Strategic Demand Reduction in homogenous multiunit auctions (where bidders may be interested in more than one unit)

How does the homogenous multi- unit auction mechanisms work? Three common auction mechanisms:  Pay-as-you bid auction  Uniform price auction  Simultaneous ascending-bid auction

‘Pay-as-you-bid’ auction Bidders each submit bids for various quantities at various prices, the auctioneer determines the market- clearing price, all bids exceeding the market-clearing price are accepted, and bidders pay their winning bids.

Uniform price auction  Bidders each submit bids for various quantities at various prices,  the auctioneer determines the market-clearing price, all bids exceeding the market-clearing price are accepted  bidders pay the market-clearing price for all units won, rather than their actual bids. Like in second price sealed bid auction  Though efficiency cannot compared to single unit second price sealed bid auction

Activity : English Auction of Jar containing ‘Coins’ Rules/Things you should know about:  This is a ‘common value’ ascending auction  No collusive bidding is allowed  Do not Jump-Bid, this undermines the entire thing  Everybody is supposed to observe the bidding process carefully and learn about others valuations from it.  You should try to make a profit, if possible  The main objective is iterative price discovery of an items of unknown value (Common Value)

Is the English auction of an item equivalent to second-price sealed bid auction? Why? Depends on the item being auctioned  It is not different in a private value case, Why? Your valuations aren’t influenced by the valuations of others just like in a second price sealed bid auction

Advantages of English Auction in a common value setting  Multiple rounds enable price discovery  Helps Reduce ‘winners curse’  Enables you to change your valuations/discover prices on the fly

Brain Teaser / Discussion How about related items (substitutes/compliments) being auctioned of concurrently using an English auction?  What is the optimal bidding strategy?  What advantage does the bidder have?

Simultaneous Ascending bid auctions Basic features:  allocates a set of M related goods among N agents via separate, concurrent English auctions for each good (M<=N)  Each auction may undergo multiple rounds of bidding

The most essential difference between multi and single unit auctions Diminishing marginal utility of each extra item should be taken into account  Definition (watered down): There is a decline in the marginal utility that person derives from consuming each additional unit of that product. This is the premise on which buffet-style restaurants operate. They entice you with "all you can eat," all the while knowing each additional plate of food provides less utility than the one before. And despite their enticement, most people will eat only until the utility they derive from additional food is slightly lower than the original Hence the marginal value of the second item in the auction may be lower than first one which implies that a bidder may not pay as much for the second as the first.

Demand and Supply of an arbitrary commodity An Illustration Price (P) Quantity (Q) PEPE Supply Demand QEQE P E is the equilibrium price Q E is the equilibrium qty Reduction in demand - Price drops - Qty drops

Demand and Supply curves in a homogenous multiunit auction An Illustration Price (P) Quantity (Q) PEPE Supply Demand Q E > 1 P E is the equilibrium price Q E is the equilibrium qty Reduction in demand - Price drops - Qty remains the same

Strategic Demand Reduction “We have some control over the prices because we are the market” Sometimes an agreement with other bidders are reached during the bidding process. ("If you give me what I want, I’ll leave you alone in the next round”)  Similar happened in 1994 FCC broadband spectrum auctions:  In round 11, PageNet decided to cut back from bidding on 3 large licenses to 2. Why? In uniform price auctions this will help one save on inframarginal (the number of items that you absolutely need) items.

How can one exploit this to bidders advantage?

A couple of questions? Does RET hold in a multiunit auction where bidders are interested in more than one item? Why so?  Answer in Appendix A of the paper due today Which one would dominate in terms of expected revenues?  Depends The goods being auctioned (whether they are substitutes or complements or totally unrelated) The number of bidders in the market.  Simultaneous Ascending bid auction has had a lot of success with the FCC spectrum auctions The main reason being, bidders having access to preferences of other bidders during the bidding process

Conclusion Must take other bidders demands into consideration  Failure to do so will drive up the prices to unfavorable levels for all participating parties  This is one way everybody is better of!

References: Klemperer, P Auction theory: A guide to the literature. Journal of Economic Surveys. Weber, R. J Making more from less: Strategic demand reduction in the FCC spectrum auctions. Journal of Economics and Management Strategy 6(3):529–548. Stone, P Randomized Strategic Demand Reduction ACM transactions Crampton, Journal of Economics and Management Strategy Crampton, Many more…