower efforts receive negative prizes. These negative prizes are used to augment the prize to the contestant with the highest effort, which better incentivizes contestants with higher abilities. When no contestants effort exceeds the threshold, all contestants equally split the initial budget (or a portion of it) to ensure their participation. We find that allowing negative prizes can increase the expected total effort dramatically. In particular, if no bound is imposed on negative prizes, the expected total effort can be arbitrarily close to the highest possible effort inducible when all contestants have the maximum ability with certainty. The above contest is shown to be the optimal mechanism for a more general class of mechanisms.

Identification and Inference in First-Price Auctions with Risk-Averse Bidders and Selective Entry

We study identification and estimation in first-price auctions with risk averse bidders and selective entry, building on a flexible entry and bidding framework we call the Affiliated Signal with Risk Aversion (AS-RA) model. This framework extends the AS model of Gentry and Li (2014) to accommodate arbitrary bidder risk aversion, thereby nesting a variety of standard models as special cases. It poses, however, a unique methodological challenge – existing results on identification with risk aversion fail in the presence of selection, while the selection-robust bounds of Gentry and Li (2014) fail in the presence of risk aversion. Motivated by this problem, we translate excludable variation in potential competition into identified sets for AS-RA primitives under various classes of restrictions on the model. We show that a single parametric restriction – on the copula governing selection into entry – is typically sufficient to restore point identification of all primitives. In contrast, a parametric form for utility yields point identification of the utility function but only partial identification of remaining primitives. Finally, we outline a simple semiparametric estimator combining Constant Relative Risk Aversion utility with a parametric signal-value copula. Simulation evidence suggests that this estimator performs very well even in small samples, underscoring the practical value of our identification results.