Optimal auctions with information acquisition

This paper studies optimal auction design in a private value setting with endogenous information gathering. We develop a general framework for modeling information acquisition when a seller wants to sell an object to one of several potential buyers, who can each gather information about their valuations prior to participation in the auction. We first demonstrate that the optimal monopoly price is always lower than the standard monopoly price. We then show that standard auctions with a reserve price remain optimal among symmetric mechanisms, but the optimal reserve price lies between the ex ante mean valuation of bidders and the standard reserve price in Myerson (1981). Finally, we show that the optimal asymmetric mechanism softens the price discrimination against “strong” bidders.     

Auctions with costly information acquisition

We characterize optimal selling mechanisms in auction environments where bidders must incur a cost to learn their valuations. These mechanisms specify for each period, as a function of the bids in previous periods, which new potential buyers should be asked to bid. In addition, these mechanisms must induce the bidders to acquire information about their valuations and to reveal this information truthfully. Using a generalized Groves principle, we prove a very general “full extraction of the surplus” result: the seller can obtain the same profit as if he had full control over the bidders’ acquisition of information and could have observed directly their valuations once they are informed. We also present appealing implementations of the optimal mechanism in special cases. For helpful comments we thank George Deltas, David Martimort, an anonymous referee, and seminar participants in Mannheim, Rutgers, Tel Aviv, Toulouse, the Society for Economic Design 2002 conference in New York, and the 2003 North American Summer Meetings of the Econometric Society in Evanston, IL. Yossi Spiegel thanks the IIBR for financial assistance and Charles Zheng thanks the NSF for grant SES-0214471.     

Sequential negotiations with costly information acquisition

Negotiations about a merger or acquisition are often sequential and only partially disclose to bidders information about each otherʼs bids. This paper explains the seller optimality of partial disclosure in a single-item private-value auction with two bidders. Each bidder can inspect the item at a nonprohibitive cost. If a revenue-maximizing seller cannot charge bidders for the information about the otherʼs bid, then the seller optimally runs a sequential second-price auction with a reserve price and a buy-now price. The seller prefers to keep the bids confidential and, sometimes, to hide the order in which he approaches the bidders.     

Access regulation with asymmetric termination costs

In many telecommunications markets incumbent providers enjoy a demand-side advantage over any entrant. However, market entrants may enjoy a supply-side advantage over the incumbent, since they are more efficient or operate on innovative technologies. Considering both a supply-side and a demand-side asymmetry, the present model analyzes the effect of two regulatory regimes: an access markup for a low cost network and reciprocal charges below the costs of a high cost network. Both regimes may have adverse effects on subscribers, market shares, and profits. It can be shown that an access markup is not generally beneficial and an access deficit not generally detrimental for the respective networks.     

The social value of public information with costly information acquisition

In a beauty contest framework, public authorities decide the accuracy of public information evaluating how it affects individual actions and private information acquisition. More precise public information increases welfare whenever its marginal cost does not exceed that of private information.     

Optimal voting schemes with costly information acquisition

A group of individuals with identical preferences must make a decision under uncertainty about which decision is best. Before the decision is made, each agent can privately acquire a costly and imperfect signal. We discuss how to design a mechanism for eliciting and aggregating the collected information so as to maximize ex-ante social welfare.We first show that, of all mechanisms, a sequential one is optimal and works as follows. At random, one agent at a time is selected to acquire information and report the resulting signal. Agents are informed of neither their position in the sequence nor of other reports. Acquiring information when called upon and reporting truthfully is an equilibrium.We next characterize the ex-ante optimal scheme among all ex-post efficient mechanisms. In this mechanism, a decision is made when the precision of the posterior exceeds a cut-off that decreases with each additional report. The restriction to ex-post efficiency is shown to be without loss when the available signals are sufficiently imprecise. On the other hand, ex-post efficient mechanisms are shown to be suboptimal when the cost of information acquisition is sufficiently small.     

Investment in information acquisition

This paper presents a simple model in which a community must decide on the amount of real investment and investment in information so as to maximise the expected utility of consumption over two periods. It is shown that under conditions involving the product of the elasticity of the marginal utility of consumption and the elasticity of the production function that optimal real investment is either a monotone function of the information or is independent of it. In the former case information is of value and it is optimal to invest a positive amount in information acquisition. In the latter case information has no value and society devotes no resources to information acquisition.     

Optimal information acquisition and monetary policy

I study optimal monetary policy with an expectational AS curve and private agents who optimally choose their amount of information pertinent to predicting policy. Shocks with time-varying variance (ARCH) induce interesting information acquisition (IA) dynamics; optimal IA affects optimal policy and vice versa. Under discretion, IA dynamics cause time-varying effectiveness of policy because of the expectational AS curve; policy may be rendered completely ineffective. In policy game equilibrium, a fall in the shock’s variance typically induces less IA and raises welfare. In one exceptional case the opposite occurs, a result which does not require implausible unstable equilibria. An agent becoming informed increases the endogenous component of economic volatility; IA therefore has a negative externality. Under commitment policy’s effectiveness is again time-varying, but policy is never completely ineffective: commitment enables the central bank to credibly limit policy’s volatility; this limits private agents’ incentive to become informed, so limits expectation-induced policy neutrality.     

Social learning and costly information acquisition

Summary. Short-lived agents want to predict a random variable q\theta and have to decide how much effort to devote to collect private information and consequently how much to rely on public information. The latter is just a noisy average of past predictions. It is shown that costly information acquisition prevents an unbounded accumulation of public information if (and only if) the marginal cost to acquire information is positive at zero (C￠(0) > 0)(C^\prime (0) > 0). When C￠(0) = 0C^\prime (0) = 0 public precision at period n, _boxclose_boxclose\tau_n, tends to infinity with n but the rate of convergence of public information to q\theta is slowed down with respect to the exogenous information case. At the market outcome agents acquire too little private information. This happens either with respect to a (decentralized) first best benchmark or, for n large, with respect to a (decentralized) second best benchmark. For high discount factors the limit point of market public precision always falls short of the welfare benchmarks whenever C￠(0) > 0C^\prime (0) > 0. In the extreme, as the discount factor tends to one public precision tends to infinity in the welfare-optimal programs while it remains bounded at the market solution. Otherwise, if C￠(0) = 0C^\prime (0) = 0 public precision accumulates in an unbounded way both at the first and second best solutions. More public information may hurt at either the market or second best solutions.     

The social value of public information with convex costs of information acquisition

In a beauty contest framework, welfare can decrease with public information if the precision of private information is exogenous, whereas welfare necessarily increases with public information if the precision is endogenous with linear costs of information acquisition. The purpose of this paper is to reconcile these results by considering nonlinear costs of information acquisition. The main result of this paper is a necessary and sufficient condition for welfare to increase with public information. Using it, we show that costs of information acquisition are linear if and only if welfare necessarily increases with public information. Thus, welfare can decrease with public information for any strictly convex costs. This is because convex costs mitigate the so-called crowding-out effect of public information on private information, thereby making the social value of public information with endogenous precision closer to that with exogenous precision.     

Competitive screening and information transmission

We consider a model in which schools and colleges compete for high-ability students, which are independently identified through a costly screening procedure. This independence creates a channel through which students' preferences affect the strategic interaction between schools: students with competing offers accept the most-preferred one, increasing the screening costs of unpopular schools. When preferences between schools are more heterogeneous, schools screen more, increasing the proportion of students with multiple offers, but paradoxically reducing the extent to which their preferences determine their outcomes. By observing the students' schools of origin, colleges can free-ride of the fierce competition that occurs during screening.     

A common value auction model with endogenous entry and information acquisition

Summary Much of the auction literature assumes both a fixed number of bidders and a fixed information setting. This sidesteps the important and often costly decisions a potential bidder must make prior to an auction: Should I enter and, if I do, what level of resources should I expend evaluating the good prior to bidding? We answer these questions for a stylized information model of a common value auction. The expected selling price is shown to be the expected value of the good minus the expected aggregate entry and information costs of the bidders. Thus, the seller indirectly pays for these costs to the bidders. There are auctions where the seller seemingly restricts the bidders' information expenditures. While this restriction does influence the entry decision, we demonstrate that the overall effect can be to improve the selling price. Finally, the probability of entry and the chosen accuracy of the information are never more in the second-price auction than in the first-price auction, and the seller prefers the second-price auction.We are grateful for the comments and suggestions of seminar participants at the University of British Columbia, Dartmouth College, the University of Wisconsin, Yale University, and the International Conference on Game Theory and Economics at SUNY Stony Brook.     

Residual claim and information acquisition in partnerships

This paper deals with a partnership facing an investment decision which is facilitated by costly but valuable information acquisition. When agents are identical in preference and endowment, it is shown that a partnership arrangement that makes one agent a residual claimant can sustain optimality, under which the residual claimant acquires information and assumes decision authority. Also, it is shown that different risk aversions and relative efficiency in information gathering determine who should be the residual claimant in an optimal partnership arrangement. Finally, an example of an optimal partnership arrangement is presented, where the residual claimant does not play any role except having a residual claim, hence a (partial) counterexample to Alchian and Demsetz's theory of classical firms.     

Access regulation and the adoption of VoIP

The introduction of packet-switched telephony in the form of Voice over Internet Protocol (VoIP) raises concerns about current regulatory practice. Access regulation has been designed for traditional telephony on public networks (PSTN). In this paper we analyze the effect of access regulation and retail price regulation of PSTN networks on the adoption of a new technology in the form of VoIP. In particular, we show that with endogenous consumer choice between PSTN and VoIP telephony, higher prices for terminating access to the PSTN network make VoIP less likely to succeed and lead to lower profits of operators that offer exclusively VoIP telephony.      

Strategic information transmission networks

We study a model of multi-player communication. Privately informed decision makers have different preferences about the actions they take, and communicate to influence each others? actions in their favor. We prove that the equilibrium capability of any player to send a truthful message to a set of players depends not only on the preference composition of those players, but also on the number of players truthfully communicating with each one of them. We establish that the equilibrium welfare depends not only on the number of truthful messages sent in equilibrium, but also on how evenly truthful messages are distributed across decision makers.     

Secret information acquisition in Cournot markets

Summary. Two-stage game models of information acquisition in stochastic oligopolies require the assumption that firms observe the precision of information chosen by their competitors before determining quantities. This paper analyzes secret information acquisition as a one-stage game. Relative to the two-stage game firms are shown to acquire less information. Policy implications based on the two-stage game yield, therefore, too high taxes or too low subsidies for research activities. For the case of heterogeneous duopoly we briefly discuss comparative statics results. Received: August 9, 1999; revised version: May 31, 2000     

The equivalence of profit-sharing licensing and per-unit royalty licensing

In a duopoly with symmetric product differentiations, we prove that profit-sharing licensing and per-unit royalty licensing are equivalent to each other regarding both the profitability and the welfare influences.     

Price regulation in insurance markets with asymmetric information

The paper presents and discusses a regulatory policy in insurance markets. It is based upon a two-sided rule: each company must propose at least one contract with full coverage and a ceiling is imposed on the level of premiums.     

Strategic transmission of information and short-term commitment

Summary. We examine the strategic role of information transmission in a repeated principal-agent relationship where the agent produces information that is useful to the principal. The agent values continuous employment for the principal because he makes a relationship-specific investment that can yield rents to him when the relationship is renewed. Assuming that the parties are sufficiently impatient, we show that full disclosure of the information produced occurs early in the relationship when the principal can commit to a long-term relationship, when the agent observes his valuation of continuous employment after making a report on information produced, or when the agent obtains a low valuation of continuous employment before making a report. By contrast, a strategic delay in the transmission of information occurs when the principal can only commit to a short-term relationship and the agent obtains a high valuation of continuous employment before making a report. Received: October 15, 1997; revised version: July 27, 1998