Multi-unit Auction Design for Salinity Management, Water Auctions and other NRM Services

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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

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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

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Outline

• 2) MAPPER a multi-unit auction trial in WA
• organized by Frank DEmden at DAFWA
• 3) HydroEcon an integrated and agent-based
  economic-environmental model that we have been
  building at UWA/Salinity CRC

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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

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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

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AN EXAMPLE BIDDING TO SAVE WATER
1 water saving practices 2 water saving
technology 3 stop irrigation
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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
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Multi-unit auctions

• Solution to lumpy bid problem allow bidders to
  bid with supply schedules (use multi-unit
  auctions)
• Example
• Will fence off 20 hectares at 50/ha, 50 hectares
  at 65/ha, etc.
• Will fence off 20 hectares at 50/ha, will fence
  and enhance the native vegetation on those 20
  hectares if paid 100/ha, etc.

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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

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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 open-cry
format) The payment is equal to the price that
would have been paid if the unit had to be
sourced from the other bidders.
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Payment rules A numerical example
2 bidders with 4 units to sale each. Total demand
is 4 units
Uniform Price 4 R1 448 R2
448 Discriminatory R1 134 R2
246 Generalized Vickrey (clinched) R1 9514
R2 7613
Bidder 1 Bidder 2
1 2 3 4 6 5 7
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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 generalized Vickrey
Payment under uniform
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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)

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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

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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

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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

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Propensity of player i to choose strategy (a,b)
Neighbours
Strategy
b choice

• Law of effect
• Experimentation
• Recency

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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) 2C(S) C(L)
  3C(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

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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?

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Results
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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

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Bidding strategies uniform auction
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Bidding strategies discriminatory
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Bidding strategies deviations in entry prices
(homogeneous bidders)
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Bidding strategies deviations in bid slopes
(homogeneous bidders)
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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)

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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

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Budgetary performance
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Social cost efficiency
Measured by the production costs of units sold
Auctions perform equivalently for the two
populations
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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

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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 ?

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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)

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Multi-unit Auction for Perennial Pasture
Establishment and Recovery (MAPPER)(a
multi-unit, uniform price auction)
Frank DEmden, NRM Development Officer, DAFWA
Esperance
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Objectives

• Strategic objective
• Reduce sedimentation of Young River Stokes
  Inlet
• Operational objective
• Establish perennial pasture filter strips
  adjacent to waterways
• Contain riparian saline discharge

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How will it work? The EOI
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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
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How will it work? The Plan
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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 gt4 ? total
ha in bid
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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

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Layers in HydroEcon
Policy layer
Farming community layer Agent-based
implementation of whole-farm models (MIDAS-type)
and auction models
Biophysical layer SWAT suite of hydrology, water
quality, and other models
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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

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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

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Thank youemail ahailu_at_are.uwa.edu.auQuestio
ns?Comments?