A computational framework for analyzing dynamic auctions: The market impact of information sharing

• Published date: 01 September 2020
• Author: Chaim Fershtman,John Asker,Jihye Jeon,Ariel Pakes
• DOI: http://doi.org/10.1111/1756-2171.12341
• Date: 01 September 2020

RAND Journal of Economics

Vol.51, No. 3, Fall 2020

pp. 805–839

A computational framework for analyzing

dynamic auctions: The market impact

of information sharing

John Asker∗,∗∗

Chaim Fershtman∗∗∗

Jihye Jeon‡

and

Ariel Pakes§,

This article develops a computational framework to analyze dynamic auctions and uses it to inves-

tigate the impact of information sharing among bidders. We show that allowing for the dynamics

implicit in many auction environments enables the emergence of equilibrium states that can only

be reached when firms are responding to dynamic incentives. The impact of information sharing

depends on the extent of dynamics and provides support for the claim that information sharing,

even of strategically important data, need not be welfare reducing. Our methodological contri-

bution is to show how to adapt the experience-based equilibrium concept to a dynamic auction

environment and to provide an implementable boundary-consistency condition that mitigates the

extent of multiple equilibria.

1. Introduction

This article develops a computational framework to analyze dynamic auctions and then

applies it to illustrate the possible implications of different rules for information exchange in

that setting.

Dynamic auctions are sequential auctions in which the state of the bidders, and therefore

their evaluation of the good that is auctioned, changes endogenously depending on the outcomes

∗UCLA; johnasker@econ.ucla.edu.

∗∗NBER.

∗∗∗Tel AvivUniversity; fersht@post.tau.ac.il.

‡Boston University; jjeon@bu.edu.

§Harvard University; apakes@fas.harvard.edu.

NBER.

We would liketo thank numerous seminar audiences for their comments and questions. We are particularly grateful to

Gautam Gowrisankaran and Mark Satterthwaite for extensivecomments. El Hadi Caoui and Chuqing Jin provided excel-

lent research assistance. Financial Assistance from the US–Israel Binational Science Foundation is greatly appreciated.

© 2020, The RAND Corporation. 805

806 / THE RAND JOURNAL OF ECONOMICS

of prior auctions. The value of winning an auction to produce aircraft or ships depends on the

backlog or the order book of the firm. Similarly,the value of winning a highway repair project or

a timber auction depends on whether the inputs currently under the control of the firm are fully

committed for the following period. The fact that the auction is dynamic implies a rich set of

strategic incentives. For example, a firm may choose to allow a competitor’s state to transition

to a point where that competitor bids less aggressively in order to win a subsequent auction at a

lower bid.

A central feature of this environment is that competing firms may not have complete infor-

mation about each other’s state variables, at every point in time. Empirically, this information

asymmetry seems an important feature of many industries. Indeed, the fact that some firms are

observed to make an effort to share information, at times illegally,underscores this general point

(see the discussion below of the antitrust treatment of information sharing in the United States

and EU).1

We provide a framework for analyzing dynamic auctions that allows for serially correlated

asymmetric information, which implies that a competitor’s prior bids are signals of his current

states. We use the framework to examine how the extent of information sharing impacts com-

petition in a dynamic sequence of procurement auctions.2The analysis sheds light on the extent

to which dynamic considerations can color the way antitrust regulators, procurement agencies,

and other policy agencies approach the regulation of information sharing. The specific model

we investigate is loosely based on the description of timber auctions in Baldwin, Marshall, and

Richard (1997), although, to keep the model simple, we make many departures from the precise

institutional features described therein. Having this specific empirical example in mind eases

much of the exposition.

In each period, twofir ms can bid for the right to harvest a lot of timber in a first-price sealed-

bid auction. Each firm has a stock of timber that it already has the right to harvest (its inventory).

This stock is private information, and its evolution is the source of dynamics. To compete in the

auction, firms must pay a participation fee and submit a bid simultaneously. A firm may also

choose to not participate. The winner of the auction, if any, receives the right to harvest the lot,

and discovers how much harvestablematerial it contains. A har vestwith a random outcome then

occurs, which depletes the stock of timber each firm has in inventory.

Our benchmark model has full revelation of the state variable every Tperiods. That is, each

firm observes the stock of unharvested timber of its competitor every Tperiods. Information

sharing is modeled as shrinking the time interval between full-revelation periods so that we can

investigate the possible implications of different rules of information exchange. We also investi-

gate a model in which firms decide whether to share information. Voluntary information sharing

involves firms making a choice every Tperiods as to whether to reveal in every period for the

next Tperiods. For voluntary information sharing to occur over the next Tperiods, all firms

must want to share information. Finally, we compare the results from these models with those we

obtain from a model with myopic firms.

The numerical analysis of this game illustrates how information sharing can affect bidding

behavior at a given state by increasing the precision of the firm’s perceptions about its competi-

tors’ states. This, in turn, shapes the desirability, and therefore the likelihood of being in different

1The account of timber auctions in Baldwin, Marshall, and Richard (1997) motivates many of our modeling

choices. Baldwin, Marshall, and Richard note several dimensions of private information, ranging from production costs

(called “overrun” in the industry), to the amount of timber in a lot (particularly in old-growth forests) and the harvesting

outcomes realized on timber lots located on private lands.

2The closest model to ours is the one estimated in the innovative contribution of Jofre-Bonet and Pesendorfer

(2003). This framework is further extended in Groeger (2014), Saini (2013), Balat (2017), and Jeziorski and Krasnokut-

skaya (2016). Jofre-Bonet and Pesendorfer’s model (and those that follow) has privateinfor mation that is conditionally

independent across states. That is, conditional on (observed) state variables, knowing the private information of a rival

last period provides no information as to the private information of the rival this period, which is not the case in our

model. In our model the competitor’s prior period bid is a signal on its current state, and that information sharing has

persistent value across periods.

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ASKER ET AL. / 807

states. An important point to bear in mind is that, conditional on the information they have, firms

bid to maximize the expected NPV of their individual profits, rather than industry profits, in the

model. On the one hand, an increase in information increases the intensity of bidding and de-

creases profits in most (but not all) states. On the other hand, because firms have more precise

information about when their competitor will be more aggressive, they are able to spend a greater

fraction of the time in states where bidding is less aggressive. These states are the ones in which

both firms’ inventory is higher. The net effect is that information sharing leads to an increase in

average profits as well as an increase in the total sales of the auctioned timber.

Through this channel increasing information increases the value of firms. However, in our

voluntary information-exchange (VIE) game, firms have difficulty committing to exchange in-

formation and most often choose not to share. In addition, we find that in a model with myopic

firms, the extent of information sharing has negligible effects.

This article also has a methodological contribution. A framework for analyzing dynamic

auctions in which a competitor’s past behavior has a direct effect on a firm’s perceptions about its

competitor’s likely action must allow for serially correlated asymmetric information. Fershtman

and Pakes (2012) considered the numerical analysis of dynamic games with serially correlated

asymmetric information, and we provide the modification required to use it in order to analyze

dynamic auctions. Perhaps more importantly, we extend their notion of a restricted experience-

based equilibrium by adding a consistency requirement on the boundary of the recurrent class of

states—-an extension that is possible to use in all dynamic games with asymmetric information.

The boundary-consistency condition refines the set of computable equilibria (or, equivalently,

mitigates potential multiple equilibria issues), and we provide intuition for when and why it can

be used. We also show how to compute and test for boundary-consistent equilibria.

The results comprise an example of what can happen when firms share information based

on the computational output from one parameterization. To that extent, the results provide a form

of a possibility result. Setting methodological contributions aside, we feel that the nature of the

possibility result is important, in that in our setting information exchange is essentially welfare

neutral, despite having a real impact on firms’ conduct (as noted in the paragraphs above). As

such, this example illustrates the conceptual issues that may need to be confronted, and the level

of care needed, in policy work or antitrust enforcement in this area.

This article is organized as follows. In the remainder of this section, we discuss the re-

lated literature and provide a brief review of the role of information sharing in antitrust policy.

Section 2 describes our baseline model, and then the information-sharing and the voluntary-

information-sharing variants of the model. In Section 3, computational details are described. A

reader not concerned with computational details can skip this section and proceed directly to Sec-

tion 4, which discusses the numerical analysis, focusing on the competitiveimpact of information

sharing. Section 5 concludes.

Related literature. Our article is closely related to the literature on the numerical analysis of dy-

namic oligopolistic games that uses the Ericson and Pakes framework (1995; for a survey of this

literature, see Doraszelski and Pakes, 2007). Recent applications of this methodology to ques-

tions related to antitrust policy include Besanko, Doraszelski, and Kryukov (2014) on predatory

pricing, and Mermelstein, Nocke, Satterthwaite, and Whinston (2020) on mergers. Within this

literature, the closest articles to ours are Saini (2013) and particularly Jeziorski and Krasnokut-

skaya (2016). Both articles apply the Markov perfect equilibrium concept to auction settings,

exploring the optimal procurement policy given capacity-constrained suppliers and subcontract-

ing, respectively.3

Jeziorski and Krasnokutskaya (2016) find that reducing the relevance of private informa-

tion (through subcontracting) lowers information rents and profits. This result contrasts with our

finding that although reducing private information decreases profits for a given state, it induces

3Both these articles build on Jofre-Bonet and Pesendorfer (2003).

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