ON DETAIL‐FREE MECHANISM DESIGN AND RATIONALITY*

Mechanism design theory has been criticized, because mechanisms depend on the detail of specification and agents’ behaviour relies on strong rationality assumptions. Hence the study of “detail‐free” mechanism design with weak rationality is important as a practical theory. This paper emphasizes that, even if we confine our attention to detail‐free mechanisms with weak rationality, there exists plenty of scope for the development of new and significant ideas. I describe my recent work along these lines, and argue that stochastic decisions work in large double auction environments, and that moral preferences improve the implementability of social choice functions.     

An optimal auction with correlated values and risk aversion

We consider an auction setting where the buyers are risk averse with correlated private valuations (CARA preferences, binary types), and characterize the optimal mechanism for a risk-neutral seller. We show that the optimal auction extracts all buyer surplus whenever the correlation is sufficiently strong (greater than 1/3 in absolute value), no matter how risk averse the buyers are. In contrast, we note that a sufficiently risk-averse seller would not use a full rent extracting mechanism for any positive correlation of the valuations even if the buyers were risk neutral.     

Optimal collusion-proof auctions

We study an optimal collusion-proof auction in an environment where subsets of bidders may collude not just on their bids but also on their participation. Despite their ability to collude on participation, informational asymmetry facing the potential colluders can be exploited significantly to weaken their collusive power. The second-best auction — i.e., the optimal auction in a collusion-free environment — can be made collusion-proof, if at least one bidder is not collusive, or there are multiple bidding cartels, or the second-best outcome involves a non-trivial probability of the object not being sold. Regardless, optimal collusion-proof auction prescribes non-trivial exclusion of collusive bidders, i.e., a refusal to sell to any collusive bidder with positive probability.     

Selling options

Contracts often take the form of options: oil fields can be abandoned, planning permission may go unused, and acquired firms can be liquidated. We consider a seller who auctions a dynamic option among N agents. After the auction, the economy evolves and the winning bidder chooses both if and when to execute the option. The revenue-maximising auction consists of an up-front bid and a contingent fee, where the latter is chosen in a Pigouvian manner, so the winning agent's choice of exercise time maximises the seller's revenue. This contingent payment is time- and state-invariant, so the seller does not have to observe post-auction information in order to implement the optimal auction. The revenue-maximising mechanism induces a dynamic distortion: the option is exercised later than under the comparable welfare-maximising mechanism.     

Asymmetric English auctions

This paper studies equilibria of the n-bidder single-object English, or open ascending price, auction in a setting with interdependent values and asymmetric bidders. Maskin (in: H. Siebert (Ed.), Privatization, Institut fur Weltwirtschaften der Universität Kiel, Kiel, 1992, pp. 115-136.) showed that if the values satisfy a “single crossing” condition, then the two-bidder English auction has an efficient equilibrium. In this paper, two extensions of the single crossing condition, the “average crossing” condition and the “cyclical crossing” condition, are introduced. The main result is that under either of these conditions the n-bidder English auction has an efficient equilibrium.     

The high/low divide: Self-selection by values in auction choice

Most prior theoretical and experimental work involving auction choice has assumed bidders find out their value after making a choice of which auction to enter. We examine whether or not bidders knowing their value prior to making a choice of which among multiple alternative auction formats to enter impacts their choice decision and/or the outcome of the auctions. The results show a strong impact on auction choice. Subjects with low values choose the first price sealed bid auction more often while subjects with high values choose the ascending auction more often. The number of bidders in each auction, revenue, efficiency and average bidder surplus all end up equalized.     

Existence of equilibrium in large double auctions

We show the existence of a pure strategy, symmetric, increasing equilibrium in double auction markets with correlated, conditionally independent private values and many participants. The equilibrium we find is arbitrarily close to fully revealing as the market size grows. Our results provide strategic foundations for price-taking behavior in large markets.     

向上叫价时钟双向拍卖机制设计

通过深入分析统一价格密封双向拍卖机制的诸多缺陷，充分借鉴单向拍卖市场上时钟拍卖的基本思想，将时钟拍卖引入双向拍卖市场，构建了一个无论从分配效率方面考虑还是从竞价风险方面考虑都优于统一价格密封双向拍卖机制，不仅为同类物品确定统一价格，还可以为不同类的物品确定其不同的价格的向上叫价时钟双向拍卖机制。     

Auctions with private uncertainty and resale opportunities

When an auction is followed by an opportunity for resale, bidder valuations are endogenously determined, reflecting anticipated profit from buying/selling in the resale market. These valuations vary with the resale market structure, can differ across auction types, and may be lower or higher than if resale were impossible. Although resale introduces a common value element to the model, revenue equivalence can hold; when it fails, this is due not to affiliation but to differences in information conveyed to the secondary market. Information linkages between markets can also lead to signaling and, in some cases, preclude separation in the auction.     

Competing auctions with endogenous quantities

Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593-1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].     

Mediation, arbitration and negotiation

We compare three common dispute resolution processes - negotiation, mediation, and arbitration - in the framework of Crawford and Sobel [V. Crawford, J. Sobel, Strategic information transmission, Econometrica 50 (6) (1982) 1431-1451]. Under negotiation, the two parties engage in (possibly arbitrarily long) face-to-face cheap talk. Under mediation, the parties communicate with a neutral third party who makes a non-binding recommendation. Under arbitration, the two parties commit to conform to the third party recommendation. We characterize and compare the optimal mediation and arbitration procedures. Both mediators and arbitrators should optimally filter information, but mediators should also add noise to it. We find that unmediated negotiation performs as well as mediation if and only if the degree of conflict between the parties is low.     

Charity auctions with multiple goods: Bidding behavior and revenue

In a charity auction with multiple goods, we show that the highest-losing bid uniform price auction revenue dominates its lowest-winning bid counterpart. Only in the highest-losing bid uniform price auction is bidding independent of the number of goods and players and revenue increasing in the number of goods.     

On optimal head starts in all-pay auctions

We consider a two-player all-pay auction with symmetric independent private values that are uniformly distributed. The designer chooses the size of a head start that is given to one of the players. The designer’s objective is to maximize a convex combination of the expected highest effort and the expected aggregate effort. Unless the weight on the highest effort is one, small head starts are always worse than no head start. Moreover, the optimal head start is strictly positive if and only if the weight on the highest effort is large enough.     

Best-of-three all-pay auctions

We study a best-of-three all-pay auction. It is shown that with values of winning and without values of losing, this auction is less productive (the players’ total expected effort is smaller) than the one-stage all-pay auction. However, with different values of losing over the contest’s stages it may be more productive than the one-stage all-pay auction.     

Revenue ranking of first-price auctions with resale

When the price setter in post-auction resale is chosen according to exogenous probabilities, Hafalir and Krishna (2008) [2] showed that the first-price auction brings more expected revenues than the second-price auction with truth-bidding bidders. We complete their revenue ranking by proving that the first-price auction produces higher expected revenues the higher the probability the auction winner sets the resale price.     

Dynamic legislative decision making when interest groups control the agenda

We consider dynamic decision making in a legislature, in which in each period legislators vote between the status quo (previous period?s policy) and a new bill. However, the agenda formation process is captured by interest groups, that is, the new bill on the agenda is determined by an all-pay auction among these groups. We show that convergence to the median voter of the legislature arises if interest groups are patient enough but not necessarily otherwise. We characterize the bound on the speed of convergence in a family of stationary equilibria in which policy bounces between right-wing and left-wing policies. We also show that convergence may be faster if organized interest groups represent only one side of the policy space, e.g., when only business and not consumer interests are organized.     

The value of an informed bidder in common value auctions

I compare two information structures in a common value first-price auction with two bidders: In one, each of the two bidders knows only his own signal about the value of the object, and in the other, one of the bidders learns his opponent's signal as well. Gaining the additional information in the second information structure makes the informed bidder worse off if the value is submodular in the bidders' signals and better off if it is supermodular. If the value is supermodular, then the seller's revenue tends to be lower with the informed bidder than without.     

An experimental test of design alternatives for the British 3G/UMTS auction

In spring 2000, the British government auctioned off licences for Third Generation mobile telecommunications services. In the preparation of the auction, two designs involving each a hybrid of an English and a sealed-bid auction were considered by the government: A discriminatory and a uniform price variant. We report an experiment on these two designs, and also compare the results to those with a pure English auction. Both hybrids are similar in efficiency, revenue differences disappear as bidders get experienced. Compared to the discriminatory format, the pure English auction induces more entry.     

A nearly optimal auction for an uninformed seller

This paper describes a nearly optimal auction mechanism that does not require previous knowledge of the distribution of values of potential buyers. The mechanism we propose builds on the new literature on the elicitation of information from experts. We extend the latter to the case where the secret information shared by the experts–potential buyers in our model–can be used against them if it becomes public knowledge.     

Commitment in sequential auctioning: advance listings and threshold prices

This paper models sequential auctioning of two perfect substitutes by a strategic seller, who learns about demand from the first-auction price. The seller holds the second auction only when the remaining demand is strong enough to cover her opportunity cost. Bidding in anticipation of such a contingent future auction is characterized, including a sufficient condition for existence of an invertible (increasing symmetric pure-strategy) bidding equilibrium that facilitates the seller’s learning. A unique invertible bidding equilibrium exists for the Dutch auction format, but only when the second auction is sufficiently discounted by the bidders. In the equilibrium, high-valuation bidders shade their bids down as if the second auction were guaranteed. To counter such strategic bidding, the seller would value ex-ante commitment to hold the second auction less often. Three forms of such commitment are analyzed: commitment to list future auctions in advance, commitment to not hold the second auction unless the first price exceeds a publicly announced threshold, and commitment to a reserve-price in the second auction. I would like to thank Georgios Katsenos, Thomas Jeitschko, Miguel Villas-Boas, George Deltas, and an anonymous referee for thorough and insightful feedback.