Auctions. Advanced Ind. Management. History, Examples. Different Formats. Bidding Strategies. Prof. Wirl SS 2016 Page 1

Transcription

1 Auctions History, Examples Different Formats Bidding Strategies Prof. Wirl SS 2016 Page 1

2 History, Examples, Introduction Definition (Molduvanu): Competitive exchange process in which each trader from one market side submits a bid, the most favorable one of which is selected by the complementary market side for the transaction. Most commonly, the bidders form the potential buyers of a commodity, and the bid-taker is a monopolistic seller. Also common is the converse constellation, where a monopsonic buyer elicits price offers from competing sellers ( procurement auction). In a narrow sense, auctions form a variety of familiar and less familiar selling and buying mechanisms for goods reaching from objects of art and collectibles to natural resources like minerals and agricultural products, to treasury bonds, construction and supply contracts, oil drilling rights and broadcasting licenses. Also take-over battles for firms or conglomerates are an explicit auction. In a broader sense, auctions provide an explicit description of price formation processes that arise from strategic interaction in markets. More general auction mechanisms with competition on both market sides, so-called double auctions, form exchange institutions that map competing price bids (buying demands) and price asks (selling offers) into an allocation of the goods among the traders. Given the vector of bids and asks (and some matching rule), the terms of trade for various quantities of one or several goods are endogenously determined. A prototypical example for double auctions are institutionalized markets of financial assets and financial derivatives. Prof. Wirl SS 2016 Page 2

3 History, Examples, Introduction Auctions are models of 'thin markets', making precise the sense in which markets 'find prices' that can 'reveal' an underlying economic value. This is shown distinctively by the fact they are the unique exchange mechanism adopted whenever competitive market prices do not exist but the object sold is of particular uniqueness and size, such as in privatizations of government enterprises, in the sale of complex procurement contracts, or seldom goods of arts; or when the resource in question does not have a price other than the terms of trade which are revealed through strategic interaction of traders, such as financial assets like stock, options, corporate or government bonds. In a sense, strategic equilibria of competitive bidding games have many efficiency properties that generalize those of competitive market equilibrium. As it is the highest (buying) asks and the lowest (selling) offers that are selected for the transaction, the resulting allocation of commodities and quantities is efficient ex post. Under appropriate conditions, equilibrium outcomes from double auctions are even efficient in an interim sense (see efficiency). Under reasonable informational assumptions, the equilibrium bids of common value auctions (see below) converge to the competitive equilibrium price as the number of bidders grows large (see also competitive market equilibrium). Auctions are modelled as bidding games of incomplete information. The bidders' (players') strategies are bid functions converting their private information about the objects in sale, and previous bids observed, into a money amount that is bid. Such bidding games provide unified descriptions of many competitive processes from diverse contexts. Together with the most common auction formats, we mention some examples below. Prof. Wirl SS 2016 Page 3

4 Examples Auction Revenues ( per capita) from licences van Damme (2002). # GSM-Liz # UMTS revenues UK Netherlands Germany Italy Austria Switzerland Belgium Danmark Prof. Wirl SS 2016 Page 4

5 Examples: Flowers A BUNCH of flowers can appear beguilingly simple, but it is a miracle of distribution. Its delicate blooms may have grown on farms scattered around the world, yet they arrived at your local florist within days of harvest. Along the way, crowded with millions of others, your stems may have been part of the endless parade under the fluorescent lights of the Dutch flower auctions. Run by co-operatives of local growers, the auctions embody logistical virtuosity. Each lot of flowers 30% of them grown abroad is unpacked, placed in buckets of water, wheeled under an electronic clock before a gallery of bidders, and then packed up again and shipped to its new owners, all before 9am each day. Over 17m stems are sold each day beneath the 39 descending-bid clocks at FloraHolland and Bloemenveiling Aalsmeer, the two biggest flower auctions. Jacques Teelen, boss of FloraHolland, boasts that within 36 hours a flower can reach any florist in Europe. Prof. Wirl SS 2016 Page 5

6 Example ebay & recent trends THE first item sold on ebay, an online marketplace, was a broken laser pointer, which was snapped up for $14.83 in September By 2002 ebay had hosted nearly $15 billion of transactions and had more registered users than Britain had people. Yet the fad for online auctions faded almost as quickly as it appeared. Only 20% of sales on ebay, which turns 20 on September 3rd, now involve auctions. Prof. Wirl SS 2016 Page 6

7 Auction Formats English: Japanese Sealed bid, second price Sealed bid, first price Dutch Equivalences? All pay auctions Auctions for shares Prof. Wirl SS 2016 Page 7

8 Further Definitions Information Private value common value affiliated (correlated) value (Milgrom-Weber). Reserve price Prof. Wirl SS 2016 Page 8

9 Auction Formats First price (sealed bid) auction: Simultaneous bidding game where the bidder that has submitted the highest bid is awarded the object and pays his own bid (which is the 'first highest' bid). The multi-object form of the first price auction is called discriminatory auction. The equilibrium bid functions of first price auctions balance the trade- off that a higher winning probability is 'bought' by a higher expected payment. As a result, the bidders' private information is revealed in the bids in shaded form only. Oligopolistic competition of price setting firms under incomplete information (Betrand competition) is an instance of a first price procurement auction. Second price (sealed bid) auction: Simultaneous bidding game where the bidder that has submitted the highest bid is awarded the object, and he pays the highest competing bid only (which is the 'second highest' bid). In second price auctions with statistically independent private valuations, each bidder has a dominant strategy to bid exactly his valuation. The second price auction also is called Vickrey auction ; its multi-object form is the uniform price auction. English (open bid) auction: Sequential bidding game where the standing bid wins the item unless another, higher bid is submitted. Bidders can submit bids as often as they want to, and they observe (hear) all previous bids. Often, a new bid has to increase the standing bid by some minimal amount (advance). The English auction is known to have been in use since antique times; from this auction format the word derives: the latin word augere means to increase. With statistically independent private valuations, an English auction is equivalent in terms of payoffs to a second price sealed bid auction. Japanese as the English, yet price is raised by clock and participants must log out if not willing to buy. Prof. Wirl SS 2016 Page 9

10 Auction Formats Dutch auction: Sequential biding game where the standing price is gradually lowered, typically by means of an exogenous counting device (a clock, or a pointer), until it is stopped by a bidder. The first bidder to halt the clock wins the item and pays the price where he stopped the wheel. Dutch auctions are strategically equivalent to first price sealed bid auctions. The name derives from the fact that many agricultural products worldwide, but in particular Dutch flowers, are sold in this way. All-pay auction: Simultaneous bidding game where the bidder that has submitted the highest bid is awarded the object, and all bidders pay their own bids. A subvariant is the second price all pay auction, also war of attrition, where each bidder pays his own bid but the winner only pays the second highest bid. For example, campaign spending and political lobbying processes are second-price all pay auctions; likewise, timing decisions on the private provision of public goods have the structure of second price all pay auctions. Auctions for shares: Divisible objects ( shares, e.g. stocks). Bidders can determine how many shares they are willing to purchase at which price, e.g. 1 share at 1, two shares at 1.5, and so on, i.e., bidders have to specify functions. Prof. Wirl SS 2016 Page 10

11 Definitions & Terms Private value auction: bidders attach to the object a purely private value. Conceptually, these subjective and individual valuations of an object (e.g., a painting of an unfamous painter) are statstically independent realizations. Common value auction: Instead of having statistically independent information, the bidders' typically obtain private signals about an unknown common value of the resource in sale which are correlated with the underlying (unknown) common value, and correlated with one another. For example, prior to auctions of oil drilling licenses, the bidding companies obtain extensive seismic information on the likely quantity of oil hidden in the earth (or sea). In order to prepare profitable bids, the bidders then have to estimate the likely information obtained by rivalling bidders. In particular, the equilibrium bids must incoporate the fact that given a bidder wins the auction, all rivalling bids will have been lower, and thus the (unknown) common value on average will assessed to be lower than it would have been estimated without having won the auction. In this sense, winning the auction is 'bad news' that must be anticipated and incorporated into the bids, in order to avoid falling prey to a so-called winner's curse. Prof. Wirl SS 2016 Page 11

12 Definitions & Terms Reserve price: Minimal amount that has to be bid in order that the the bid-taker concedes his property rights for the object to the highest bidder. If the highest bid fails to reach at least the reserve price, the auctioneer keeps the object (abstains from a sale). Although reserve prices reduce the probability of a sale, they can improve the seller's expected returns because they force bidders with higher valuations to bid more than they otherwise would. Appropriately designed reserve prices thus are devices to extract more of the bidders' information rents (see the entry on rents). Prof. Wirl SS 2016 Page 12

13 Bidding Strategies Private Value Second Price auction θ willingness to pay of bidder i, private value Bid of bidder i max. bid of others Payoff Therefore, truthful bidding is undominated. Prof. Wirl SS 2016 Page 13

14 Bidding Strategies Private Value First Price auction Trade off: A higher bid increases the probability of winning but reduces the payoff since the winning bidder must pay his bid. Assumptions: two bidders (i, j) with private values θ i and θ i uniformly distributed over [0, 1] Prof. Wirl SS 2016 Page 14

15 Bidding Strategies Private Value First Price auction (cont.) Assume linear bidding strategies of both bidders p i = probability of i winning => payoff: Winning thus: from the point of equality on: thus: Payoff: i.e., bid only half of Your valuation General for n symmetric bidders: α = (n 1)/n Prof. Wirl SS 2016 Page 15

16 Bidding Strategies Common Value Winner s Curse First Price Auction Example: 5 persons bid for a purse with unknown content, where each receives the unbiased signal Accounting for the unbiased signal, restriction to integers and trying to make some money suggest the bidding strategy: With expected gain: 1. This is wrong, because only the highest signal wins = loss 1. Accounting for winner s curse: => expected gain = 1/5. Prof. Wirl SS 2016 Page 16

17 Revenue Equivalence Theorem Problem: Which auction format should be favored? Consider any auction satisfying 1. The good is allocated efficiently 2. A bidder with reservation price 0 cannot profit All auctions satisfying 1 and 2 deliver the same expected revenue for the seller. Prof. Wirl SS 2016 Page 17

18 Extension: Auctions with Affiliated Values Milgrom-Weber (1982) Prof. Wirl SS 2016 Page 18

19 Bidding for Shares Bidders maximize their difference between benefits v(q) = q q 2 and their expenditures, pq. from Milgrom, Putting Auction Theory to Work, Chapter 7, Cambridge University Press 2004 Competitive bidding would result from equating marginal revenues to the price resulting in: p * (q) = 1 2q, i.e., a globally defined and as expected downward sloping bidding function with market clearing at p = 1-2/N. For strategic bidders we get (assuming symmetry and market clearing), Differentiating yields the differential equation: Problem: No boundary condition => infinitely many solutions. Prof. Wirl SS 2016 Page 19

20 Bidding for Shares This characterization produces indeterminacy even assuming declining bidding function, $ P(z) = a bz, a > 0, b > 0, (L) 1.0 Market clearing, u = q = 1/N at the marking clearing point, q = 1/N. Possibility of low price equilibria (blue strategy). However, these linear bidding functions lack global sense. The blue line would bid for small quantities above the marginal benefit while, the yellow one would bid a positive price beyond the saturation level (at q = ½). Only the red line makes sense over the entire and possible outcome p(0) = v (0) = Linear function P(q) in Wilson s bidding for shares in a uniform price auction, N = 4. q Prof. Wirl SS 2016 Page 20

21 Internet Auctions ebay Prof. Wirl SS 2016 Page 21

22 Internet Auctions Sniping (Ockenfels and Roth) Prof. Wirl SS 2016 Page 22

23 Shubik s dollar auction 1. (As in any auction) the dollar bill goes to the highest bidder, who pays whatever the high bid was. Each new bid has to be higher than the current high bid, and the game ends when there is no new bid within a specified time limit. 2. (Unlike at Sotheby's!) the second-highest bidder also has to pay the amount of his last bid and gets nothing in return. You really don't want to be the second-highest bidder. Prof. Wirl SS 2016 Page 23

24 Shubik s dollar auction Shubik's two rules swiftly lead to madness. "Do I hear 10 cents?" asks the auctioneer "5 cents?" Well, it's a dollar bill, and anyone can have it for a penny. So someone says 1 cent. The auctioneer accepts the bid. Now anyone can have the dollar bill for 2 cents. That's still better than the rate Chase Manhattan gives you, so someone says 2 cents. It would be crazy not to. The second bid puts the first bidder in the uncomfortable position of being the second-highest bidder. Should the bidding stop now, he would be charged 1 cent for nothing. So this person has particular reason to make a new bid "3 cents." And so on Maybe you're way ahead of me. You might think that the bill will finally go for the full price of $1.00 a sad comment on greed, that no one got a bargain. If so, you'd be way too optimistic. Eventually someone does bid $1.00. That leaves someone else with a second-highest bid of 99 cents or less. If the bidding stops at $1.00, the underbidder is in the hole for as much as 99 cents. So this person has incentive to bid $1.01 for the dollar bill. Provided he wins, he would be out only a penny (for paying $1.01 for a dollar bill). That's better than losing 99 cents. That leads the $1.00 bidder to top that bid. Shubik wrote, "There is a pause and hesitation in the group as the bid goes through the one dollar barrier. From then on, there is a duel with bursts of speed until tension builds, bidding then slows and finally peters out." No matter what the stage of the bidding, the second-highest bidder can improve his position by almost a dollar by barely topping the current high bid. Yet the predicament of the second-highest bidder gets worse and worse! This peculiar game leads to a bad case of buyer's remorse. The highest bidder pays far more than a dollar for a dollar, and the second-highest bidder pays far more than a dollar for nothing. Prof. Wirl SS 2016 Page 24

25 Shubik s dollar auction Computer scientist Marvin Minsky learned of the game and popularized it at MIT. Shubik reported: "Experience with the game has shown that it is possible to 'sell' a dollar bill for considerably more than a dollar. A total of payments between three and five dollars is not uncommon." Possibly W. C. Fields said it best: "If at first you don't succeed, try, try again. Then quit. No use being a damn fool about it." Shubik's dollar auction demonstrates the difficulty of using von Neumann and Morgenstern's game theory in certain situations. The dollar auction game is conceptually simple and contains no surprise features or hidden information. It ought to be a "textbook case" of game theory. It ought to be a profitable game, too. The game dangles a potential profit of up to a dollar in front of the bidders, and that profit is no illusion. Besides, no one is forced to make a bid. Surely a rational player can't lose. The players who bid up a dollar to many times its value must be acting "irrationally." It is more difficult to decide where they go wrong. Maybe the problem is that there is no obvious place to draw the line between a rational bid and an irrational one. Shubik wrote of the dollar auction that "a game theory analysis alone will probably never be adequate to explain such a process." Prof. Wirl SS 2016 Page 25