Dynamic Pricing and Auction - Department of Industrial Engineering ...

Understanding the scope fordynamic pricingD1D2Srice PrP2P1Quantity

Some important observations• It appears that prices should change dynamicallydepending on the market condition◦ In fact dynamic pricing has a history which is as old as thehuman civilization◦ Fixed pricing has a history which is only 100 years old.• Dynamic pricing ensures perfect competition◦ No consumer or the producer is large enough to controlthe market.◦ Efficient allocation of resources◦ The economy is at its production possibility frontier• If dynamic pricing is so natural why did people gofor fixed pricing?

Advantages of ffixed pricing• Convenient◦ Easy to model◦ Designed to recover the cost of production(break-even)◦ Difficulty in estimating demand• Decrease price uncertainty in the market◦ Loyal customers• An instrument to control the market• …

Some insights into traditional(Fixed) pricing methods

A six step procedure forsetting up price• Selecting the pricing objective• Determining the demand• Estimating the cost• Analyzing competition• Selecting a pricing method• Selecting the final price

Selecting the pricing objectives• Maximizing the current profit◦ Estimate t demand d and cost associated with alternativetiprices and choose the one that produces maximum profit/cash flow/ rate of return on investment• Estimating the demand !!,• Govt. restrictions !!• Competitor’s reaction !!• Market penetration strategy◦ Maximizing i i the market share◦ Price sensitive market◦ Higher sales volume leads to lower cost• Market skimming◦ High prices to skim the market before the substitutearrives• Product-quality-leadershipleadership◦ Higher prices based on higher quality

Determining demand• Estimating demand curve• Price sensitivity of the customers• Price elasticity of demand• Demand sets the ceiling of the price

Estimating cost• Costs sets floor of the price• Fixed cost• Variable cost

Analyzing competition• Competitor’s cost, price and offers• Stay as close as possible

Selecting a pricing method• Markup pricing◦ Unit price = unit cost / (1 – markup on sales)• Target return pricing◦ Unit cost + [(desired return*invested capital)/unit sales]• Perceived value pricing◦ Service, warranty, reliability etc.• Value pricing◦ Quality Vs. Price• Going rate pricing◦ Competitor’s price• Sealed-bid pricing/ Auctions

Was the traditional pricingreally fixed?• Volume discounts?• Bargaining and Negotiations?• Product mix pricing?• Promotional pricing?i • …

E-Commerce as a driver ofdynamic pricingi• What buyers can do◦ Gets instant price comparisons◦ Instant search for the substitutes that fits the budget• What sellers can do◦ Monitor customer behavior and instant tailoring ofcustomized price◦ Change price on the fly after sensing demandd• Both can do◦ Instant negotiation on price• Auctions• Exchanges• Internet has created a conducive environment forperfect competition hence dynamic pricing isbecoming a reality

E-Commerce as a driver ofdynamic pricing• Transaction cost for implementing the dynamicpricing i have been reduced d by◦ Eliminating the need for people to be physicallypresent in time and space◦ Reducing the search cost◦ Reducing the menu cost of informing the changedprice• Increased number of customers, competitors,and increased amount of information has leadto price uncertainty and demand volatility.• Companies are finding that using a single fixedprice in these volatile market is inefficient andineffective

Defining Dynamic Pricing• Dynamic pricing is defined as the buyingand selling of goods and services in freemarkets where the prices fluctuate inresponse to changing supply and demand.• Also called flexible pricing/ customizedpricing• Includes two aspects◦ Price dispersion◦ price differentiation

Price dispersion• Spatial◦ Several seller offers a given item indifferent prices• Temporal◦ A seller varies the price of a given itemover the time◦ Ex: Seasonal discounts

Price DifferentiationBased on one product• First degree differentiation◦ Perfect differentiation◦ Same product, different price for different people◦ Extracts maximum consumer surplus from the market◦ Ex: Auction• Second degree differentiation◦ Non-linear pricing◦ Different quantity for different unit price but the rule is same for eachindividual◦ Ex: Volume discounts, Utility prices• Third degree differentiation◦ Group pricing◦ Same unit price for any quantity but unit price is different for differentgroups of people◦ Ex. Telecom pricing for business and households

Price DifferentiationBased on one product which can be customized• Addition or deletion of attributes• Decreased substitutability• Customized product• Ex.: Dell – Computers with customizedfeatures• Ex: Airline industry – Productdifferentiation based on refund policy

Dynamic pricing successstories• Airline Industry◦ Yield management• Priceline.com◦ Negotiation with major airlines to fill upthe vacant seat with the marginalrevenue• Online auctions• …

Dynamic pricing failure stories• DVDs from Amazon.com◦ Lost customer loyalty• Buy.com◦ Price competion◦ Profit is low or even sometimes negative

Conditions under which dynamicpricing will be successful• Customer must be heterogeneous in theirwillingness to pay• Market must be segmentable• Reselling at a higher price should be prohibited• The cost of segmenting and price differentiationmust not exceed the revenue due to pricecustomization• Customer should feel fairness in dynamic pricing• Dynamic pricing must be based on sophisticatedmathematical models.

Models for dynamic pricing• Inventory based model◦ Models based on inventory type, inventory levels andcustomer service levels• Data driven models◦ Models based on statistical techniques that uses the dataavailable on customer preferences and buying patterns• Auctions◦ Models where prices vary based on the market condition• Machine learning models◦ Models based on online learning• Simulation models

Auction

Auction• An oldest form of market◦ A history of at least 500 BC◦ From Babylonian auction to eBay• Theoretical studies started in 1970 with◦ Organization of Petroleum Exporting Countries (OPEC)increased the price◦ US Dept of Interior decided to action the drilling rights in thecostal area◦ Economists were hired by the organizations to design biddingstrategies• Federal communication commission (FCC)◦ Radio spectrum auction◦ Resulted a revenue of 23 billion US$• New Zealand Spectrum auction◦ Vickrey Auction◦ Winning bid NZ$100, 000 – second highest bid NZ$ 6 !!

A framework for classifying theauctions• Resources• Market structure• Preference structure• Bid structure• Bidding rule• Matching supply to demand• Information feedback• Nature of the goodhttp://www.eecs.harvard.edu/econcs/pubs/ehandbook.pdf

Classification based on the resources• Identify the set of resources over which the negotiation is tobe conducted• Single item single unit• Single item multiple l unit◦ Multi-unit auction• Multiple Items◦ Combinatorial auction◦ Homogeneous items or heterogeneous items◦ Sequential or simultaneous• Items with multiple attributes◦ Pricing out mechanism for non-priced attributes throughsome utility function◦ Multi attribute auction

Classification based on MarketStructure• An auction is a mechanism for negotiationbetween buyers and seller• One seller – multiple buyer◦ Forward auction• One buyer – multiple seller◦ Reverse auction• Multiple buyers – multiple sellers◦ Double auction◦ Trading securities and financial instruments

Classification based on Bidding rules• Ascending bid auction◦ English auction◦ Reserve price◦ Bid Increment• Descending bid auction◦ Dutch auction• Sealed-bid auction◦ First-price◦ Second-price (Vickrey auction)

Classification based on Preferencestructure• Preference defines an agent’s utility for differentoutcomes• In case of multi unit auctions◦ Agent may show a decrease in marginal utility foradditional units of the product• In case of multi-attribute auction◦ Agent ‘s preference structure for different attributes is tobe designed d in terms of scoring rules used to signalinformation

Classification based on Bid structure• Structure of a bid defines the flexibility with whichan agent can express his resource requirement• Ex: In single-itemitem single-unit auction it is simplythe buyer’s willing ness to pay or accept.• Ex: In single-item multi-unit case the buyer needsto specify both quantity and price• Ex: In case of multi-item case a bid may bespecified as all-or-nothing over a basket of items.

Classification based on Payment rule• First price• Second price• All pay

Classification based on Matchingsupply with demand• Market clearing or winner determinationtiproblem• Single sourcing◦ A sorting problem• Multiple l sourcing◦ A combinatorial problem• The problems range from simple sortingproblems to NP-Hard Optimizationproblems

Classification based on Informationfeedback• Auction protocol based on direct or indirectmechanism• Direct mechanism◦ No feedback• Price signal◦ Ex. First-price sealed bid auction• Indirect Mechanism◦ Feedback on the state of the auction• Price signal• Provisional allocation◦ English auction

Issues involved in onlineauction• Strategic Issues◦ Economic Issues (Auction design issues)◦ Business Issues (Business rules)◦ ..• Implementation Issues◦ Modeling the decision making process◦ Computational Issues◦ Security

Economic Considerations

Auction Design Problem• Design auction that have somedesirable property p to satisfy theauctioneers need◦ Modeling preference, behavior andinformation available to the agents◦ Designing g mechanisms in which theagent strategies result in the outcomeswith the desirable properties.

Two approaches for auctiondesign• Game theoretic/mechanism ti h i design approach◦ In this model the equilibrium state is defined by thecondition that the agent plays the best responsestrategy to each other and cannot benefit fromunilateral deviation to an alternate strategy◦ Rationality assumption• Price taking or competitive equilibrium approach◦ In this model the equilibrium state is defined by thecondition that an agent plays a best response to thecurrent price and allocation in the market, withoutmodeling the strategies of the other agents or the effectof its own action on the future state of the market◦ Myopic, best response

Game theoretic/mechanismdesign approach

Modeling bidders valuation of aproduct• Private value model◦ Each participant has a potentially different value for good inthe question◦ Symmetric (or asymmetric)• All the bidders draw their values from a common distribution• Common value model◦ The good in the question has the same value for all theparticipants• Interdependent Value Models◦ Each bidder has only an estimate regarding the value.◦ This estimate t may change after getting the price signal fromothers.

Auction mechanism designgoals• Pareto efficiency◦ Design an auction that results in a Pareto efficientoutcome◦ The item under consideration goes to the person whoneeds it most (He may not pay the highest amount)◦ After trade should not be possible• Profit maximization◦ Design an auction that yields the highest expectedprofit to the seller◦ The item should go to the person who pays the highestamount.

Efficiency Vs. optimality• Optimal auctions are designed to maximize the expected revenue of theseller by using a set of tools including posing a reserve price or chargingan entry fee, whereas the objective of efficient auctions is to maximizethe social welfare, the sum of the players' surplus.• Efficient i design aims to maximize i the system welfare, whereas theoptimal design aims to maximize the seller's individual revenue.• Since optimality and efficiency usually cannot be achievedsimultaneously, the auction designers have to make the choice before hestates the rules of the auction.• A financial self-interested agent may prefer the optimal auctions while a• A financial self-interested agent may prefer the optimal auctions, while apublic agent like the government may prefer the efficient auctions to gainmore social welfare. Nevertheless, all agents need to balance optimalityand efficiency to make the auctions practical.

The concept of efficiency and profitmaximization i and three popular mechanisms• Efficiency◦ All the major action formats are efficientassuming the bidder is truthful• Optimality◦ First price auction and English auctionsare optimal.◦ What about the second price auction?◦ It becomes optimal if an appropriatereserve price is set.

Modeling the basic auction mechanisms• Auction is a Bayesian game◦ Bidders are the players◦ The problem is either to find a Bayes-Nash equilibrium point forefficient allocation or to propos a mechanism based on revelationprinciplep◦ Incentive-compatible direct mechanisms yield the same Bayes-Nashequilibrium point as the original problem• The formulation help finding the efficient allocation• Assumptions of the basic model◦ n bidders◦ Bidder’s values are independent and identical random variables withdistribution function F(V) and density function f(V)(symmetric, independent bidders)◦ Bidders are risk neutrality◦ They show no collusion or predatory behavior• Under this assumption all the basic auction formats are efficientand generate same revenue

Bidding Strategy in second priceauction• In a second price under IPV setting and with riskneutral bidders bidding truthfully is a dominantstrategy• The item under consideration goes to the bidderwho values it most.• The value is measured in terms of price. So theitem must go to the bidder with highest valuationfor the product.• Considering the bid as a proxy for the valuation,the item may go to the highest bidder. But, whatis the guarantee that the all the bidders bidtruthfully?

Bidding Strategy in second priceauction• A case of two bidders◦ Let the valuations are v 1 , and v 2◦ Let the bids are b 1 and b 2◦ Expected payoff of 1 st bidder isprob[b 1 ≥ b 2 ][v 1 -b 2 ]If v 1 >b 2 then in order to win the bidder 1 will make b 1 ashigh as possible. This happens when he sets b 1 =v 1If v 1

Revenue in second priceauctionn bidders independently draw their valuations from distribution function F(.) and density function f (.)Bidders' values: { v1, v2, ... , v n} (under IID assumption,i.e., i each is a independent and identicallydistributed random variable)Order statistics: { v(1) , v(2) , ... , v( n )} (arranged in ascending order)thn!Density of k lowest: f( v( k ))=f v F v F v( k −1)!( n−k)!k−1n−k().[ ()] .[1 − ()]Uniform distribution case, i.e., for U[0,1]th n!k−1Density of k lowest: f( v( k )) = . v .[1 −v]( k−1)!( n−k)!(This is a β distribution with paremeters k and ( n- k+ 1)thkMean value of k order statistic: E( v( k ))=( n + 1)nd( n −1)Mean value of 2 order statistic: E( v(2)) =( n +1)(expected revenue for the auctioneer)n−k

Density of the k th lowest order statisticthDensity of k lowest:Pr{ x< x ≤ x+dx}( k )=Pr{[ P{[ x < one of the X ' s ≤ x+ dx ] ∩[ X ≤ x for ( k −1) X ' s]At limit when dx → 0 :i i i∩[ X > x for the remaining ( n−k) X ' s]}[ F( x+ dx) −F( x)]f v ) = c c [ F( x)] .[1 −F( x)]dxn!k−1n−kf ( v( )) = kf ( x)[ ).[ F ( x)] .[1 F ( x)]( k−1)!( n−k)!−n n−1 k−1n−k(( k ) 1 k −1ii

Bidding Strategy in 1 stprice auctionE[Gain]=( v - b) Pr( winning)Optimal bid is the one that maximizes this expectationfor bidders with distribution function F(.) and density function f(.)( n −1)Optimal bid = b* =vnTo see the result, we have to develop the bidding strategy for the bidders

Eq. 1Eq. 1(Eq. 1)Eq. 2

Eq. 3Eq. 4

Eq. 4Eq. 5Eq. 6

tRevenue in 1 st price auction• The winning (highest) bid is the bid ofthe person with the highest orderstatistic:stMean value of 1 order statistic: E( v ) =(1)n( n +1)( n−1) ( n−1) n ( n−1)Expected Payment = E( v()(1)) = =n n ( n+ 1) ( n+1)

Revenue EquivalenceTheorem• Under IPV setting with risk neutralbidders, the expected price paid for theobject is same under first price auctionand the second price auction.

Strategic equivalence of the auctions• A first price auction is strategicallyequivalent to Dutch auction for riskneutral bidders under IPV setting• A second price auction is strategicallyequivalent to English auction for riskneutral bidders under IPV setting• Therefore the revenue generated fromall the common auction formats are thesame

Optimal Mechanisms• Increasing the expected revenue• Two ways◦ Increasing the number of bidders◦ Setting up a reserve price

More Bidders=higher Expected PayoffFor n bidders with IPV and V~U(50,100):

Reserve Prices• A minimum price, r, below which theseller does not sell the item◦ “Excludes” some bidders with v < r• Proper reserve price increasesrevenue

Why set a reserve price?• Consider two bidders in a 2nd price auction): (auctioneer’s value = 0,reservation price = r) )◦ If both the bids are above r• E[Gain]=No change◦ If both the bids are below r• E[Loss] ≤ r[F(r)] 2◦ r: loss, P[x

Calculating the optimal reserve priceGiven r, assume the seller raises it to r+ δ.(Assume value to seller is 0)Good move: if there is exactly a single bidder bidding above (r+ δ )].n-1Pr · ( ) .[1- ( δ )]= nF r F r+Gain = δBad move: if the highest bid is between r and (r+ δ ).n-1Pr = n· F () r ·[ F ( r +δ) - F ()] rLoss = r

Calculating the optimal reserve priceNet expected gain per increment in r *n-1 n-1nFr · () .[1- Fr ( + δ)]. δ nFr · () .[ Fr ( + δ)- Fr ()]. r∆ ( δ ) =δ−Taking the limit:n-1∆ ( δ) = nF · () r .{[1- F ()] r −f (). r r}lim δ →0Setting ∆=0:[1- Fr(*)]r*=f(*)rδ

Relaxing the basic assumptions◦ Risk aversion• Worried about not winning• Bids higherh• Prefers English auction◦ Asymmetric valuations• Strong Vs. Weak bidder◦ Reputation ti effect• Aggressive

Interdependencies• Interdependent values -a bidder’s valuation isaffected by knowing the valuation of other bidders◦ Each bidder has only a partial information about thevalue of the item being sold in the form of a signal,which is a random variable• Pure common value – item has the same valuefor all bidders. Each bidder has only an(unbiased) estimate/signal of the value prior tothe auction

Revenue Calculation• English auction and second price auctions are nolonger equivalent• English auctions are likely to yield more revenuethan both 1 st and 2 nd price auctions.• More information flow is likely to increase thevalue of the object. Therefore, releasing all theinformation about the item being sold theauctioneer may yield more profit.

Winner’s Curse• The winner curse takes place when winner paystoo much, due to their failure to anticipate andcorrect their bidding strategy• The winner is the bidder with highest signal.• Winning means that everybody else had a lowerestimate• To correct winner’s curse bidders have to “shave”their bids further (1st price “shave” +WC “shave”)

The Winner DeterminationProblem and its Complexity

A simple winner determination problemWhat kind of auction?◦ single-item◦ single-unit max∑vxiii◦ single winnerst . ∑ xi≤1◦ forward auctionixi∈{0,1}◦ price only bidsWhere viis the price of item i,xiis a binary variable indicatingpurchasing decision on item iHowdowesolveit?we ◦ A simple sortingproblem !!

Winner determination problem incomplex auction formats• Multi unit auctions• Multi Attribute auctions◦ Forward auction◦ Reverse Auction◦ Constraint types• Divisible bid• Indivisible bid• Price Schedule• Multi-item auctions◦ Forward auction◦ Reverse Auction◦ Constraints types• Number of winningsuppliers• Budget limit on trades• Market share constraints• Representationconstraints• Volume discounts◦ Reverse auction◦ Constraint types• Single sourcing• Multiple pe sourcing• Double auctions andexchanges◦ Trading securities andfinancial instruments◦ Continuous double auction• Clears continuously◦ Clearinghouse auction• Periodic clearing◦ Constraint types• Aggregation• Divisibility• Homogeneous /heterogeneous items

Multi unit auctions• Forward auction◦ Maximization of selling price• Reverse Auction◦ Minimization of procurement cost• Bid types◦ Divisible i iblbid◦ Indivisible bid◦ Price Schedule

Multiunit auction with divisible bidsBidder (i) Bid (p i , q i ) max ∑ px i i1(20, 30) 3 Total quantity soldist .∑ xi≤ Q2i(30, 30) 1 Total quantity soldxi≤qix ≥ 0∀i34 (10, 30)5(25, 20) 2Total Quantity to Sell =100Total Quantity Sold =100(15, 60) 4 (Only 20 units are sold)Total Revenue=30*30+25*20+20*30+15*20Total quantity soldiWhereiThe buyer ipiis unit priceqiis the quantityQ is the total demand,x i is the decision variable• Each bid is represented as a pricequantity ty pair (p i, q i )• Again a simple sorting problem• Last chosen bid gets partial allocation!!

Multiunit auction with indivisible bidsBidder (i) Bid (p max pqxi ,q i )∑i i i1 (20, 30)(30, 30)123 st .∑xiiqxiii≤ Q∈{0,1}∀i3(15, 60)4 (10, 30)5(25, 20) 2Total Quantity to Sell =100Total Quantity Sold =80Total Revenue=30*30+25*20+20*30Wherei The buyer ipiis unit priceqiis the quantityQ is the total demand,x i is the decision variablei• Each bid is represented as a price quantity pair(p i, q i )• A knapsack problem!!• What is the complexity if solved by Branch andBound Algorithm?• A greedy algorithm does exist

Multiunit auction with price schedulefor volume discount bids• Price schedule for i th seller is represented asis the per unit price for the quantities in the intervalx 211 1Mx N i11min ∑∑ pzij ij+ pqxij ij ijx i= 1 j=1st .zij−( qij− q ) xij

Multi –item forward auctionsSet of items to be sold = {A, B, C, D, E}Two bidders submit the bundled bidsBundles of Bidder 1 Bundles of Bidder 2[100, {A,C,D}] [50, {E}][150, {A,B,C}][200, {C, E}]Only one bundlefrom each buyerEach item j isconsidered onlyonce[50, {A,B}][75, {B,C}][75, {D, E}]set of items to be soldthebidsetfrombidderibidder ip i (S) Price offered by bidder i for bundle S

Multi –item forward auctions-A set packing problem• Given: A set of subsets S = S_1, ...,S m of the universal set U_• Problem: What is the largest numberof mutually disjoint subsets from S?

Adding Business rules as side Constraintsfurther increases the complexity• Number of Winning Suppliers◦ Multi sourcing• Budget Limits on Trades◦ How much I can spend• Marketshare Constraints◦ How much business to allocate to each winner• Reservation Prices◦ What is the minimum price below which the seller willnot sell the product , i.e. minimum bid price

Double Auctions• A multiple buyer and multiple seller auction• Used in financial institutions for over a hundredyears◦ Ex. New York stock exchange• Two types◦ Continuous double auction, which clears continuously◦ Clearinghouse or call auction, which clears periodically

Determining the equilibrium point indouble auction(Supply)Sellers’Asks(Demand)Buyers’Bids11Equilibrium69425 83 10Price109876543211 2 3 4SupplyDemandQuantity

Winner determination problem indouble auction• The problem is to maximize market surplus. Wheresurplus is defined as the difference between the bidsand asks• In the last example where 4 sellers try to sell a singleunit of some homogeneous good, and 4 buyers bid tobuy a single unit each, the winner determination problemcan be formulated asmaxs.t4∑j=1x ijxij44∑∑i= 1 j=1≤ 1 ∀i( pj− pi) x∈{ 0,1} ∀i,jij

Other Considerations During Doubleauction problem formulation• Aggregation◦ Role of market maker in disassembling andreassembling bundles of items◦ Consideration of either buy side items or sell side itemsor both• Divisibility◦ Ability to satisfy a fraction of agent’s bids and asks• Homogeneous/Heterogeneous goods

Classification of Online Auction TypesONEBUYERSMANYBilateralWeb-based salesSELLE ERSONEMANYnegotiationsWeb-based procurement(Reverse) auctionsauctionsC2C and B2CWeb-basedexchangesC2B and B2B

Online design issues• Choice of appropriate mechanism◦ Currently the English auction is the dominant mechanismon the Internet.◦ Second price which is not well adopted in traditionalauctions has become an important option.• Bid constraint◦ Minimum bid• Reserve price◦ Maximum bid• Buy-now price• Auction Duration◦ Ending rules• Multi-unit auctions and handling complex auctionformats◦ Quick response time◦ Appropriate algorithms

Integrating Online Auctions into aFirm’s Business Model• B2C surplus auctions◦ A firm may use auctions to dispose ofsurplus inventory• B2C Auctions as a Regular SalesChannel• B2B surplus auctions• B2B procurement auctions• Use of auction intermediaries

Fraud in online auctions• Auction frauds constitute the largest part of all Internet frauds(60 %)(Internet Fraud Complaint Center (IFCC))• IFCC classifies auction frauds into six categories◦ Non-delivery of goods◦ misrepresentation of the items◦ Triangulation• The perpetrator buys items from an online merchant using stolencredit card number and then sells them to unsuspecting buyers.◦ Fee staking• Fee stacking occurs when a seller keeps adding hidden charges◦ Selling of black-market goods• Illegally copied software packages, audio CDs, movie CDs andgames• Improper packaging and does not offer any form of warrantee orinstruction manual that may have come along with the originalgoods.◦ Multiple bidding and Shill bidding (Cheating)

Cheating• Cheating unlike other fraud categoriesleaves no direct evidence of itsoccurrence• Some of the reasons that encouragecheating over the Internet◦ Cheap pseudonyms◦ Greater information asymmetry◦ Lack of personal contact◦ The tolerance of bidders

Types of fCheatingCheating inAuctionInduced bybidderInduced by auctioneerMultiple biddingBid shadingRingsShill biddingFalse bidsCheating in electronic auction

Auction at e-Bay-Models• All eBay auctions use a ascending-bid formatwhich is a hybrid of English and Second priceauction. with the important distinction that thereis a fixed end time set by the seller.Models:• Standard Auction• Reserve Price Auction• Buy It Now Price• Dutch Auction◦ Distorted version of Dutch auction◦ Multi-unit unit auction with volume discount

The Proxy Bidding and BidIncrement• The proxy mechanism allows a bidder to submit a maximum bid (i.e.,maximum willingness to pay) with a guarantee that eBay will raise thebidder’s active offer automatically until the bidder’s maximum bid value isreached.• The bid placed by the proxy system is referred as the bidder’s proxy bid.• In a reserve price auction, the seller’s reserve price is treated like anyother bid; if the buyer’s offer meets or exceeds the reserve (secret) bidset by the seller, the buyer’s bid would be raised to that priceimmediately.• EBay enforces a minimum bid increment that, along with the current askprice, determines a lower bound on bids the server will accept.• The bid increment table specified by eBay defines a schedule in whichthe increments increases as the current ask price increases.Auction at e-Bay

Data available to a bidder• Item description• Number of bids• ID of all the bidders• Time of their bid and the bid amount◦ Except that of the highest bidder• Time remaining until the end of the auction,• Whether or not the reserve price has been met,• The current ask price (list price).◦ The list price is the second highest price plus a smallincrement as specified in the bid increment table of eBay.Auction at e-Bay

Bidding Strategies• Single bid engagement◦ Evaluator◦ Late bidder◦ Sniper• Multiple bid engagement.◦ Skeptic◦ UnmaskingAuction at e-Bay

References• Everything you wanted to know about double auctionhttp://www.sci.brooklyn.cuny.edu/~parsons/projects/mech-design/publications/cda.pdf• Auction, bidding and exchange design, Jayant Kalagnanam, Davis Parkeshttp://www.eecs.harvard.edu/econcs/pubs/ehandbook.pdf• Optimality and Efficiency in Auctions Design: A Survey Roger L. Zhan1 and Zuo-Jun Max Shen2plaza.ufl.edu/zhan/paper/zhanShenV2.pdfpdf• Auction Theoryhttp://ocw.mit.edu/NR/rdonlyres/Engineering-Systems-Division/ESD-260JFall2003/2CECCCEB-0165-42A3-B86A-B4BBA5A6930B/0/l18ch22auctheory.pdf• Auction Theory and practices◦ http://www.nuff.ox.ac.uk/users/klemperer/VirtualBook/VirtualBookCoverSheet.asp• Insight and analysis of online auctions http://delivery.acm.org/10.1145/390000/384160/p42-bapna.pdf?key1=384160&key2=1358585711&coll=GUIDE&dl=GUIDE,ACM&CFID=15885574&CFTOKEN=47438457• Managing Online Auctions: Current Business and Research Issueshttp://mansci.journal.informs.org/cgi/reprint/49/11/1457?maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&fulltext=Managing+Online+Auctions%3A+Current+Business+and+Research+Issues+&searchid=1&FIRSTINDEX=0&sortspec=relevance&resourcetype=HWCIT