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  1. Auction Markets Jon Levin Winter 2010 Economics 136

  2. Multi-Unit Auctions

  3. Treasury auctions Auction-rate securities IPO auctions Privatization Electricity markets Asset sales Condominium sales Wine/Art/Antiques Auto auctions Natural resources Radio spectrum Emissions permits Airport landing slots Bus routes Procurement contracts Sponsored search Internet display ads eBay marketplace Examples

  4. Sequential auctions • Auction houses often sell identical goods sequentially (e.g. lots of wine). • What happens at sequential auctions? • Should you bid your value in the first auction? • Are early prices higher or lower than later prices?

  5. Sotheby Wine Auctions Source: Ashenfelter (1989, Journal of Economic Perspectives)

  6. Declining Prices

  7. A puzzle? • Standard theory: in a symmetric private value setting, prices need not be equal across sequential first or second-price auctions, but… • Weber’s Theorem. Equilibrium prices should follow a random walk: E[pt+1|p1…pt]=pt • Yet the “declining price anomaly appears to be quite robust – wine, art, cattle, etc – and variants observed with non-identical items. • This remains something of an open puzzle.

  8. Simultaneous Sales of Identical items • Consider auction for k identical items. • Possible “one-shot” auction methods • “Uniform price” (clock and sealed bid) • “Discriminatory price” (pay-your-bid and Vickrey). • We will see that one important issue is whether bidders want just one item, or are potentially interested in winning several items.

  9. “Uniform price” auctions • Sellers often want to run an auction in which all winners pay the same “uniform” price. • Perceived as “fair”; achieves “price discovery” • Uniform price formats • Clock auction: seller announces a sequence of prices and bidders name quantities until a market-clearing price is found and auction ends. • Sealed bidding: participants bid a price-quantity schedule and bids are used to determine the uniform market-clearing price.

  10. British CO2 Auctions • Greenhouse Gas Emissions Trading Scheme Auction, United Kingdom, 2002. • UK government aimed to spend 215 million British pounds to get firms reduce CO2 emissions. • Clock auction used to determine • What price to pay per unit? • Which firms to reward?

  11. Greenhouse Auction Rules • Auctioneer calls out price • Price starts high and decreases each round. • Each round, bidders state tons of CO2 they will abate • Tons abated can only decrease as prices decrease. • Auctioneer multiplies tons of abatement times price. • If total cost exceeds budget, lowers the price • When total cost first falls short of budget, auction ends and that allocation is implemented • Auction results • 38 bidders (34 winners), 4m metric tons of CO2 reduction. • Price per metric ton: £215m/4m= £53.75

  12. Graphical treatment P UK “Demand Curve, defined so that Q*P(Q)=£215m p1 p2 Falling prices trace out a “supply curve”. p* Q

  13. Sealed bid version • Uniform-price sealed bid auction • Auctioneer posts its demand curve • Bidders submit “supply curves” - i.e. how much they will supply at each price. • Individual supply curves are aggregated to form an aggregate supply curve. • Price is set so that supply = demand.

  14. Strategic equivalence? • Are clock and sealed auctions strategically equivalent? • Suppose bidders in the clock auction observe only the prices and that prices decline in a fixed sequence. • Bidders are then effectively being asked to reveal their supply curves from the top down, with no new information each round other than that the current price is relevant. • So yes, the clock auction is strategically equivalent to a sealed bid auction in which supply curves get written down in advance. • Equivalence may fail if more information is revealed each round.

  15. Incentives with Uniform Price • Suppose each bidder wants a single item. • Values are drawn from U[0,1]. • n bidders, k items with n>k. • Bidders submit bids: price = k+1 highest bid. Theorem. For a bidder with single item demand, it is a dominant strategy to bid one’s value. • Proof. Similar to the second price case.

  16. Demand reduction • Example: three items for sale • Bidder 1: value 120 and wants 1 item. • Bidder 2: value 110 and wants 1 item. • Bidder 3: value 100 and wants 1 item. • Bidder 4: value 105 and wants 2 items. • Consider what happens with “truthful” bidding • Bids are 120, 110, 105, 105, 100. • Three highest bids are winners • Fourth highest bid is 105 => winners pay 105 each.

  17. Demand reduction • Example: three items for sale • Bidder 1: value 120 and wants 1 item. • Bidder 2: value 110 and wants 1 item. • Bidder 3: value 100 and wants 1 item. • Bidder 4: value 105 and wants 2 items. • “Demand reduction” by bidder 4 • If he bids 105, he wins 1 item and pays 105. • If he bids 101, bids are 120, 110, 101, 101, 100. • He still wins 1 and lowers the price to 101!

  18. Example, cont. • Again, three items and values • Bidder 1: 120 • Bidder 2: 110 • Bidder 3: 100 • Bidder 4: 115 and wants two units. • Demand reduction by bidder 4 • Bid 115 for both units => wins two, price =110. • Bid 115 for first unit, 100 for second => wins 1, p=100. • Bidder four optimally exercises “market power”.

  19. Demand Reduction Picture Supply Q=3 P b1 Opponent Bids and demand curve b2 “Residual supply curve” Multi-unit bidder wants to maximize profit by behaving as a monopsonist against the residual supply curve. b3 b4 3 Q

  20. Low Price Equilibrium Supply Expanded supply P “Residual supply curve” in a “regular” equilbrium Residual supply curve in a low price equilibrium Residual supply curve if seller “adds elasticity” 3 Q

  21. Multi-Unit Auctions and Financial Assets

  22. Today’s Lecture • Uniform price sealed bid auctions • Virtues: simple, “fair”, reveal “market price” • Concerns: demand reduction, “low price” eqm • Comparison to alternatives • Discriminatory price auctions • Vickrey auction • Application to financial markets • Extensions to multiple goods

  23. Uniform-price sealed bid auction Auctioneer posts its supply curve Bidders submit “demand curves” - i.e. how much they want at each price. Individual demand curves are aggregated to form an aggregate demand curve. Price is set so that supply = demand Demands at the market clearing price are satisfied.

  24. Incentives with Uniform Price • N bidders, Kitems with N>K • Each bidder wants one unit, values U[0,1]. • Bids submitted (offer to buy one unit at some price) • Market clearing price = any price between the kth highest bid and the K+1th highest bid (why?) • Assume lowest clearing price: K+1 highest bid. Theorem. For a bidder with single item demand, it is a dominant strategy to bid one’s value. • Proof. Similar to the second price case. • Theorem is not true if bidders want multiple units (next slide!)

  25. Demand reduction • Example: three items for sale • Bidder 1: value 120 and wants 1 item. • Bidder 2: value 110 and wants 1 item. • Bidder 3: value 100 and wants 1 item. • Bidder 4: value 105 and wants 2 items. • Consider what happens with “truthful” bidding • Bids are 120, 110, 105, 105, 100. • Three highest bids are winners • Fourth highest bid is 105 => winners pay 105 each.

  26. Demand reduction • Example: three items for sale • Bidder 1: value 120 and wants 1 item. • Bidder 2: value 110 and wants 1 item. • Bidder 3: value 100 and wants 1 item. • Bidder 4: value 105 and wants 2 items. • “Demand reduction” by bidder 4 • If he bids 105, he wins 1 item and pays 105. • If he bids 101, bids are 120, 110, 101, 101, 100. • He still wins 1 and lowers the price to 101!

  27. Example, cont. • Again, three items and values • Bidder 1: 120 • Bidder 2: 110 • Bidder 3: 100 • Bidder 4: 115 and wants two units. • Demand reduction by bidder 4 • Bid 115 for both units => wins two, price =110. • Bid 115 for first unit, 100 for second => wins 1, p=100. • Bidder four optimally exercises “market power”.

  28. Demand Reduction • General model • N bidders, K items, where 2k<N. • Each bidder has positive value for at least two items. • Bidder values random, but always satisfy v1j≥ v2j • Theorem.In the k+1 price auction, it is weakly dominant to bid true value for first unit. However: • there is no equilibrium in which bidders all bid their full values for both items, and • there is no equilibrium in undominated strategies that is efficient for all realized valuations.

  29. “Low price” Equilibria • With fixed supply, uniform price auction can have equilibria with low prices due to demand reduction. • Example: three units, three bidders. • Bidders value units at 10, want as many as possible. • The price “should be” 10 if there is competition. • What if each bidder offers to buy one unit for 10, and no additional units at any price above zero. • Bidders split the units, price is zero! • Because a bidder who wants to purchase additional units has to pay ten, there is no reason to demand more. The low price bidding is a Nash equilibrium!

  30. Making supply elastic • Suppose the seller offers • To sell 3 units at any price • To sell 4 units if (and only if) price exceeds 4 • Claim: Any Nash equilibrium for bidders involves selling four units at a price of at least 4. • If bidders bid (10,0), each bidder gets 1 unit, p=0. • Each bidder has incentive to bid (10,4) => win two units and price increases to four. Profit of 2*(10-4)=12>10. • Equilibrium will have one bidder winning two items, and fifth highest bid somewhere between 4 and 10. • Somewhat surprisingly, seller has managed to increase supply and yet also increase prices.

  31. California electricity crisis • The California electricity crisis of 2001 • Prices go from around $45 megawatt-hour to as high as $1400. • Paul Joskow of MIT: “California electricity crisis is what happens when a vertical supply curve intersects a vertical demand curve.” • Steep supply/demand: during the crisis a 5% lowering of demand (or increase in supply) would have lowered prices by 50%! • Borenstein, Bushnell, Wolak (AER, 2003): vertical demand because consumers don’t react to price, vertical supply because generators strategically withhold power. • Remedies? • Create elasticity in electricity demand (how?). • Restrict slope of submitted supply curves. • Encourage build-out of additional capacity (how?). • Forward contracts (unravel the market!).

  32. Increasing Returns… • Discussion implicitly focused on bidders with decreasing marginal values who submit downward-sloping demand curves. • What if there are scale economies? • Two units for sale • Bidder 1 offers 10 for one unit. • Bidder 2 offers 5 for first unit and 11 for second. • There is no uniform price that clears the market! • Not much is known about performance of uniform price auctions where there are scale economies.

  33. Expanding the example… Two units for sale Bidder 1 offers 10 for one unit. Bidder 2 offers 5 for first unit and 11 for second. Consider possible prices At p < 8, demand = 3 At p = 8, demand = 1 or 3 At p in (8,10), demand = 1 At p = 10, demand = 0 or 1 At p > 10, demand = 0 Problem: demand “crosses” supply at price = 8, but at that price, Bidder 1 demands 1, and Bidder 2 demands 0 or 2 but is unwilling to buy 1! So can’t have demand=supply!!!

  34. Discriminatory Price Auctions • Alternative is a “pay-your-bid” format • Bidders submit bids (offers to buy different quantities at different prices) • Seller finds price where supply=demand • All bids above clearing price are satisfied, but winners pay their bid rather than the clearing price.

  35. Example • Example: three items for sale • Bidder 1: value 120 and wants 1 item. • Bidder 2: value 110 and wants 1 item. • Bidder 3: value 100 and wants 1 item. • Bidder 4: value 105 and wants 2 items. • Suppose “truthful bids” • Bidder 1: (1, 120) “buy one at any price < 120” • Bidder 2: (1, 110) • Bidder 3: (1, 100) • Bidder 4: (2, 105) • Outcome: 1, 2, 4 win and pay 120, 110, 105. • Is this an equilibrium? Why or why not?

  36. Example, cont. • Example • Bidders 1, 2, 3 want 1 item and values 120, 110, 100. • Bidder 4: wants two items and value 105. • Possible equilibrium bids? • Bidder 1: (1, 105) • Bidder 2: (1, 105) • Bidder 3: (1, 100) • Bidder 4: (2, 105) • So 1, 2, 4 win and all pay 105. Is this an eqm? Why or why not?

  37. Example, cont. • Example • Bidders 1, 2, 3 want 1 item and values 120, 110, 100. • Bidder 4: wants two items and value 105. • Possible equilibrium bids? • Bidder 1: (1, 100 + penny) • Bidder 2: (1, 100 + penny) • Bidder 3: (1, 100) • Bidder 4: (2, 100 + penny) • So 1, 2, 4 win and all pay 100 + penny. Is this an eqm? • The actual equilibrium involves mixed strategies with bids distributed between 100 and 105!

  38. Uniform vs. Discriminatory • Both auctions can be inefficient. • Both auctions create an incentive to “reduce demand” if bidders want multiple units. • Does one lead to higher prices? • Not clear in general. • Does one lead to higher or lower participation or reveal more useful information? • Sometimes argued that uniform price auction is good for small bidders b/c its easy to participate and get the “market price”, but discriminatory price can sometimes be painful for large high-value bidder.

  39. US Treasury Experience • US Treasuy historically ran discriminatory auctions (since the 1970s) to sell bonds. • Beginning in 1992, switched to uniform price. • Rationale • Aim for more liquid market (transparency) • Encourage broader participation • Encourage competition (slightly vague) • Features of the market: large, highly liquid • There is some “price impact” from the new issuance. • There is also a “when-issued” market that runs prior to the auction, so participants can guage likely price. • Many participants (75-85 bidders), but relatively small number of primary dealers win a lot of the bonds.

  40. Treasury experience, cont. • Evidence from US transition • Switch to uniform price led to somewhat lower spread between auction price and WI price (but not very large or stat. significant). • Somewhat more volatility between auction price and WI price b/c more dispersed bids w/ uniform price auction. • Awards to primary dealers similar under the two types of auctions, but share of awards to the very top dealers decreased with uniform price. • Debate in other countries: possible that design may matter more if market is thinner or less transparent.

  41. TARP Warrant Auctions • As part of TARP, Treasury received warrants from banks that were “bailed out” • Warrants give holder a right to buy the stock at some “strike price” at any point over the next 10 years. • Like an option except that when a warrant is exercised, the firm issues new shares rather than buying back shares (so there is dilution) • Treasury negotiated with banks to sell them back the warrants but some negotiations failed, leaving treasury to dispose of the warrants. • Question: how to design an auction to sell the warrants?

  42. Warrant auctions, cont. • Questions one must address • Uniform price or discriminatory? • Sell all warrants at once, or over time? • Sealed bid or ascending auction? • Potential for a “winners curse” • Treasury (via auction agent) decided on a standard treasury format, ran three in fall. • Evidence from JPM auction (largest at $1 bn) suggests a large price impact (auction price 30% below subsequent after-market price. • Now treasury must consider whether this was a big number, and whether to change the design. What data would you want to look at?

  43. An Efficient Auction? • Back to our example with three items for sale • Bidder 1: value 120 and wants 1 item. • Bidder 2: value 110 and wants 1 item. • Bidder 3: value 100 and wants 1 item. • Bidder 4: value 105 and wants 2 items. • Is there a pricing rule that would make it a dominant strategy for each bidder to bid truthfully – and would lead to an efficient allocation of the items?

  44. “Vickrey” Prices • Set price for each bidder equal to the value per unit the bidder “displaces. • Equivalently: use submitted values to compute total value with and without the bidder present. • Set price for the bidder so that his profit equals the value he creates. • Vickrey pricing makes bidding truthfully a dominant strategy. • But Vickrey prices are not uniform prices!

  45. Vickrey pricing • Example: three items for sale • Bidder 1: value 120 and wants 1 item. • Bidder 2: value 110 and wants 1 item. • Bidder 3: value 100 and wants 1 item. • Bidder 4: value 105 and wants 2 items. • Vickrey pricing if truthful bids • Bidders 1 and 2 win, pay 105 each (displace 4). • Bidder 4 wins one unit, pays 100 (displaces 3).

  46. Vickrey pricing, again • Example: three items for sale • Bidder 1: value 120 and wants 1 item. • Bidder 2: value 110 and wants 1 item. • Bidder 3: value 100 and wants 1 item. • Bidder 4: value 115 and wants 2 items. • Vickrey pricing if truthful bids • Bidder 1 wins and pays 110 (displaces bidder 2). • Bidder 4 wins two units, pays 100 for first unit (displaces bidder 3) and 110 for second (displaces bidder 2).

  47. General Lessons • Uniform price auctions have fairness, transparency virtues • But encourage demand reduction when bidders want multiple units • Also create the possibility of low price “collusive seeming” equilibria (making supply elastic can help with this problem). • Discriminatory price auctions also encourage demand reduction, but sometimes viewed as a way to raise revenue from high value bidders – although revenue implications generally unclear. • Vickrey pricing can eliminate demand reduction and restore efficiency, but the uniform price property is lost.

  48. Multi-Item Auctions and Matching

  49. Multiple Kinds of Goods • Can we design successful auctions that allow for multiple kinds of goods? • Spectrum licenses covering different cities. • Electricity delivered from/to different places. • Multiple kinds of financial assets. • Emissions reductions in different years. • Different kinds of sponsored search placements.

  50. General issues • What would be desirable properties? • Auction finds “market clearing” prices (uniform price) • Auction is strategyproof (Vickrey), or nearly so. • Auction is relatively simple, robust to collusion, etc. • The challenge • Bidder preferences may be complex and complex preferences are hard to state in sealed bid auction. • Complementarities (like increasing returns) may imply that market clearing prices don’t exist. • Auction complexity and strategy can be serious issues.