Ranking asymmetric auctions

We compare the expected revenue in first- and second-price auctions with asymmetric bidders. We consider “close to uniform” distributions with identical supports and show that in the case of identical supports the expected revenue in second-price auctions may exceed that in first-price auctions. We also show that asymmetry over lower valuations has a stronger negative impact on the expected revenue in first-price auctions than in second-price auctions. However, asymmetry over high valuations always increases the revenue in first-price auctions.     

Monotonicity in asymmetric first-price auctions with affiliation

I study monotonicity of equilibrium strategies in first-price auctions with asymmetric bidders, risk aversion, affiliated types, and interdependent values. Every mixed-strategy equilibrium is shown to be outcome-equivalent to a monotone pure-strategy equilibrium under the “priority rule” for breaking ties. This provides a missing link to establish uniqueness in the “general symmetric model” of Milgrom and Weber (Econometrica 50:1089–1122, 1982). Non-monotone equilibria can exist under the “coin-flip rule” but they are distinguishable: all non-monotone equilibria have positive probability of ties whereas all monotone equilibria have zero probability of ties. This provides a justification for the standard empirical practice of restricting attention to monotone strategies. Hendricks et al. (2003) provide an overview of recent empirical work. For a survey of experimental work, see Kagel and Levin (2002).     

Comparing first and second price auctions with asymmetric bidders

We study procurement auctions in which, as is common in practice, a group of sellers (incumbents, qualified bidders) is given an advantage, based, for example, on better reliability, quality, or incumbency status. We show conditions under which for any given first price handicap auction, there is a simple second-price design which dominates it. This generalizes a previous result for the case of an auction with one insider and one outsider (Mares and Swinkels in J Econ Theory, 2013) and sharpens our understanding of the classical result by Maskin and Riley (Rev Econ Stud 67:413–438, 2000).     

Asymptotic revenue equivalence of asymmetric auctions with interdependent values

We prove an asymptotic revenue equivalence among weakly asymmetric auctions with interdependent values, in which bidders have either asymmetric utility functions or asymmetric distributions of signals.     

A Dynkin game with asymmetric information

We study a Dynkin game with asymmetric information. The game has a random expiry time, which is exponentially distributed and independent of the underlying process. The players have asymmetric information on the expiry time, namely only one of the players is able to observe its occurrence. We propose a set of conditions under which we solve the saddle point equilibrium and study the implications of the information asymmetry. Results are illustrated with an explicit example.     

Characterization and computation of nash-equilibria for auctions with incomplete information

We consider a continuous sealed-bid auction model for an indivisible object with two bidders and incomplete information on both sides where the bidders' evaluations are assumed to be independently distributed on some real intervals. The price the winner (the highest bidder) has to pay is a given convex combination of the highest and the second highest (lowest) bid. It is shown that, for all but the second highest bid-price auction, all equilibrium-strategies are continuously differentiable and strictly monotonically increasing, and moreover, that the set of Nash-equilibria is completely characterized by a boundary value problem for a system of singular differential equations. In the case of symmetric data (independently and identically distributed true values) and for a particular class of asymmetric distributions (including uniform distributions), the boundary value problem is solved explicitly and uniquely.     

On the impact of low-balling: Experimental results in asymmetric auctions

The paper reports on a series of asymmetric auction experiments with private-independent values and two buyers. Maskin and Riley (2000) showed, under some conditions, that if one buyer has a greater probability than the other of not being able to bid, first-price auctions could yield lower revenues to the seller than second-price auctions. The data rejected this prediction because of an important overbidding when subjects received low values in first-price auctions. In this asymmetric setting, the observed overbidding cannot be explained by the usual risk aversion hypothesis and the detection of a learning pattern indicates that subjects used more an adaptive behaviour than a static one. An ad hoc bidding strategy for the buyers who are the most likely to bid explains the observed low bids better than the risk neutral equilibrium strategy. Finally, as subjects appear to have bid in equilibrium as if there were two other competitors instead of only one, their bidding behaviour can be thought to have displayed an over anxiousness about winning. Received: January 1999/Final version June 2001     

Contracting with asymmetric demand information in supply chains

We solve a buyback contract design problem for a supplier who is working with a retailer who possesses private information about the demand distribution. We model the retailer’s private information as a space of either discrete or continuous demand states so that only the retailer knows its demand state and the demand for the product is stochastically increasing in the state. We focus on contracts that are viable in practice, where the buyback price being strictly less than the wholesale price, which is itself strictly less than the retail price. We derive the optimal (for the supplier) buyback contract that allows for arbitrary allocation of profits to the retailer (subject to the retailer’s reservation profit requirements) and show that in the limit this contract leads to the first-best solution with the supplier keeping the entire channel’s profit (after the retailer’s reservation profit).     

Equilibrium and revenue in a family of common-value first-price auctions with differential information

We study a discrete common-value auction environment with two asymmetrically informed bidders. Equilibrium of the first-price auction is in mixed strategies, which we characterize using a doubly recursive solution method. The distribution of bids for the ex post strong player stochastically dominates that for the ex post weak player. This result complements Maskin and Riley’s (Rev Econ Stud 67:413–438, 2000) similar result for asymmetric private-value auctions. Finally, comparison with the dominance-solvable equilibrium in a second-price auction shows the Milgrom–Weber (Econometrica 50:1089–1122, 1982a) finding that the second-price auction yields at least as much revenue as the first-price auction fails with asymmetry: in some cases the first-price auction provides greater expected revenue, in some cases less.     

Contingency management under asymmetric information

We model a monopolist supplier whose supply to multiple buyers is disrupted. The supplier can take costly, speed-dependent actions, to restore supply. Buyers experience private backorder costs that are unknown to the supplier. We analyze the supplier's optimal contract structure and explore the impact of an alternate supplier.     

Patent-investment games under asymmetric information

This paper analyzes preemptive patenting in a two-stage real options game where an incumbent firm competes with a potential entrant firm for the patent of a substitute product in a product market with profit flow uncertainty. The incumbent suffers loss of monopoly in the product market if the entrant acquires the patent of a substitute product and later commercializes the product. Our patent-investment game model assumes that the entrant has complete information on the incumbent’s commercialization cost while the incumbent only knows the distribution of the entrant’s cost. We investigate the impact of information asymmetry on the preemption strategies adopted by the two competing firms on patenting the substitute product by comparing the optimal preemption strategies and the real option value functions of the two competing firms under complete information and information asymmetry. Our analysis reveals that the informationally disadvantaged incumbent always suffers from loss in its real option value of investment since it tends to act more aggressively in competing for the patent. On the other hand, the real option value of investment of the informationally advantaged entrant may be undermined or enhanced. The incumbent’s aggressive response under information asymmetry may lead to reversal of winner in the patent race. We also examine how information asymmetry may affect the occurrence of sleeping patent and the corresponding expected duration between the two stages of patenting and product commercialization.     

Supply chain coordination with controllable lead time and asymmetric information

This paper considers coordinated decisions in a decentralized supply chain consisting of a vendor and a buyer with controllable lead time. We analyze two supply chain inventory models. In the first model we assume the vendor has complete information about the buyer’s cost structure. By taking both the vendor and the buyer’s individual rationalities into consideration, a side payment coordination mechanism is designed to realize supply chain Pareto dominance. In the second model we consider a setting where the buyer possesses private cost information. We design the coordination mechanism by using principal-agent model to induce the buyer to report his true cost structure. The solution procedures are also developed to get the optimal solutions of these two models. The results of numerical examples show that shortening lead time to certain extent can reduce inventory cost and the coordination mechanisms designed for both symmetric and asymmetric information situations are effective.     

Non-cooperative joint replenishment under asymmetric information

We consider jointly replenishing n ex-ante identical firms that operate under an EOQ like setting using a non-cooperative game under asymmetric information. In this game, each firm, upon being privately informed about its demand rate (or inventory cost rate), submits a private contribution to an intermediary that specifies how much it is willing to pay for its replenishment per unit of time and the intermediary determines the maximum feasible frequency for the joint orders that would finance the fixed replenishment cost. We show that a Bayesian Nash equilibrium exists and characterize the equilibrium in this game. We also show that the contributions are monotone increasing in each firm’s type. We finally conduct a numerical study to compare the equilibrium to solutions obtained under independent and cooperative ordering, and under full information. The results show that while information asymmetry eliminates free-riding in the contributions game, the resulting aggregate contributions are not as high as under full information, leading to higher aggregate costs.     

Large auctions with risk-averse bidders

We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as ${n\longrightarrow \infty }We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as n? ￥{n\longrightarrow \infty } with risk-averse bidders is strictly below the risk-neutral limit. Therefore, these auction mechanisms are not revenue equivalent to large k-price auctions even to leading-order as n? ￥{n\longrightarrow \infty }.     

All-pay auctions with risk-averse players

We study independent private-value all-pay auctions with risk-averse players. We show that: (1) Players with low values bid lower and players with high values bid higher than they would bid in the risk neutral case. (2) Players with low values bid lower and players with high values bid higher than they would bid in a first-price auction. (3) Players’ expected utilities in an all-pay auction are lower than in a first-price auction. We also use perturbation analysis to calculate explicit approximations of the equilibrium strategies of risk-averse players and the seller’s expected revenue. In particular, we show that in all-pay auctions the seller’s expected payoff in the risk-averse case may be either higher or lower than in the risk neutral case.     

Preemptive patenting under uncertainty and asymmetric information

This paper examines the investment behaviour of an incumbent and a potential entrant that are competing for a patent with a stochastic payoff. We incorporate asymmetric information into the model by assuming that the challenger has complete information about the incumbent whereas the latter does not know the precise value of its opponent’s investment cost. We find that even a small probability of being preempted gives the informationally-disadvantaged firm an incentive to invest at the breakeven point where it is indifferent between investing and being preempted. By investing inefficiently early to protect its market share, the incumbent gives up not only its option to delay the investment, but also reduces the value of the firm by an amount that increases with the investment cost incurred and the potential loss of market share.     

Dominant strategies, superior information, and winner's curse in second-price auctions

In a general model of common-value second-price auctions with differential information, we show equivalence between the following characteristics of a bidder: (i) having a dominant strategy; (ii) possessing superior information; (iii) being immune from winner's curse. When a dominant strategy exists, it is given by the conditional expectation of the common value with respect to bidder's information field; if the dominant strategy is used, other bidders cannot make a profit. Final version November 2001     

A new equilibrium in the one-sided asymmetric information market with pairwise meetings

We reconsider the model used by Serrano and Yosha (1993) who were interested in information revelation in markets with pairwise meetings. We prove that there exists an additional equilibrium not detected in the original paper and show that this equilibrium is characterized by incomplete revelation of information which was not the case of the other already identified equilibria of the model.