Game Theory and Auctions

Transcription

1 Game Theory and Auctions Dr Christoph Stork

2 What is Game Theory? Mathematically capture behaviour in strategic situations (games) in which an individual's success in making choices depends on the choices of others Psychologists call the theory of social situations Economist: Game theory Dominance: when one strategy is better than another strategy for one player, no matter how that player's opponents may play Intransitivity: one strategy may be better or worse than another strategy for one player, depending on how the player's opponents may play

3 Applications Auctions (spectrum, licences, art, cattle) Wage bargaining: trade unions vs employers Price setting in oligopolies Contract negotiations Tendering for government projects Voting in Parliament Corruption in institutions

4 Prisoner's Dilemma Two partners in a crime who have been captured by the police. The police does not have evidence against them but both were carrying guns Each suspect is placed in a separate cell, and offered the opportunity to confess to the crime. If neither suspect confesses, they will only be charged is illegal possession of fire arms and be jailed for a year. If one prisoner confesses and the other does not, the prisoner who confesses testifies against the other in exchange for going free, the other is jailed for 10 years If both prisoners confess, then both are given a reduced term, but both are convicted for 5 years in jail.

5 Not Confess Confess Not Confess Confess

6 Prisoner's Dilemma No matter what a suspect believes his partner is going to do, it is always best to confess: Dominant Strategy If the partner in the other cell is not confessing, it is possible to go free. If the partner in the other cell is confessing, it is possible to get 5 years instead of 10 years in prison Yet if neither confessed, both would only get 1 year, which for both together would be the best. This conflict between the pursuit of individual goals and the common good is at the heart of many game theoretic problems.

7 Changes to Game What if Game is repeated? Players can talk to each other?

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11 Two- person Zero-sum game L A C B R Stretch of beach with eighty sunbathers evenly distributed along it. 2 ice-cream sellers: you are one Best positions for you and the other ice-cream seller are A and B (minimise the average distance any sunbather has to walk for an ice-cream Starting at position A, and that the other starting at B, You sell to the region LAC, and the other seller sells to the region CBR by moving a little to the right you can increase your expected sales by capturing some of the other seller s market other seller will realise that by moving a little to the left he can recapture those of his previous customers to the right of C Shuffling continuing until each seller is at the centre of the beach, with equal sales

12 Move Not Move Move Not Move

13 What happens if bathers are lazy? L A C B R Me The other guys

14 Lazy Bathers Move Not Move Move Not Move

15 Zeno Lounge Bar GAME Promotion No Promotion Promotion El Cubano No Promotion

16 Structure of an Extensive Form Game

17 Nash Equilibrium A combination of player,s strategies that are best responses to each other? Examples: Going out with mates International Trade agreements

18 Types of Auctions

19 Exercise: LTE Spectrum Auction 3*10 Mhz in 2.2 GHZ band: Consignment A, B and C, each having 2*5 Mhz You receive a piece of paper with your company name, the value the spectrum is worth to your business and the maximum financial resources you have You will be discussing your bidding strategy with your business partners before bidding The winner and the final amount will be announced after each round Your personal bonus will be Economic value for you business minus accepted bid price 5 companies are allowed to bid: MTC, Leo, Telecom Namibia, ITN, Africa Online

20 Open Outcry Auction Bidders are in the same room and indicate the price they are willing to pay as it is called in an ascending manner or descending manner The winner is the one that offers the highest price The winner could either pay the prize he/she indicated or can be offered to pay the nearest lower price depending on the auction design When the bidder pays the price he bid for it is called the first price auction and when he is offered to pay the next higher price, which is lower than the winning bid, it is called the second lowest price bid or second price auction

21 Dutch auction Auctioneer begins with a high asking price which is lowered until some participant is willing to accept the auctioneer's price, or a predetermined reserve price (the seller's minimum acceptable price) is reached The winning participant pays the last announced price. Also known as: Clock auction or open-outcry descending-price auction the bidding strategy and results of this auction are equivalent to those in a sealed first-price auction. Dutch auction is named for its use in the Dutch Tulip Craze

22 Single Sealed bid Bidders submit the highest price they are willing and able to pay in a sealed envelope Regulator opens all bids in the presence of bidders and reads out the bids Highest bidder is the winner Depending on the design of the auction the winner could pay the highest price they bid for or the second highest bid First-price sealed-bid auction (Used at the London Gold Exchange) Second-price sealed-bid auctions (Vickrey auctions) Bidders reveal their true value for the licence Paying a lower price than they bid for could reward the winner

23 English auction: Open Ascending-bid auctions A type of sequential second price auction in which an auctioneer directs participants to beat the current, standing bid (by increment) New bids must increase the current bid by a predefined increment The auction ends when no participant is willing to outbid the current standing bid Participant who placed the current bid is the winner and pays the amount bid Winning bidder needs only to outbid the next highest bidder by the minimum increment. Thus the winner, effectively, pays an amount equal to (slightly higher than) the second highest bid

24 Combinatorial/ Packaged Auction Bidders have an interest in winning various licences that are complementary Bidder is allowed to bid for a combination of licences he wants or for each individual one separately The bidder will tend to offer the true value reflection of the licences in an open simultaneous or sequential auction However, it is complex to run and participate in a simultaneous package than sequential packaged auctions because the choices could be too many and confusing

25 Multi-Unit Auction Several items are sold: Each at the same price (a uniform price auction) or at different prices (a discriminatory price auction) Uniform Auction fixed number of identical units of a commodity are sold for the same price Each bidder in the auction bids a price and a quantity The price bid is considered the maximum price they are willing to pay per item, and the quantity is the number of units they wish to purchase at that price Typically these bids are sealed - not revealed to the other buyers until the auction closes The auctioneer then serves the highest bidder first, giving them the number of units requested, then the second highest bidder and so forth until the supply of the commodity is exhausted. All bidders then pay a per unit price equal to the lowest winning bid (the lowest bid out of the buyers who actually received one or more units of the commodity) - regardless of their actual bid. Some variations of this auction have the winners paying the highest losing bid rather than the lowest winning bid Discriminatory auction: Highest bidder is the winner but the winners might have bid different prices for each unit

26 Simultaneous Ascending Auction Most common form of auction used to allocate spectrum licences globally Bid for each item separately in each round The price goes up in each round The bids are sealed but announced at the beginning of each round Reserve price is placed on bidding on an item, bid must be more than the last bid by some determined margin Auction continues to take place until there are no new bids on any of the items There are penalties and restriction on how many items to bid for and for withdrawing or remaining inactive in the auction The winners are the highest bidders for a particular item This type of auction is regarded as transparent, fair, revenue maximising and efficient in determining the market value of the licence