Descending Price Optimally Coordinates Search. INFORMS, Nov 2018

Transcription

1 Descending Price Optimally Coordinates Search Robert Kleinberg Bo Waggoner Glen Weyl Cornell Microsoft NYC Microsoft NYC INFORMS, Nov / 11

2 Overview Challenge: market design with information acquisition costs 1 Background 2 Descending Price Optimally Coordinates Search. Kleinberg, Waggoner, Weyl EC Recent related work 3 / 11

3 Background: optimal search Weitzman 1979: Pandora s Box Problem Each alternative i = 1,..., n has: known value distribution D i known cost of inspection: c i when/if cost is paid, value v i drawn 4 / 11

4 Background: optimal search Weitzman 1979: Pandora s Box Problem Each alternative i = 1,..., n has: known value distribution D i known cost of inspection: c i when/if cost is paid, value v i drawn Challenge: inspect sequentially, stop and choose one. maximize ( value sum of costs ) 4 / 11

5 Background: optimal search Weitzman 1979: Pandora s Box Problem Each alternative i = 1,..., n has: known value distribution D i known cost of inspection: c i when/if cost is paid, value v i drawn Challenge: inspect sequentially, stop and choose one. maximize ( value sum of costs ) models a set of bidders cost of entry, information acquisition, etc. 4 / 11

6 Background continued Optimal algorithm: Clock Compute indices σ i (D i, c i ) Cllock descends from + When it hits σ i : inspect, paying c i and learning v i When it hits v i : stop and choose i σ 1 σ 3 σ 2 c 1 c 2 c 3 D 1 D 2 D 3 5 / 11

7 Background continued Optimal algorithm: Clock Compute indices σ i (D i, c i ) Cllock descends from + When it hits σ i : inspect, paying c i and learning v i When it hits v i : stop and choose i σ 3 v 1 σ 2 c 2 c 3 D 1 D 2 D 3 5 / 11

8 Model: Single Item with Inspection Each bidder i = 1,..., n has: private cost c i, distribution D i parameters from common-knowledge distributions 6 / 11

9 Model: Single Item with Inspection Each bidder i = 1,..., n has: private cost c i, distribution D i parameters from common-knowledge distributions can inspect secretly at any time, v i D i 6 / 11

10 Model: Single Item with Inspection Each bidder i = 1,..., n has: private cost c i, distribution D i parameters from common-knowledge distributions can inspect secretly at any time, v i D i inspection is mandatory before obtaining item 6 / 11

11 Pitfalls of other auctions Ascending and sealed-bid auctions can fail: 7 / 11

12 Pitfalls of other auctions Ascending and sealed-bid auctions can fail: Many bidders, values Bernoulli(ɛ) Must decide early: drop out or inspect? 7 / 11

13 Pitfalls of other auctions Ascending and sealed-bid auctions can fail: Many bidders, values Bernoulli(ɛ) Must decide early: drop out or inspect? If many drop out: high-value winner is not found If many inspect: wasted inspection costs (unsupportable in equilibrium.) 7 / 11

14 Pitfalls of other auctions Ascending and sealed-bid auctions can fail: Many bidders, values Bernoulli(ɛ) Must decide early: drop out or inspect? If many drop out: high-value winner is not found If many inspect: wasted inspection costs (unsupportable in equilibrium.) = inspection is not coordinated 7 / 11

15 Intuition: benefit of the Dutch Allow bidders to wait while price descends If item is claimed early: no wasted inspection cost If item is available late: inspection has high returns 8 / 11

16 Main result Theorem The Dutch auction with inspection is strategically equivalent to the Dutch auction without inspection. 9 / 11

17 Main result Theorem The Dutch auction with inspection is strategically equivalent to the Dutch auction without inspection. (c i, D i ) corresponds to a distribution F i of values Given equilibrium for F 1,..., F n, bid b i (v i ): 9 / 11

18 Main result Theorem The Dutch auction with inspection is strategically equivalent to the Dutch auction without inspection. (c i, D i ) corresponds to a distribution F i of values Given equilibrium for F 1,..., F n, bid b i (v i ): Inspect when price reaches b i (σ i ). 9 / 11

19 Main result Theorem The Dutch auction with inspection is strategically equivalent to the Dutch auction without inspection. (c i, D i ) corresponds to a distribution F i of values Given equilibrium for F 1,..., F n, bid b i (v i ): Inspect when price reaches b i (σ i ). Claim item when price reaches b i (v i ). 9 / 11

20 Main result Theorem The Dutch auction with inspection is strategically equivalent to the Dutch auction without inspection. (c i, D i ) corresponds to a distribution F i of values Given equilibrium for F 1,..., F n, bid b i (v i ): Inspect when price reaches b i (σ i ). Claim item when price reaches b i (v i ). Equivalence of (optimal) welfare! 9 / 11

21 Results continued Implications: Welfare ( 1 1 e) First-Best Symmetric bidders = fully efficient Revenue implications / 11

22 Extensions, ideas Channel Auctions. Azevedo, Pennock, Weyl. The Marshallian Match. Waggoner, Weyl (forthcoming). Two-sided market Each side places bids on possible matches When descending clock = sum of bids: inspect or match 11 / 11

23 Extensions, ideas Channel Auctions. Azevedo, Pennock, Weyl. The Marshallian Match. Waggoner, Weyl (forthcoming). Two-sided market Each side places bids on possible matches When descending clock = sum of bids: inspect or match Thanks! 11 / 11