The linkage principle is a finding of
auction theory
Auction theory is an applied branch of economics which deals with how bidders act in auction markets and researches how the features of auction markets Incentivisation, incentivise predictable outcomes. Auction theory is a tool used to inform the ...
. It states that
auction house
An auction is usually a process of buying and selling goods or services by offering them up for bids, taking bids, and then selling the item to the highest bidder or buying the item from the lowest bidder. Some exceptions to this definition ex ...
s have an incentive to
pre-commit to revealing all available information about each lot, positive or negative. The linkage principle is seen in the
art market
The art market is the marketplace of buyers and sellers trading in commodities, services, and works of art.
The art market operates in an economic model that considers more than supply and demand: it is a hybrid type of prediction market where a ...
with the tradition of auctioneers hiring art experts to examine each lot and pre-commit to provide a truthful estimate of its value.
The discovery of the linkage principle was most useful in determining optimal
strategy
Strategy (from Greek στρατηγία ''stratēgia'', "art of troop leader; office of general, command, generalship") is a general plan to achieve one or more long-term or overall goals under conditions of uncertainty. In the sense of the "art ...
for countries in the process of auctioning off
drilling rights
Mineral rights are property rights to exploit an area for the minerals it harbors. Mineral rights can be separate from property ownership (see Split estate). Mineral rights can refer to sedentary minerals that do not move below the Earth's surfac ...
(as well as other
natural resources
Natural resources are resources that are drawn from nature and used with few modifications. This includes the sources of valued characteristics such as commercial and industrial use, aesthetic value, scientific interest and cultural value. O ...
, such as logging rights in Canada). An independent assessment of the land in question is now a standard feature of most
auctions
An auction is usually a process of buying and selling goods or services by offering them up for bids, taking bids, and then selling the item to the highest bidder or buying the item from the lowest bidder. Some exceptions to this definition ex ...
, even if the seller country may believe that the assessment is likely to lower the value of the land rather than confirm or raise a pre-existing valuation.
Failure to reveal information leads to the winning
bidder
Bidding is an offer (often competitive) to set a price tag by an individual or business for a product or service ''or'' a demand that something be done. Bidding is used to determine the cost or value of something.
Bidding can be performed by ...
incurring the discovery costs himself and lowering his maximum bid due to the expenses incurred in acquiring information. If he is not able to get an independent assessment, then his bids will take into account the possibility of downside risk. Both scenarios can be shown to lower the expected revenue of the seller. The expected sale price is raised by lowering these discovery costs of the winning bidder, and instead providing information to all bidders for free.
Use in FCC auction
Speaking of
FCC
The Federal Communications Commission (FCC) is an independent agency of the United States federal government that regulates communications by radio, television, wire, satellite, and cable across the United States. The FCC maintains jurisdictio ...
spectrum auctions
A spectrum auction is a process whereby a government uses an auction system to sell the rights to transmit signals over specific bands of the electromagnetic spectrum and to assign scarce spectrum resources. Depending on the specific auction form ...
, Evan Kwerel said, "In the end, the FCC chose an ascending bid mechanism, largely because we believed that providing bidders with more information would likely increase
efficiency
Efficiency is the often measurable ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and without ...
and, as shown by
Paul Milgrom
Paul Robert Milgrom (born April 20, 1948) is an American economist. He is the Shirley and Leonard Ely Professor of Humanities and Sciences at Stanford University, the Stanford University School of Humanities and Sciences, a position he has held ...
and
Robert J. Weber, mitigate the winner's curse. (Kwerel, 2004, p.xvii)
The result alluded to by Kwerel is known as the linkage principle and was developed by Milgrom and Weber (1982). Milgrom (2004) recasts the linkage principle as the 'publicity effect.' It provided a theoretical foundation for the
intuition
Intuition is the ability to acquire knowledge without recourse to conscious reasoning. Different fields use the word "intuition" in very different ways, including but not limited to: direct access to unconscious knowledge; unconscious cognition; ...
driving the major design choice by the FCC between an ascending bid and
sealed bid auction
Auction theory is an applied branch of economics which deals with how bidders act in auction markets and researches how the features of auction markets incentivise predictable outcomes. Auction theory is a tool used to inform the design of real-w ...
.
Formal derivation
According to Perry and Reny:
The linkage principle has come to be considered one of the fundamental lessons provided by auction theory. The significance and general acceptance of the linkage principle as a guide to auction design, even in contexts beyond single-unit auctions, is highlighted by the recent design of the spectrum auction held by the FCC, which contains an open-auction component. Although the experts agreed that collusion
Collusion is a deceitful agreement or secret cooperation between two or more parties to limit open competition by deceiving, misleading or defrauding others of their legal right. Collusion is not always considered illegal. It can be used to att ...
among the bidders (which ultimately did occur; The Economist, May 17, 1997, p. 86) is more easily sustained within an open auction, in the end the faith placed in the linkage principle outweighed this concern and an open auction format was employed. Indeed, according to McMillan (1994), the experts "judged he negative collusion effectto be outweighed by the bidders' ability to learn from others' bids in the open auction."
The linkage principle implies that open auctions generally lead to higher expected prices than
sealed-bid auctions. As stated by Milgrom and Weber (1982, p.1095),
"One explanation of this inequality is that when bidders are uncertain about their valuations, they can acquire useful information by scrutinizing the bidding behavior of their competitors during the course of an scending-bidauction. That extra information weakens the winner's curse and leads to more aggressive bidding in the scending-bidauction, which accounts for the higher expected price."
The linkage principle also implies that the
auctioneer
An auction is usually a process of buying and selling goods or services by offering them up for bids, taking bids, and then selling the item to the highest bidder or buying the item from the lowest bidder. Some exceptions to this definition ex ...
maximizes the expected price by always fully revealing all information it has regarding the object being sold completely. In the words of Milgrom and Weber (1982,p. 1096), "Honesty is the best policy."
In order to provide a statement of the linkage principle, we follow the presentation of Krishna, which notes that the linkage principle "was first set forth and used by Milgrom and Weber (1982)." (Krishna, 2002, p. 111) We begin by defining the necessary concepts and
notation
In linguistics and semiotics, a notation is a system of graphics or symbols, characters and abbreviated expressions, used (for example) in artistic and scientific disciplines to represent technical facts and quantities by convention. Therefore, ...
required to state the linkage principle. Define a standard auction format to be one in which the high bidder wins. Suppose that each bidder, receives a signal regarding the value of the object. We assume the
valuation to each bidder depends on its own observed
signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
and symmetrically upon the unobserved signals of the other bidders (so that the signals of the other bidders can be interchanged without affecting a given bidder's value). More specifically, assume all signals are drawn from the interval and that for all we can write the value of bidder as
where the function is
symmetric
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
in the last components.
We now define other random variables and mappings with respect to bidder 1, but because of the assumed symmetry, they are the same for all bidders. Define
random variables
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
to be the largest, second largest, etc., from among
. Let
denote the
distribution Distribution may refer to:
Mathematics
*Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations
* Probability distribution, the probability of a particular value or value range of a vari ...
of
conditional on
, i.e.,