Transcript The interests of multi-unit auctions for agri

Multi-unit Auction Design
for Salinity Management, Water Auctions and
other NRM Services
by
Atakelty Hailu
School of Agricultural and Resource Economics
University of Western Australia
CAER Workshop Presentation, Sydney, 1 February 2007
Outline
• Three main elements in presentation
• 1) Multi-unit auctions (Based on research done jointly
with Sophie Thoyer (ENSAM/Lameta) and published as
Multi-unit auction format design, Journal of Economic
Interaction and Coordination, volume 1: 129-146, 2006 )
• how multi-unit auctions could improve
conservation/water auctions
• design of multi-unit auctions
• what payment rules: pay-as-bid, uniform
pricing (or Vickrey pricing)
• report results from computational
experiments
Outline …
2) MAPPER – a multi-unit auction trial in WA
• organized by Frank D’Emden at DAFWA
3) HydroEcon – an integrated and agent-based
economic-environmental model that we have been
building at UWA/Salinity CRC
Auctions for conservation
Auctions are increasingly used to purchase conservation
services and, in some cases, to (re)-allocate water user
rights:
• Examples:
• US Conservation Reserve Program (CRP), since
1985
• BushTender
• MBI Pilot Auctions in Australia (MBI1 and MBI2)
• Water buybacks: Purchase of water for
environmental flows – one sided auctions
Examples: Georgia, Texas, Oregon
The lumpy bid problem
• Conservation auctions and water auctions are generally
single bid auctions (lumpy bids):
• a bid consists of a single price-quantity pair
• example:
• will conserve 20 hectares if paid $2000 a
year
• will forgo 2000 KL if paid $500
• A bidder can submit different bids but they would be
independent bids/projects (not nested or incremental
bids)
• Reality: increasing marginal costs of forgoing water,
conservation services, etc
AN EXAMPLE: BIDDING TO
SAVE WATER
Opportunity cost/unit of water saved
3
1: water saving practices
2: water saving technology
3: stop irrigation
2
1
Quantity of water saved
The lumpy bid problem …
• Single bid auctions might discourage bidding with
large quantities – average cost of delivering service
increases with size of project
• Losses of potential contracts and misallocation of
conservation contracts
• Differences in marginal costs are not exploited well
• Leads to budgetary and social efficiency losses
MCost
$/unit
Farmer 2
Farmer 1
Q
Multi-unit auctions
Solution to lumpy bid problem: allow bidders to
bid with supply schedules (use multi-unit
auctions)
Example:
1) Will fence off 20 hectares at $50/ha, 50
hectares at $65/ha, etc.
2) Will fence off 20 hectares at $50/ha, will fence
and enhance the native vegetation on those 20
hectares if paid $100/ha, etc.
Multi-unit auctions
Multi-unit auctions are widely in financial and
electricity markets:
• Electricity market (UK, US, Australia)
• Allocation of foreign currency
• Sale of Treasury bonds
• However, the choice of payment formats is a
subject of controversy
Multi-unit auctions: payment rule
matters!
Discriminatory pricing (pay-as-bid): each winning bidder is paid
based on its own bid, i.e. payment equals the cost (area under
the curve) implied by the bid
Uniform pricing: winning bidders are paid the clearing price –
the marginal winner/loser sets the price
Generalized Vickrey (Clinched or Ausubel auction in an opencry format): The payment is equal to the price that would have
been paid if the unit had to be sourced from the other bidders.
Payment rules: A numerical example
2 bidders with 4 units to sale each. Total demand is 4 units
Bidder 1
1
3
6
7
Bidder 2
Uniform: Price = 4
R1 = 4+4=8 R2 = 4+4=8
2
4
5
9
Discriminatory:
R1 = 1+3=4 R2 = 2+4=6
Generalized Vickrey (clinched)
R1 = 9+5=14 R2 = 7+6=13
Payment rules …
Supply schedule by bidder i
Qi(b)
Cut-off price
Residual demand facing bidder i
Di(b) = DT -  Q-i(b)
Payment under discriminatory
Payment under uniform
Payment under generalized
Vickrey
What auction design?
• Economic theory does not provide a complete picture of
auction perforamce ranking in the case of multi-unit auctions
(no RET):
• Bidding truthfully under generalized Vickrey is a weakly
dominant strategy. Supply inflation otherwise. No closed
form solution.
• Controversy on the best payment scheme ( Binmore and
Swierzbinski 2000)
• Few empirical data analyses (Wolfram, 1998)
• Simplified experiments (Alemgeest et al, 1998; Kagel and
Levine, 2001; etc.)
• Need for rapid simulations: development of agent-based
models (Bower and Bunn, 2001, Binmore and Swierzbinski
2000)
The experimental auction setting
• We use agent-based modelling or computational
experiments to explore the issue
• Sealed-bid multi-unit procurement auction:
- bidders (farmers) are allowed to make multiple
bids
- the regulator has a target (demand level), chooses
the clearing price and buys units accordingly.
- payments depend on auction format:
discriminatory, uniform and generalized Vickrey
The agent-based model

Agent-based models use computational experiments
– An artificial society of bidders (bidder agents)
– Agents with cost and capacity characteristics and
learning rules
– Agents – do not get tired, bored, etc – an issue
with complex auctions if people are used (losers
spoiling experiments if they are not winning)
 Each agent i has a true cost function
Pi = ai + bi Q
 Agents update bids through reinforcement learning.
After each auction, it exploits the outcomes of
previous bids or experiments with new bids:
BiL = ai L(t) + bi L(t) Q
Reinforcement learning algorithm
–
(Roth & Erev GEB 1995; Erev & Roth AER 1998)
Asserts that the propensity to use an action or a strategy is
positively related to the results obtained from it (exploiting
known strategies)
–
And agents also experiment with strategies similar to those
that they have tried and benefited from
–
Recent experience has more impact than past experience
–
Learning algorithm suitable for the auction problem:
individual learning - no need to evaluate payoffs of
foregone strategies – no need to know about other bidders’
strategies
Propensity of player i to choose strategy (a,b):
a choice
Neighbours of (c,d)
Neighbours
Strategy
(c,d)
Strategy
b choice
• Law of effect
• Experimentation
• Recency
Experimental set up of simulation
•Simulation experiments with two populations having the
same aggregate supply
- Homogeneous population: 6 bidders, ms =2
- Heterogeneous population: 2 small (S), 2 medium (M)
and 2 large (L)
With capacity: ms(S) = 1 ms(L) = 3 ms(M) = 2
With cost structure: C(M)= 2*C(S) ; C(L) = 3*C(S)
*** scale effect is removed: a medium one is exactly like 2
small ones in terms of cost structure
• Auction outcomes simulated for different degrees of
rationing: from 10 to 60% of aggregate capacity
Evaluating auction performance
• Comparing auction outcomes:
• Two efficiency criteria:
- budgetary efficiency
- outlay per unit
- allocation allocation
- social cost per unit of service or good
purchased through the auction
-Are you sourcing the service/good
from the least cost providers?
Results
Homogeneous population: bidding strategies
•
Different patterns of bidding strategies under the three auction
formats
•
Vickrey leads to the highest frequency of truthful bidding
(and highest proportion of Nash equilibria)
•
Uniform format leads to overbidding:
- with supply inflation observed at low demand levels
- a mix of high flat bidding and supply inflation at high
demand levels
•
Bidding under the discriminatory is the least sincere.
High flat bidding is the most frequent strategy but
supply inflation observed for low levels of demand
0.6
0.2
0.4
true curve
D = 7.2
D = 6.0
D = 4.8
D = 3.6
D = 2.4
D = 1.2
0.0
auction clearing price (uniform)
0.8
Bidding strategies: uniform auction
-0.5
0.0
0.5
1.0
quantity
1.5
2.0
0.6
true curve
0.4
D = 7.2
D = 6.0
D = 4.8
0.2
D = 3.6
D = 2.4
D = 1.2
0.0
auction clearing price (discrim.)
0.8
Bidding strategies: discriminatory
-0.5
0.0
0.5
1.0
quantity
1.5
2.0
0.05
0.10
0.15
Vickrey
Discrim.
Uniform
0.00
MSD a (learnt entry price)
0.20
0.25
Bidding strategies:
deviations in entry prices (homogeneous bidders)
1
2
3
4
demand
5
6
7
0.04
0.06
Vickrey
Discrim.
Uniform
0.02
MSD b (learnt supply slope)
0.08
Bidding strategies:
deviations in bid slopes (homogeneous bidders)
1
2
3
4
demand
5
6
7
Heterogeneous population: bidding
strategies
• Discriminatory: strategies are not sensitive to size –
big and small misrepresent true costs
• Uniform and Vickrey: coordination at high prices
- large bidders adopt a “supply inflation” strategy
- small bidders “free ride” on the risks taken by the
bigger ones (are more truthful)
Budgetary performance: summary
• Uniform and Vickrey auctions lead to similar results
for most levels of demand.
• Uniform and Vickrey perform better than
Discriminatory auction when competition is not very
weak
• When competition is very weak, Vickrey rule is the
worst performer
• Outlays with a heterogeneous population slightly
higher than with a homogeneous population
0.6
Budgetary performance
0.4
0.3
0.2
0.1
outlay per unit
0.5
Vickrey
Discrim.
Uniform
1
2
3
4
demand
5
6
7
Social cost efficiency
0.15
0.10
Vickrey
Discrim.
Uniform
0.05
production cost per unit
0.20
Measured by the production costs of units sold:
Auctions perform equivalently for the two populations
1
2
3
4
demand
5
6
7
Further research…
• Further refinements needed:
• Remove assumption of linear bidding curves
• Other sources of competition
• consider changes in number of bidders in addition to
changes in the degree of rationing
Conclusion
•
Computational experiments useful for completing the picture:
Compared to existing theoretical results, it depicts a richer
pattern of bidding strategies that depend on the interplay
between heterogeneity in the bidder population and the degree
of rationing (competition) in the auction
•
Discriminatory the least performer except when competition is
very weak
Policy advice ?
•
Policy advice
• Experiment with multi-unit auctions – they can
only improve auctions
• And experiment with payment formats other
than discriminatory pricing
• Uniform pricing could be attractive:
• simple and familiar
• “equitable”
• lower information demand on bidders (“you
get paid what the market offers”)
• potential budgetary savings and efficiency
• learning about true opportunity costs (more
truthful bidding)
Multi-unit Auction for
Perennial Pasture
Establishment and Recovery
(MAPPER)
(a multi-unit, uniform price auction)
Frank D’Emden, NRM Development
Officer, DAFWA Esperance
Objectives
Strategic objective
• Reduce sedimentation of Young River & Stokes Inlet
Operational objective
• Establish perennial pasture filter strips adjacent to
waterways
• Contain riparian saline discharge
How will it work?
The EOI
Auction for Perennial Pastures
=
Expression of Interest
Closing Date: 15/1/07
WHAT IS THE AUCTION FOR PERENNIAL PASTURES?
The Auction for Perennial Pastures aims to develop voluntary partnerships
with landholders for the establishment and rehabilitation of perennial pastures
in the Young River catchment. The project, organised by the Department of
Agriculture and Food WA with assistance from the Esperance Regional
Forum and the University of Western Australia, is funded by the South Coast
Regional Initiative Planning Team (SCRIPT) through the National Action Plan
for Salinity and Water Quality and the Natural Heritage Trust. All landholders
within the Young River Catchment are invited to participate in the auction.
The objective is to reduce sediments flowing into the Young River and Stokes
Inlet through the establishment and maintenance of perennial pastures on
sloping land. A secondary aim is to control dryland salinity where it is
contributing to stream bank erosion.
SUBMITTING A TENDER
The aim of this tender is to allow landholders to bid in flexible ways. You are
encouraged to nominate an area or different areas on your farm where you
could plant perennial pastures in 2007. The value of your bid should reflect
the associated establishment costs. You are also allowed to nominate the
prices (in dollars per hectare) that you would like to receive to proceed with
each level of your nominated perennial cover. For example, you could submit
How will it work?
The Bid
• Up to 3 ‘incremental’ bids
• $/ha may vary between increments
AREA ID* (ha)
Total area (ha)
Bid ($/ha)
Tender amount
1 (50)
50
65
$3,250
2 (20)
70
70
$4,900
3 (20)
90
80
$7,200
* Use the same ID number on the property map
How will it work?
The Plan
Environmental Benefit Index (under
progress)
• Reflects objectives
• Prioritises operational objectives
EBI = R + 2(F + S)
∑
Where: R = ha on recharge zone
F = ha on filter/buffer
S = ha on slope >4%
∑ = total ha in bid
HydroEcon
 HydroEcon has been in development for the last
three years within a dryland salinity CRC project
 Motivation: provide a virtual laboratory for testing
the economic and environmental effects of policy
interventions aimed at land use practices
The model has three layers (components) – next
slide
Layers in HydroEcon
Policy layer
Farming community layer
Agent-based implementation of wholefarm models (MIDAS-type) and auction
models
Biophysical layer
SWAT suite of hydrology, water quality,
and other models
Application
 The Katanning region in WA has been selected as
the area for its first application
A catchment with an area of about 300,000 ha
Mixed crop and livestock (sheep) farms
The farm model
eight crop, pasture and tree land uses
 using data from MIDAS and also from recent
work by Ross Kingwell and others in relation
to salinity management
Application …
However, the model is developed in such a
way that its structure is transferable to other
catchments (e.g. number and nature of crop
enterprises can be varied)
Although that does not mean it is ‘easy’ to
set-it up (or parameterize it) for other
catchments
Both MIDAS and the SWAT models
require substantial amounts of data
Thank you
email: [email protected]
Questions?
Comments?