AUCTIONSCSE 311A: Introduction to Intelligent Agents Using Science Fiction

Spring 2020

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• English Auction:• Auctioneer starts the bidding at some “reservation price”• Bidders then shout out ascending prices• Once bidders stop shouting, the last bidder gets the good at that

price

GAMES

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• Japanese Auction:• All bidders start out standing• Auctioneer calls out prices in ascending order• When the price reaches a level that a bidder is not willing to pay,

that bidder sits down• The last person standing gets the good at the last price

GAMES

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• Dutch Auction:• Auctioneer calls out prices in decreasing order• When the price reaches a level that a bidder is willing to pay,

that bidder shouts “mine!”• That bidder gets the good at that price

GAMES

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• Sealed-Bid First-Price Auction:• Each bidder writes down his/her name and his/her bid on a

piece of paper and passes it to the auctioneer• The bidder with the highest bid gets the good and pays the

amount on his/her bid

GAMES

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• Sealed-Bid Second-Price Auction:• Each bidder writes down his/her name and his/her bid on a

piece of paper and passes it to the auctioneer• The bidder with the highest bid gets the good and pays the

amount on the second highest bid

GAMES

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• Definition of Auctions• A protocol that allows agents to indicate their interests in one or more resources and that

uses these indications of interest to determine both an allocation of resources and a set of payments

• How much do I want those chocolates and how much am I willing to pay for them?

• Defined by three rules:• Bidding rules: Who can bid, when they can bid, and how to bid• Clearing rules: Who gets what and how much do they pay • Information rules: Who knows what and when about the state of auction

• Goal of Auctions:• To allocate a set of resources to a set of self-interested agents • Resources are allocated to agents who value them most

INTRODUCTION

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INTRODUCTION

English Japanese Dutch 1st Price 2nd Price

Duration iterative iterative starting price, iterative constant constant

Valuation Revealed During Auction

UB on everyone’s valuation except

winner’s

UB on everyone’s valuation except winner’s

none none none

Jump Bids yes no n/a n/a n/a

Bids Revealed yes yes only the winner’s

only the winner’s

only a LB bound on the

winner’s

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INTRODUCTIONiterative sealed-bid

1st price Dutch Sealed-Bid First-Price

2nd price English, Japanese

Sealed-Bid Second-Price

• Similarities between sealed-bid first-price and Dutch auctions:• A bidder must decide on the amount he is willing to bid (assuming that he will win it)• Winner pays his bid• All bidders know the highest winning bid and that everyone else’s bid is lower• No one knows the actual bid of non-winners, except the bidders themselves• Both auctions are also strategically equivalent (optimal strategies for bidders in both

auctions are identical)

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INTRODUCTIONiterative sealed-bid

1st price Dutch Sealed-Bid First-Price

2nd price English, Japanese

Sealed-Bid Second-Price

• Similarities between sealed-bid second-price and Japanese/English auctions:• A bidder must decide on the amount he is willing to bid (assuming that he will win it)• All bidders know the second-highest bid

• Differences between sealed-bid second-price and Japanese/English auctions:• Winner pays his bid in Japanese/English auctions; pays 2nd highest bid in 2nd price auction• Everyone knows everyone’s bid in Japanese/English auctions; no one knows anyone’s bid in

the 2nd price auction

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• Applications:• Artwork by Christie’s• Network bandwidth by FCC (700 MHz spectrum in 2008, 600 MHz spectrum in 2015)• Government contracts (bids and tenders)• Impounded vehicles by local police• Anything and everything on ebay!

INTRODUCTION

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• Common auction protocol:• Bid call: The auctioneer broadcasts the resources that are up for auction, a call for bids, and

rules of the auction• Bid collection: Bidders transmit their bids to the auctioneer• Winner determination: the auctioneer determines, depending on the rules of the auction,

the winning bidder(s), the resources that they win, and the prices that they pay• Clearing: The auctioneer informs the depots about the resulting resource allocation

INTRODUCTION

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• Common auction protocol:• Bid call: The auctioneer broadcasts the resources that are up for auction, a call for bids, and

rules of the auction• Bid collection: Bidders transmit their bids to the auctioneer• Winner determination: the auctioneer determines, depending on the rules of the auction,

the winning bidder(s), the resources that they win, and the prices that they pay• Clearing: The auctioneer informs the depots about the resulting resource allocation

INTRODUCTION

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• Winner determination in single-unit auctions:• English auction: Last bidder wins, pays his bid• Japanese auction: Last remaining bidder wins, pays his bid• Dutch auction: First bidder wins, pays his bid• Sealed-bid first-price auction: Highest bidder wins, pays his bid• Vickrey auction: Highest bidder wins, pays second highest bid

• Assuming bidders are honest,• English auction: Bidders continue bidding until their true valuations only• Japanese auction: Bidders remain standing until their true valuations only• Dutch auction: Bidders shout “mine” at true valuations only• Sealed-bid first-price auction: Bidders bid their true valuations only• Vickrey auction: Bidders bid their true valuations only

WINNER DETERMINATION

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• Winner determination in single-unit auctions:• English auction: Last bidder wins, pays his bid• Japanese auction: Last remaining bidder wins, pays his bid• Dutch auction: First bidder wins, pays his bid• Sealed-bid first-price auction: Highest bidder wins, pays his bid• Vickrey auction: Highest bidder wins, pays second highest bid

WINNER DETERMINATION

Why so many auctions? What are the tradeoffs? Hint: If you are an auctioneer, which auction would you prefer (you get the most money)?

If you are a bidder, which auction would you prefer (you spend the least money)?

If you are bidder, which auction will you be most honest in?

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• Vickrey auction:• Incentive compatible (no incentive to not bid according to true valuation)• Strategy proof (no incentive to hide true valuation)

WINNER DETERMINATION

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• Vickrey auction:• Incentive compatible (no incentive to not bid according to true valuation)• Strategy proof (no incentive to hide true valuation)

• Assumes the auctioneer doesn’t lie about the second highest bid• Not collusion proof• Possible to pay more if the second highest bidder knows your valuation and doesn’t like

you :)

WINNER DETERMINATION

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• How to auction off multiple k units of identical goods? • Assume each bidder only wants 1 unit.

• English auction: Last k bidders win, pay their bids• Japanese auction: Last remaining k bidders win, pay their bids• Dutch auction: First k bidders win, pay their bids• Sealed-bid first-price auction: Highest k bidders win, pay their bids• Vickrey auction: Highest k bidders win, pay their next highest bids (discriminatory pricing

rule) or pay the k+1th bid (uniform pricing rule)

• What if each bidder might want more than 1 unit?• English auction: Also shouts out the number of units they want to buy• Japanese auction: Also shouts out the number of units they want to buy• Dutch auction: Also shouts out the number of units they want to buy• Sealed-bid first-price auction: Also indicates the number of units they want to buy• Vickrey auction: Also indicates the number of units they want to buy

MULTI-UNIT AUCTION

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• How to auction off multiple units of multiple types of goods?

• Types of valuations:• Substitutability: either S or T is good

• V(S) + V(T) > V(S ⋃ T)• e.g., S = blue shoe, T = red shoe

• Complementarity: need both S and T• V(S) + V(T) < V(S ⋃ T)• e.g., S = left shoe, T = right shoe

• Auctioning off substitutable goods is easier. • Auction off goods sequentially• Allow for bid withdrawals

• Will bid withdrawals result in an infinite auction sequence?

MULTI-UNIT MULTI-GOOD AUCTION

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• Auctioning off complementary goods is a little harder:• Parallel (English) auctions:

• Auction off goods in parallel synchronized rounds• Bids in the auctions can increase only up to a certain amount in each round

• Bidder who bids in one auction has a good idea if he will win in the other auction• Used to auction off wireless spectrum by the government (contiguous spectrum is

worth more than disjointed spectrum) • Bidders can still win only a subset of goods…

MULTI-UNIT MULTI-GOOD AUCTION

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• Combinatorial auctions:• Bids now include bundle of goods and their prices• Usually associated with sealed bid auctions• Example: 3 bidders, 2 items a and b

• Bidder 1: ({a}, $6), ({a,b}, $6)• Bidder 2: ({a,b}, $8)• Bidder 3: ({b}, $5), ({a,b}, $5)• Winner: Bidder 1 gets a, bidder 3 gets b.• Payment:

• Sealed-bid first-price: Bidder 1 pays $6, bidder 3 pays $5• Sealed-bid second-price: Bidder 1 pays $3, bidder 3 pays $2

• Also called Generalized Vickrey auction or Vickrey-Clarke-Groves (VCG) auction.

MULTI-UNIT MULTI-GOOD AUCTION

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• Combinatorial auctions:• Bids now include bundle of goods and their prices• Usually associated with sealed bid auctions• Example: 3 bidders, 2 items a and b

• Bidder 1: ({a}, $6), ({a,b}, $6)• Bidder 2: ({a,b}, $8)• Bidder 3: ({b}, $5), ({a,b}, $5)• Winner: Bidder 1 gets a, bidder 3 gets b.• Payment:

• Sealed-bid first-price: Bidder 1 pays $6, bidder 3 pays $5• Sealed-bid second-price: Bidder 1 pays $3, bidder 3 pays $2

• Also called Generalized Vickrey auction or Vickrey-Clarke-Groves (VCG) auction.

MULTI-UNIT MULTI-GOOD AUCTION

Any problems with this auction? Hint: What is the maximum number of unique bids?

Answer: Exponential in the number of goods!

Hint: What is the complexity of the winner determination problem? Answer: NP-Complete

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• Auctioning off complementary goods is a little harder:• Combinatorial auctions:

• A very active area of research• Robocup Rescue• Trading Agents Competition (TAC)

• Different types of markets, including power markets

• Research topics:• Heuristics to improve winner determination in combinatorial auctions• Decentralized winner determination (without the need for an auctioneer)• False-name proof auctions (nothing to gain from creating multiple accounts to bid)

• Is the VCG auction false-name proof?

MULTI-UNIT MULTI-GOOD AUCTION

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• VCG is not false-name proof:• True scenario:

• Bidder 1: ({a}, $6), ({b}, $5), ({a,b}, $11)• Bidder 2: ({a,b}, $8)• Winner: Bidder 1 gets a and b.• Payment: Bidder 1 pays $8

• Fake scenario with Bidder 1 also bidding as Bidder 3• Bidder 1: ({a}, $6), ({a,b}, $6)• Bidder 2: ({a,b}, $8)• Bidder 3: ({b}, $5), ({a,b}, $5)• Winner: Bidder 1 gets a, bidder 3 gets b.• Payment: Bidder 1 pays $3, bidder 3 pays $2

MULTI-UNIT MULTI-GOOD AUCTION

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• FCC spectrum reallocation (2015): • Sell radio spectrum to telecom company• Buy radio spectrum from TV broadcasters• Governments sells higher than they buy, so they make a profit

• Issues:• Value of spectrums to telecom companies depend on • Repurposing spectrum from broadcast TV to telecom

• broadcasters are paid not to use their spectrums• telecom companies pay for it.• government predicts to get about 25 billion from the auction

APPLICATIONS

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• Reverse (descending-price) auction for broadcasters (= sellers)• stations declare they are willing to stop broadcasting at a given initially high price• consider stations’ round robin:

• check to see if the station could feasibly be “repacked” into the reduced band, given interference constraints

• if so, which means we can let the station continue to broadcast, offer it lower compensation; offer is a take-it-or-leave-it

• if not, which means that we must buy this station’s broadcasting rights, then we “freeze” the offered price (i.e., station will get that price if auction terminates)

• Forward (ascending-price) auction for telecom companies (= buyers)• prices in each region increase while demand exceeds supply

• When auctions terminate, ensure revenue target is met• if not, grow the size of the reduced band (i.e., clear less spectrum) and continue auctions• supply will drop (some broadcasters can’t sell anymore)• bids by telecom companies will go (fighting for a smaller chunk of the spectrum)

INCENTIVE AUCTION

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DOUBLE AUCTIONS

Figure 7: Market clearing example: bid 8 and part of ask 6 are the last to clear.

• Post-clearing orderbooks are published for each cleared time slot, giving the un-cleared bidsand asks, without broker information. In the example, the orderbook would include two asks((!3, 15), (!7, 16)), and two bids ((5,!14), (7,!12)).

• Brokers are informed about their own executed transactions.

• Updated cash and market positions are computed and communicated to individual brokers.

• All orders that arrived before the start of the clearing process are discarded.

5.3 Wholesale suppliers and buyers

To ensure liquidity to the wholesale market, the simulation includes both wholesale energy providersas well as wholesale buyers. The wholesale suppliers are called Generation Companies, or Gencosfor short. Each Genco g has a nominal capacity Cg, a fixed cost/MWh cg, a commitment leadtime!g, and a reliability value rg. Actual capacity Cg,s in time slot s varies around the nominal valueby either a mean-reverting random walk, or by current weather conditions in the case of windturbines. Given a variability parameter v, a mean-reversion rate m, and a uniformly distributedrandom value " on [0..1], the random walk is defined as

Cg,s = Cg,s!1 + v(2" ! 1)Cg + vm(Cg ! Cg,s!1) (14)

At any given time, each Genco is “in operation” with a probability rg. If a Genco is in operation,it will submit an ask to the market for its uncommitted capacity at its fixed cost in each future

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Willing to buy up to 5MWh for at most $28 per

MWh

Willing to sell up to 3MWh for at least

$5 per MWh

27Figure 7: Market clearing example: bid 8 and part of ask 6 are the last to clear.

• Post-clearing orderbooks are published for each cleared time slot, giving the un-cleared bidsand asks, without broker information. In the example, the orderbook would include two asks((!3, 15), (!7, 16)), and two bids ((5,!14), (7,!12)).

• Brokers are informed about their own executed transactions.

• Updated cash and market positions are computed and communicated to individual brokers.

• All orders that arrived before the start of the clearing process are discarded.

5.3 Wholesale suppliers and buyers

To ensure liquidity to the wholesale market, the simulation includes both wholesale energy providersas well as wholesale buyers. The wholesale suppliers are called Generation Companies, or Gencosfor short. Each Genco g has a nominal capacity Cg, a fixed cost/MWh cg, a commitment leadtime!g, and a reliability value rg. Actual capacity Cg,s in time slot s varies around the nominal valueby either a mean-reverting random walk, or by current weather conditions in the case of windturbines. Given a variability parameter v, a mean-reversion rate m, and a uniformly distributedrandom value " on [0..1], the random walk is defined as

Cg,s = Cg,s!1 + v(2" ! 1)Cg + vm(Cg ! Cg,s!1) (14)

At any given time, each Genco is “in operation” with a probability rg. If a Genco is in operation,it will submit an ask to the market for its uncommitted capacity at its fixed cost in each future

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DOUBLE AUCTIONS

Clearing price: $16 and 27MWh

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