Repeated Auctions with the Right of First Refusal and Asymmetric Information

Abstract

This paper characterizes a set of Nash equilibria in a first-price sealed-bid auction with the right of first refusal using two bidders and asymmetric information regarding the bidders’ value distributions. The equilibria for multiple bidders and a more general value distribution are also presented

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Repeated Auctions with the Right of First Refusal and Asymmetric Information
Hayley H. Chouinard
Assistant Professor
School of Economic Sciences
PO Box 646210
Washington State University
Pullman, Washington 99164-6210
Phone: (509) 335-8739
Fax: (509) 335-1173
E-mail: chouinard@wsu.edu

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Repeated Auctions with the Right of First Refusal and Asymmetric Information
Abstract
This paper characterizes a set of Nash equilibria in a first-price sealed-bid auction
with the right of first refusal using two bidders and asymmetric information regarding
the bidders’ value distributions. The equilibria for multiple bidders and a more general
value distribution are also presented.
Keywords: repeated auction; right of first refusal; asymmetric information
JEL classification: C72; D44; D82

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1. Introduction
A repeated auction is an infinite series of auctions used to award the same, indivisible
object in each period. Some repeated auctions include the right of first refusal, where
the incumbent has the opportunity to continue to hold the right to the awarded
object by matching the best bid of any entering bidder in each period. This paper
characterizes a set of Nash equilibria in a first-price repeated auction with the right
of first refusal and asymmetric information.
Repeated auctions have been studied since Demsetz [4] called for the use of fran-
chise bidding to award monopoly contracts. It has been found that the treatment
of and assumptions concerning the incumbent affects the outcome of the repeated
auction. The importance of the incumbent is seen in Osmundsen [11] when repeated
auctions are applied to nonrenewable resource extraction franchises, and in Laffont
and Tirole [8] as incumbent’s make investment choices in the first period. Here, the
specifics of the incumbent position affect the outcomes, and may characterize actual
repeated auctions.
Often the bidders in repeated auctions are assumed to be the same in each pe-
riod making collusion among bidders an important aspect of the repeated auction
process. Such collusion is the focus of the work discussed in Phillips, Menkhaus, and
Coatney [12], Fabra [5], Aoyagi [1], and Skrzypacz and Hopenhayn [13]. However,
the characteristics of the object or length of the periods may make the assumption
of a different pool of entrant bidders in each period more realistic. In this work, the
entrant bidders are not the same in each period.
The right of first refusal exists in many different types of contracts that can be
thought of as repeated auctions. Undeveloped land, residential property, and com-
mercial property contracts all may include the right of first refusal to provide current
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tenants the option to the property in the next period. Securities sales by owners
often allow other owners the right of first refusal in order to control ownership from
period to period. Employment contracts, especially those of athletes and entertainers
may empower the current employer with the right of first refusal in future periods
as encouragement to support those unproven talents early in their careers. Similarly,
various types of investment settings provide investors the right of first refusal on devel-
oped innovation as an incentive to invest in research. Often, procurement contracts,
such as those for municipal garbage collection or cable television service, include the
right of first refusal. Also, many of the concession contracts in US National Parks
also include the right of first refusal to provide consistent service.
This article is the first to model the equilibria in a first price repeated auction
with the right of first refusal. Others have considered the theory of the right of
first refusal. Walker [15] examines the legal aspects of the right of first refusal. He
provides an excellent discussion of the purpose and uses of the right, including insuring
against bargaining breakdown and inhibiting exit from a market, but also warns of
the potential to limit competitive bidding. In the first economic analysis of the right
of first refusal, Kahan [7] models the value of the right in negotiations. He logically
presents that the value of the right will depend on the relative valuations of the good.
However, Kahan does not consider the right of first refusal in an auction context.
Additional theory and an experimental examination of the right of first refusal is
presented in Grosskopf and Roth [6]. They conclude that the specific characteristics
of the right can work to advantage or disadvantage the right holder. Chouinard [3]
models one-period, first-price auctions for National Park concession contracts with
and without the right of first refusal. She concludes the elimination of the right
increases the service provided by concessioners. Finally, Bikhchandani, Lippman and
Ryan [2] discuss the impacts of the right of first refusal on the seller and potential
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buyers. They rigorously model the right in a second price auction, and conclude that
the right is inefficient (the bidder with the highest value does not necessarily win),
and the seller will forego surplus.
Using techniques similar to Bikhchandani, Lippman and Ryan, equilibria of first-
price repeated auctions with the right of first refusal are modelled. Here, initially,
two bidders with uniform value functions are considered. The model is first extended
to investigate multiple bidders and then second, a more general value function. Com-
parisons with auctions without the right of first refusal are given and the efficiency
of the auctions are considered.
2. Models and results
There are 2 risk neutral players participating in infinitely repeated auctions for the
same object, such as a monopoly right. At the beginning of each period the seller
puts the monopoly right for one period up for bid. In the first auction, typical bidder
i’s valuation, vi, is independently drawn from the uniform distribution. The values
are normalized to lie on the support [0,1]. The valuation distribution is common
knowledge. In subsequent auctions, the entrant’s value is independently drawn from
the unit uniform distribution, and the incumbent’s value is common knowledge. The
revelation of the incumbent’s value is similar to the work of Vickrey [14], where it
is assumed one bidder knows the valuation of the other. Landsberger, Rubinstein,
Wolfstetter and Zamir [9] evaluate first price auctions given the ranking of bidder
evaluations is known. They suggest this knowledge may come from previous auction
experience, access to other’s financial resources or other idiosyncratic features of bid-
ders. In the types of auctions considered here, it is reasonable that entrant bidders
may be able to observe the incumbent, as one period of the repeated auction may
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