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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 (firstname.lastname@example.org).
Prepared for the Eastern Economic Association
New York, March 1, 2009
Radford Schantz, US Department of the Interior
Walter Stromquist, Swarthmore College
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.Background
… 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
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
“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
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.
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 programAuction models needed
- 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
Minimum bid, bmin
Bidding fee (ignore the fee for today!)
Minimum bid $128 thousand
No bidding fee
U = “value parameter”
V is related to U:
V = v(U)
(increasing, but not usually linear)
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 “prior distribution”).
H (u) = Pr ( U ≤ u )
estimates of value based on their private signals and other
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:
(same as the minimum bid!)
H(u) in the example
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.)
q(n) = Pr (N = n) = (3n/n!) exp(-3) for n = 0, 1, 2…
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.
WE’RE NOT DOING THIS TODAY.
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.
Now Ri is an ESTIMATING ERROR. The evaluator knows its own Xi, but not Ri or the other evaluators’ signals.
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
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*.)
x* = 1.67814
(…so it takes an encouraging signal to justify a bid,
but not an exceptionally rare signal.)
Here is g:
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.
Probability of no bid at all: 0.597
Probability of bid above $ 250 thousand: 0.026
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).