AUCTIONS. Vito Fragnelli Transportnet Genova - December 11, 2008

Transcription

1 1 AUCTIONS Vito Fragnelli Transportnet Genova - December 11, 2008

2 1 INTRODUCTION 2 1 Introduction Auction is an efficient and flexible selling mechanism for bilateral markets One side has an active role while the other has a passive one Auctions may be used for selling items or for purchasing items (reverse auction) HERE: selling auction The seller sets the rules, choosing the auction type Auctions profit from scarcity of goods and from competition among buyers

3 1 INTRODUCTION 3 Very short history The first recorded auction took place in Babylon in 500 B.C. for assigning daughters to possible husbands (women without beauty had to pay for entering the auction) In the Roman world auctions were very usual for selling slaves and spoils ( auction is after Latin augere = to increase) The Roman Empire was auctioned in 193 A.D. by the Praetorian Guard after killing the emperor Pertinax The winner, Didius Julianus, was beheaded two months later when Septimus Severus conquered Rome: the most outstanding example of winner s curse The word auction appears in the Oxford English Dictionary in 1595 for the first time The first auction house, the Stockholms Auktionwerk, was opened in 1674 In 1744 Sotheby s was established, followed by Christie s in 1766

4 1 INTRODUCTION 4 Auctions are very common, but the underlying mechanism could be very complex The mechanism has to satisfy no rule, except that all the details have to be made public One dollar auction (Shubik, 1971) Web auctions

5 1 INTRODUCTION 5 Agents of an auction auctioneer seller (sometimes the auctioneer himself) buyers or bidders

6 1 INTRODUCTION 6 Auction features *Numberofitems: one several - each winner gets one item - a winner may get more than one item * Auctionrules: admittance - open -close bid - aloud -sealed winner -... *Paymentrules: one per item - reserve price - highest bidder - highest bidder with unique bid - lowest bidder with unique bid - first price - second price more than one per item - several -all

7 1 INTRODUCTION 7 Auctions are usual when no market price exists and/or the quality of the good is uncertain Wines Paintings Flowers Fish Bonds Oil drilling rights Loans with unknown risk...

8 1 INTRODUCTION 8 Private value Each bidder knows his own valuation of the item that is private information to himself; the valuation is independent from those of the other bidders The value of an item derives from the utility of its possession Common value At the end of the auction the item has the same value for all the bidders, but at the beginning of the auction it may be only estimated using different private information or signals The value of an item derives from the utility of its resale

9 1 INTRODUCTION 9 Why to use an auction mechanism? It allows selling an object or a good at a high price also when the seller has no idea of its actual value, often in a short time The price is stated by the buyers that may have better information about the item (the seller may fix a reserve price) A suitable mechanism protects the weak seller or maximizes the profit of a strong seller The seller may increase his information about the actual value of the item

10 1 INTRODUCTION 10 Which is the best auction mechanism? Usually, the seller and the buyers have different points of view They take into account: time (flowers, fish, perishable goods) collusions (rings) necessity of presence

11 2 TYPES OF AUCTION 11 2 Types of auction 2.1 English auction It is the most popular auction; it is called also open-outcry auction or ascending-price auction The auctioneer proposes an opening price and the bidders bid increasing amounts (the increasing may be fixed or free) The item goes to the highest bidder that pays his bid, unless there exists a higher reserve price or other rights (state) The auctioneer plays a relevant role asking for further bids The presence of the buyer is necessary The competition and the enthusiasm may push up the price Variation The price rises continuously and the buyers announce they drop out (after dropping out they may or may not re-enter)

12 2 TYPES OF AUCTION Dutch auction Its name is after the selling mechanism of flowers in the Netherlands; it is called also descendingprice auction It is usual also for fish market A counter goes down quickly and when a buyer accepts the current price stops the counter (and the auction), gets the item and pays the current price The whole procedure requires few seconds Also in this case the presence of the buyer is necessary, but it is easy to be represented

13 2 TYPES OF AUCTION First-price sealed-bid auction Each buyer submits a bid in a sealed envelope (or a similar way); the bids may be submitted at thesametimeorbeforeadeadline When the envelopes are opened, the highest bidder gets the item and pays the bid The winner s curse is possible The whole procedure my require months The presence of the buyer is not necessary

14 2 TYPES OF AUCTION Second-price sealed-bid auction or Vickrey auction Its name is after William Vickrey, Bank of Sweden prize for Economics in 1996 (Vickrey, 1961) The mechanism is similar to the first-price sealed-bid auction, but the winner pays the second highest bid (the bids may be different so the price may be also higher) The importance of this type of auction is that it favours truthful bids The truthful bid is a weakly dominant strategy (Milgrom, 1989) Using a lower bid the buyer may lose the item for a price below his valuation, while with a higher bid he may obtain the item for a price larger than his valuation

15 3 EQUIVALENCE RESULTS 15 3 Equivalence results The English auction is (quite) equivalent to the Vickrey auction The Dutch auction is equivalent to the first-price sealed-bid auction Revenue Equivalence Theorem - RET (see Klemperer, 2004) Assume each of a given number of risk-neutral potential buyers of an object has a privately known signal independently drawn from a common, strictly increasing, atomless distribution. Then any auction mechanism in which: (i) the object always goes to the buyer with the highest signal, and (ii) any bidder with the lowest-feasible signal expects zero surplus, yields the same expected revenue (and results in each bidder making the same expected payment as a function of his signal). Luckily, the hypotheses of the theorem are hardly met: otherwise, why to think to an optimal mechanism?

16 4 AUCTION STRATEGIES 16 4 Auction strategies Several elements may influence the outcome of an auction risk-aversion or risk-neutrality private or common value information, mainly asymmetry In theory when bidders have common values (RET does not hold) the revenues may be ranked as English auction, Vickrey auction and Dutch auction and first-price sealed-bid auction at the same level, according to the capacity of generating information when bidders have private values but are risk-averse (RET does not hold) Dutch auction and first-price sealed-bid auction give the same revenue, larger than English auction and Vickrey auction that give also the same revenue (risk-aversion generates higher bids as buyers try to avoid losing item)

17 4 AUCTION STRATEGIES Auction strategies for the bidder English auction The bidder should offer a little bit more than the last bid, until his valuation is reached and then drop out Dutch auction The bidder may only stop the counter at his valuation First-price sealed-bid auction The bidder faces the tradeoff between to increase his profit (lower bid) and to increase his chance to win (higher bid) Vickrey auction According to Milgrom, the bidder may only offer his true valuation

18 5 WINNER S CURSE 18 5 Winner s curse Basically, each winner thinks that if the other bidders offered less then the value of the item could be lower than his bid In the Dutch auction and first-price sealed-bid auction there is also the possibility to get the object at a lower price Make an experiment at:

19 6 COLLUSION 19 6 Collusion Ring Some buyers agree for making reduced bids; the group assigns the item among them and share the gain Subrings are possible The more an auction favours information exchange, the more collusions are possible; consequently, the ranking is English auction, Vickrey auction, first-price sealed-bid auction and Dutch auction Collusion may involve the seller and some buyers, aiming to raise the final price Sealed-bid auctions may be manipulated colluding with the auctioneer

20 6 COLLUSION 20 In 1999 Germany sold ten blocks of spectrums in a simultaneous ascending auction; a new bid had to increase the previous highest bid of 10% Mannesmann offered millions of DM for blocks from 1 to 5 and 20 millions of DM for blocks from 6 to 10 T-Mobil interpreted it as offer 20 millions of DM for blocks from 1 to 5 and leave blocks from 6 to 10

21 7 MULTIPLE ITEMS AUCTIONS 21 7 Multiple items auctions Several identical (perfect or good substitutes) items are assigned at the end of the auction If each bidder may win at most one object usually he submits a unique offer If a bidder may obtain more than one object he submit as many offers as the items he is interested in The winners pay the same price (uniform pricing) or different prices (discriminatory pricing) Vickrey pricing requires that each buyer bids for all the identical items (the different bids reflect the subadditive valuations) The last winner pays the first losing bid, the next to last winner pays the second losing bid and so on till the highest bidder b 1 b 2 b k+2 b k b k+1 b 2k b 2k+1

22 7 MULTIPLE ITEMS AUCTIONS 22 In case the items are complementary their values are superadditive, so the seller may profit of the increasing interest of the buyers to obtain an item after that he already obtained a complementary one Aparticularcaseisthecombinatorial auction in which different items are auctioned The bidder may offers both for a single item and for bundles of items Some interesting features arise: computational assign the items, maximizing the revenue (NP-complete problem) economic provide incentives for truthful bids (Vickrey auction) other efficient representation and communication

23 8 UMTS AUCTIONS 23 8 UMTS auctions The market structure may be simplified as incumbents (operators of 2G telecom) and entrants (potential new operators) Incumbents have the infrastructure, established customers, brand-name recognition Entrants have to be encouraged in participating the auction (mandating roaming)

24 8 UMTS AUCTIONS The UK auction: a success March-April 2000 Anglo-Dutch mechanism An ascending auction reduces the bidders to the number of licenses plus one A sealed-bid first auction eliminates the last bidder An ascending auction assigns the spectrum The revenues were 650 euros per capita

25 8 UMTS AUCTIONS The Italian auction: a bad example October 2000 Round-ascending mechanism Registration of interested operators; elimination of not suitable ones; at least one license less than the number of bidders Six bidders for five licenses At each round the bidders have to offer at least 5 % more of the worst bid of the previous round After four rounds (two days) Blu quit, just over the reserve price The revenues were 240 euros per capita

26 8 UMTS AUCTIONS The Turkish and the Swiss auctions: two failures Turkey Two licenses in sequencing auctions, where the selling price of the first auction represented the reserve price of the second one A firm offered a very large amount for the first license, so that no operator took part in the second auction and the second license went unsold A very good way to be a monopolist!!! Switzerland Due to last-minute joint-bidding permission, the number of bidders shrank to the number of licenses, that were sold at the reserve price (very low), with a revenue of 20 euros per capita

27 9 TRANSPORTATION AUCTIONS 27 9 Transportation auctions Several proposals exist for applying auction mechanisms to transportation market (slots) HERE Airports Railways

28 9 TRANSPORTATION AUCTIONS Rassenti, Smith, Bulfin A Combinatorial Auction Mechanism for Airport Time Slot Allocation The demand for a take-off slot in the originating airport is not independent from the requirement of a landing slot in the destination airport The standard approach is an auction mechanism at each airport and an after market for selling exceeding slots or buying necessary slots The new approach is a combinatorial sealed-bid auction for allocating the pair of slots required by a flight

29 9 TRANSPORTATION AUCTIONS Brewer, Plott A Binary Conflict Ascending Price (BICAP) Mechanism for the Decentralized Allocation of the Right to Use Railroad Tracks How to shift from a centralized to a decentralized management in selling access to railway systems? Train paths are not independent in an integrated timetable A timetable poses technical, economic and political problems Complementary and substitute paths In the BICAP mechanism agents bid for railroad slot, in real time

30 9 TRANSPORTATION AUCTIONS 30 The mechanism works like a set of simultaneous ascending auctions, each for operating a different train Three elements are involved: a set of feasible outcome allocations a message space through which agents interact each other and with the allocation authority an outcome rule to determine a unique feasible allocation The aim is to maximize the total bid from trains with feasibility constraints Each auction ends when there is no further increase in the bid after a certain period of time and the winner pays his bid The experiments confirm that a decentralized mechanism can solve some of the technical aspects of the rail scheduling problem and yield efficient allocations, with a strong design consistency

31 9 TRANSPORTATION AUCTIONS Nilsson Allocation of Track Capacity. Experimental Evidence on the Use of Priority Auctioning in the Railway Industry This approach is a modification of that by Brewer and Plott, introducing a second-price auction álavickrey The operators submit bids for preferred and alternative paths The operators may change their bids if a higher offer was made The final price is computed considering the alternative situation in which the winner is not present

32 9 TRANSPORTATION AUCTIONS 32 Example 1 (from Nilsson) A B A B A B C A B C a b c solutions have value 2/3 As there is no conflict, a pays 165 for C, withaprofitof75 c gets A and b gets B, with a value of /3 180 = 330 without c, b gets B and a gets A, with a value of /3 111 = 254 the value of allocations excluding c is 2/3 180 = 120 c pays = 134, withaprofitof76 without b, c gets A and B, with a value of /3 162 = 318 the value of allocations excluding b is 210 b pays = 108, withaprofitof12

33 9 TRANSPORTATION AUCTIONS Nilsson Towards a Welfare Enhancing Process to Manage Railway Infrastructure Access This approach looks for a train schedule that maximizes the benefits, addressing also the incentive problem, i.e. the need that operators reveal their value of track access This procedure composed by four steps: 1. the operators register their preferred trains departure and arrival times, alternative paths and submit one bid for each path (willingness-to-pay vs. preferred scheduling) 2. the manager identifies a value-maximising allocation and the price for each path; 3. if there are no conflicts for paths between operators, all get their preferred choices and the process terminates with the operators paying their bids for the assigned path otherwise the operators that have not been allocated their best choice have the opportunity to reconsider their initial train path specifications 4. the process is repeated as long as anyone wants to make changes in bids or path specifications The allocation process may provide relevant information about scarcity of capacity and, consequently, for investment planning Sometimes competition may lead to socially inefficient solutions

34 9 TRANSPORTATION AUCTIONS Borndörfer, Grötschel, Lukac, Mitusch, Schlechte, Schultz, Tanner An Auctioning Approach to Railway Slot Allocation Railway network offers more combinatorial aspects than airport situations This proposal uses an iterative combinatorial auction that takes place in a sequel of rounds Each round consists of two stages: each operator submits simultaneously a set of bids that, jointly with the set of standing bids, represents the set of live bids the optimization machinery is applied on the set of live bids and computes the set of bids accepted in the round, which becomes the new set of standing bids During the optimization process the aim is a conflict-free slot schedule that maximizes the network income The auction ends if for a fixed number of rounds, the total income does not change (e.g. there is no new bid) This approach allows for bidding for train connections (rolling stock management, interdependency of trains) and/or for regular scheduling of trains

35 10 REFERENCES References Borndörfer R, Grötschel M, Lukac S, Mitusch K, Schlechte T, Schultz S, Tanner A (2005) An Auctioning Approach to Railway Slot Allocation ZIB Report ZR Brewer PJ, Plott CR (1996) A Binary Conflict Ascending Price (BICAP) Mechanism for the Decentralized Allocation of the Right to Use Railroad Tracks International Journal of Industrial Organization 14 : Klemperer P (2004) Auctions: Theory and Practice, Princeton University Press, USA. available on line at Krishna V (2002) Auction Theory Academic Press, USA. Milgrom P (1989) Auctions and Bidding: A Primer Journal of Economic Perspectives 3 : Nilsson JE (1999) Allocation of Track Capacity. Experimental Evidence on the Use of Priority Auctioning in the Railway Industry International Journal of Industrial Organization 17 : Nilsson JE (2002) Towards a Welfare Enhancing Process to Manage Railway Infrastructure Access Transportation Research A 36 : Rassenti SJ, Smith VL, Bulfin RL (1982) A Combinatorial Auction Mechanism for Airport Time Slot Allocation The Bell Journal of Economics 13 : Shubik M (1971) The Dollar Auction Game: A Paradox in Noncooperative Behavior and Escalation The Journal of Conflict Resolution 15 : Vickrey W (1961) Counterspeculation, Auctions, and Competitive Sealed Tenders Journal of Finance 16 : 8-37.

36 CONTENTS 36 Contents 1 Introduction 2 2 Types of auction Englishauction Dutchauction First-pricesealed-bidauction Second-price sealed-bid auction or Vickrey auction Equivalence results 15 4 Auction strategies Auctionstrategiesforthebidder Winner s curse 18 6 Collusion 19 7 Multiple items auctions 21 8 UMTS auctions The UK auction: a success TheItalianauction:abadexample TheTurkishandtheSwissauctions:twofailures Transportation auctions Rassenti, Smith, Bulfin A Combinatorial Auction Mechanism for Airport Time Slot Allocation Brewer, Plott A Binary Conflict Ascending Price (BICAP) Mechanism for the Decentralized Allocation of the Right to Use Railroad Tracks... 29

37 CONTENTS Nilsson Allocation of Track Capacity. Experimental Evidence on the Use of Priority Auctioning in the Railway Industry Nilsson Towards a Welfare Enhancing Process to Manage Railway Infrastructure Access Borndörfer, Grötschel, Lukac, Mitusch, Schlechte, Schultz, Tanner An Auctioning Approach to Railway Slot Allocation References 35