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A Bidding Model for Auctions of Offshore Alternative Energy Sites. Prepared for the Eastern Economic Association New York, March 1, 2009 by Radford Schantz, US Department of the Interior (Radford.Schantz@mms.gov) and Walter Stromquist, Swarthmore College (mail@walterstromquist.com).

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a bidding model for auctions of offshore alternative energy sites

A Bidding Modelfor Auctions of Offshore Alternative Energy Sites

Prepared for the Eastern Economic Association

New York, March 1, 2009


Radford Schantz, US Department of the Interior



Walter Stromquist, Swarthmore College


Energy production sites on public land are auctioned under a variety of authorities and using various auction formats. The focus in this paper is on:

oil and gas leases, for which (partly) we have an auction model, and,

alternative energy site leases, where the future auction format is a subject of discussion and planning.

oil and gas lease auctions
Offshore: first-price sealed-bid…

… must be auctioned; there is no process of noncompetitive award.

The main authority is the Outer Continenal Shelf Lands Act (1953), 43 USC 1331.

Onshore: second-price open ascending…

… auctioned when there is competitive interest. Absent that interest, an onshore lease can be awarded noncompetitively.

The main authority is the Federal Onshore Oil and Gas Leasing Reform Act (1987).

Oil and Gas Lease Auctions
alternative energy site auctions

BLM administers wind energy rights-of-way (ROW). The main authority is the Federal Land Policy and Management Act (1976), 43 USC 1701.

Three basic types of ROW: energy testing; site testing; and commercial development.

Sometimes first-come, first-serve noncompetitive process…. competitive process if plan requires it or if more than one applicant shows substantive interest.

Alternative energy site auctions
offshore alternative energy
Section 388 of the Energy Policy Act of 2005 amended the OCS Lands Act and gave Interior authority to grant leases for alternative energy activities.

“COMPETITIVE OR NONCOMPETITIVE BASIS- …the Secretary shall issue a lease, easement, or right-of- way on a competitive basis unless the Secretary determines after public notice of a proposed lease, easement, or right-of-way that there is no competitive interest.”

Offshore alternative energy
first offshore leases planned
First offshore leases planned

Measurement leases: for five years or more, but they cannot be converted into commercial leases. Forty nominations were received…16 areas that we consider top priority.

auction models needed
Offshore oil and gas: we routinely use a lease sale forecasting model, IMODEL, described next…

Lack models for onshore energies…

Seeking to develop auction models for offshore alternative energy…

to help to determine the best auction format(s) for this new program

Auction models needed
the bidding model
The Bidding Model
  • First Price, Sealed Bid Auctions
  • Common-value model
  • Public and private information
  • Symmetric equilibrium strategies
  • Special features:

- Number of potential bidders is a random variable

May be determined inside the model, from an equilibrium condition

- Role for uninformed bidders

In special cases, may determine effective minimum bid for informed bidders

- Flexible private information model

Additive errors, but they apply to a transformed version of value

rules of the auction
Rules of the Auction
  • Seller announces

Minimum bid, bmin

Bidding fee (ignore the fee for today!)

  • Anyone can bid
  • Highest bidder takes the property, pays amount of highest bid.
  • Bidders do not know how many other bidders there are.

Minimum bid $128 thousand

No bidding fee

the common value
The Common Value
  • Value of property = V, same for all bidders.
  • Model V as a random variable
  • We use an intermediate random variable:

U = “value parameter”

V is related to U:

V = v(U)

(increasing, but not usually linear)

  • Why the extra level of complication?

We want to use additive errors, but it isn’t plausible that estimating errors are independent of the size of V. But errors might be independent of some transformed version of V, and that is U.

the common value public information
The Common Value:Public Information
  • All public information is represented by a probability distribution on U.

(the “prior distribution”).

  • Represent the prior by a cumulative distribution function (cdf):

H (u) = Pr ( U ≤ u )

  • This determines a prior distribution on V itself.
  • H may be continuous, discrete, or mixed.
  • Bidders effectively use H as a prior distribution, and update their

estimates of value based on their private signals and other


  • H and the value function v(U) are common knowledge.
the common value public information1
The common value:Public information

With probability 0.20, the property is “successful”

U = + 1/2

V = + $ 1 million

With probability 0.80, the property is “a failure”

U = – 1/2

V = – $ 90 thousand

Prior mean value of the tract:

$128 thousand

(same as the minimum bid!)

H(u) in the example

how many bidders
How many bidders?

We call the potential bidders “EVALUATORS.”

If they get private signals, they are “INFORMED EVALUATORS.”

Otherwise, they are “UNINFORMED EVALUATORS.”

(It seems wrong to call them all “bidders,” since they might choose

not to bid.)

  • The number of INFORMED EVALUATORS is a random variable, N.
  • TODAY’S EXAMPLE: N is Poisson, with mean m = 3.

q(n) = Pr (N = n) = (3n/n!) exp(-3) for n = 0, 1, 2…

how many bidders1
How many bidders?
  • In the model, N is always Poisson. The user can specify the mean, m.
  • OR: The user might let the model determine m internally.

User specifies an “information cost,” k

All evaluators may decide whether to “buy” a private signal

(and so become informed evaluators)

At equilibrium, they each choose to do so with some common

probability p, chosen so that the expected profit for

informed evaluators is exactly k.

The consequence: N is Poisson, with mean m determined by k.


uninformed evaluators
Uninformed evaluators
  • Do uninformed evaluators matter?

Not usually.

Sometimes, yes. Suppose that the lowest possible value of V is

$200 thousand, but the minimum bid is $128 thousand.

Then uninformed evaluators can rationally bid $200 thousand,

and somebody surely will do so.

This “uninformed bid” replaces the legal minimum as the

starting point for the informed bidders.

The uninformed evaluators have no effect in today’s example.

private signals
  • Each informed evaluator receives private information in the form of a PRIVATE SIGNAL. The i-th evaluator’s signal is Xi. We model each signal as a random variable.

Now Ri is an ESTIMATING ERROR. The evaluator knows its own Xi, but not Ri or the other evaluators’ signals.

  • We assume that estimating errors are INDEPENDENT and NORMALLY DISTRIBUTED. (They are independent of U, V, N, and each other.)
  • The standard deviation of the private signals is the same for all evaluators. It is a model parameter, . TODAY WE’LL USE  = 2.
private signals example
  • Left curve: distribution of private signals if U = - 1/2
  • Right curve: distribution of private signals if U = +1/2
  • Evaluators update their “success probabilities” based on their private signals (and other circumstances).
summary of the inputs
Summary of the inputs
  • Inputs to the model:

Bmin and fee Rules of the auction

v ( ) Defines value, V = v(U)

H ( ) Public (prior) distribution for U

m Mean number of informed evaluators

(or specify information cost, k)

 standard deviation for estimating errors

  • All of these are entered by the user, and are assumed to be common knowledge.
analyzing the game
Analyzing the Game
  • This is a non-cooperative game.
  • Let’s find a symmetric equilibrium strategy:

x* = smallest private signal that justifies a bid

g(x) = optimal bid by an evaluator with signal x

(assume that g(x) is increasing, and defined when x  x*.)

  • This model does not look for asymmetric equilibriums.
  • This is a hard calculation! But not that hard. Standard theory applies.
the symmetric equilibrium strategy
The symmetric equilibrium strategy

x* = 1.67814

(…so it takes an encouraging signal to justify a bid,

but not an exceptionally rare signal.)

Here is g:

how does bidding depend on m
How does bidding depend on m?

Equilibrium bidding strategy for m = 1, 2, 3, 4

(m = mean number of informed evaluators)

More competition ->

Be more reluctant to bid at all

But bid higher if you have a very favorable signal.

distribution function for the high bid
Distribution function for the High Bid

Probability of no bid at all: 0.597

Probability of bid above $ 250 thousand: 0.026

outputs from the model in the example
Outputs from the model (in the example)
  • Expected number of bidders:

Each evaluator bids if its private signal is at least x*.

If the tract is a success, this requires

x* = 1.67814

so estimation error is 1.17824

which happens with probability 0.278.

If the tract is a failure, it happens with probability 0.138.

So, with three informed evaluators, the expected number of bids is

(3)(0.278) = 0.834 (if success)

(3)(0.138) = 0.414 (if failure)

or 0.498 (averaged over cases).

In this example, we should expect to get about ½ of a bid (on average).

more outputs from the model
More outputs from the model
  • Expected number of bids
  • Probability of getting at least one bid
  • Expected value of highest bid, if there is a bid
  • Expected revenue to seller
  • The model can also give the distribution of these variables.
empirical testing
Empirical testing
  • The model needs testing!
  • The Interior Department maintains an extensive historical database of offshore leases bid on, amounts of bids, bidder identities, and physical characteristics of the properties.
  • What else should we be doing with this model?