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AssignmentwithMoneyShort145

# AssignmentwithMoneyShort145 - Multi-Unit Auction Ichiro...

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Multi-Unit Auction Ichiro Obara UCLA March 8, 2010 Obara (UCLA) Multi-Unit Auction March 8, 2010 1 / 20

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Multi-Unit Auction Multi-Unit Auction Obara (UCLA) Multi-Unit Auction March 8, 2010 2 / 20
Multi-Unit Auction Assignment with money Assignment with money We studied how to allocate many “goods” in room assignment problems and matching problems. We used preferences rather than monetary values. In auction, only one good is allocated. Each bidder’s preference is represented by his or her value. Can we use auctions to allocate many goods? Yes. We briefly discuss the notion of efficiency in this case and introduce a mechanism (a type of auction) to implement an efficient allocation. Obara (UCLA) Multi-Unit Auction March 8, 2010 3 / 20

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Multi-Unit Auction Assignment with money Assignment with money We focus on the following special environment. The set of individuals is N = { 1 , ..., N } . Each individual needs just one good (call it “house”). The set of available houses is M = { h 1 , ..., h M } , M N , owned by one seller. Individual j ’s utility from h i is v i , j > 0. If individual j buys h i and pays p , then j ’s payoff is v i , j - p . Assume that the seller’s utility from each house is 0. Obara (UCLA) Multi-Unit Auction March 8, 2010 4 / 20
Multi-Unit Auction Efficient Allocation Efficient Allocation An allocation μ : M N assigns each house to one individual. An allocation μ is efficient if there is no other μ 0 that makes everyone weakly better off and someone strictly better off. Obara (UCLA) Multi-Unit Auction March 8, 2010 5 / 20

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Multi-Unit Auction Efficient Allocation Efficient Allocation Efficient allocations are different when utility can be measured by money.
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