Concordance among Holdouts Scott Duke Kominers Department of Economics, Harvard University and Harvard Business School (joint work with E. Glen Weyl, Harvard Society of Fellows) Market Design Workshop Harvard Business School May 14, 2010 Kominers and Weyl (2010) May 14, 2010 1
Concordance Among Holdouts Introduction The Holdout Problem: A Simple Example Ten farmers own (privately valued) farms Kominers and Weyl (2010) May 14, 2010 2
Concordance Among Holdouts Introduction The Holdout Problem: A Simple Example Ten farmers own (privately valued) farms 2 3 4 5 6 7 8 9 10 1 Kominers and Weyl (2010) May 14, 2010 2
Concordance Among Holdouts Introduction The Holdout Problem: A Simple Example Ten farmers own (privately valued) farms You want to buy the farms and build an airfield (worth 90) Kominers and Weyl (2010) May 14, 2010 2
Concordance Among Holdouts Introduction The Holdout Problem: A Simple Example Ten farmers own (privately valued) farms You want to buy the farms and build an airfield (worth 90) All you know is that farmers’ values are uniformly drawn from { 1 , . . . , 10 } (expected total value 55) Kominers and Weyl (2010) May 14, 2010 2
Concordance Among Holdouts Introduction The Holdout Problem: A Simple Example Ten farmers own (privately valued) farms You want to buy the farms and build an airfield (worth 90) All you know is that farmers’ values are uniformly drawn from { 1 , . . . , 10 } (expected total value 55) What should you do?? Kominers and Weyl (2010) May 14, 2010 2
Concordance Among Holdouts Introduction The Holdout Problem: A Simple Example Ten farmers own (privately valued) farms 2 3 4 5 6 7 8 9 10 1 You want to buy the farms and build an airfield (worth 90) All you know is that farmers’ values are uniformly drawn from { 1 , . . . , 10 } (expected total value 55) What should you do?? Take-it-or-leave-it offers of 1 , . . . , 10 (total 55)? Kominers and Weyl (2010) May 14, 2010 2
Concordance Among Holdouts Introduction The Holdout Problem: A Simple Example Ten farmers own (privately valued) farms 2 3 4 5 6 7 8 9 10 1 You want to buy the farms and build an airfield (worth 90) All you know is that farmers’ values are uniformly drawn from { 1 , . . . , 10 } (expected total value 55) What should you do?? Take-it-or-leave-it offers of 1 , . . . , 10 (total 55)? Take-it-or-leave-it offers of 8 (total 80)? Kominers and Weyl (2010) May 14, 2010 2
Concordance Among Holdouts Introduction The Holdout Problem: A Simple Example Ten farmers own (privately valued) farms You want to buy the farms and build an airfield (worth 90) All you know is that farmers’ values are uniformly drawn from { 1 , . . . , 10 } (expected total value 55) What should you do?? Take-it-or-leave-it offers of 1 , . . . , 10 (total 55)? Take-it-or-leave-it offers of 8 (total 80)? Self-assessment: ask each farmer to reveal his value? Kominers and Weyl (2010) May 14, 2010 2
Concordance Among Holdouts Introduction The Holdout Problem: A Simple Example Ten farmers own (privately valued) farms 2 3 4 5 6 7 8 9 10 1 You want to buy the farms and build an airfield (worth 90) All you know is that farmers’ values are uniformly drawn from { 1 , . . . , 10 } (expected total value 55) What should you do?? Take-it-or-leave-it offers of 1 , . . . , 10 (total 55)? Take-it-or-leave-it offers of 8 (total 80)? Self-assessment: ask each farmer to reveal his value? Eminent domain: take land and pay each farmer 1 (total 10)? Kominers and Weyl (2010) May 14, 2010 2
Concordance Among Holdouts Introduction The Holdout Problem: A Simple Example Ten farmers own (privately valued) farms You want to buy the farms and build an airfield (worth 90) All you know is that farmers’ values are uniformly drawn from { 1 , . . . , 10 } (expected total value 55) What should you do?? Take-it-or-leave-it offers of 1 , . . . , 10 (total 55)? Take-it-or-leave-it offers of 8 (total 80)? Self-assessment: ask each farmer to reveal his value? Eminent domain: take land and pay each farmer 1 (total 10)? Kominers and Weyl (2010) May 14, 2010 2
Concordance Among Holdouts Introduction The Holdout Problem Holdout is pervasive. Perfect complements problems land assembly, corporate acquisitions, spectrum recovery All trade dries up as N → ∞ . Institutions for reducing holdout are primitive. Takings; voting-based procedures Sharp contrast to the case of auctions for substitutes, where even na¨ ıve designs are efficient as N → ∞ (Bulow & Klemperer (1996)) Kominers and Weyl (2010) May 14, 2010 3
Concordance Among Holdouts Introduction Our Contributions 1 Introduce holdout as a market design problem Design goals straightforwardness, bilateral efficiency, partial property rights 2 Propose a class of solutions Design principle — “Concordance” — which ensures key goals Concordance mechanisms: a market design for holdout Kominers and Weyl (2010) May 14, 2010 4
Concordance Among Holdouts Introduction Road Map 1 Introduction 2 Road Map ( ⇐ we are here) Kominers and Weyl (2010) May 14, 2010 5
Concordance Among Holdouts Introduction Road Map 1 Introduction 2 Road Map ( ⇐ we are here) 3 Model Market Design Goals Applications Kominers and Weyl (2010) May 14, 2010 5
Concordance Among Holdouts Introduction Road Map 1 Introduction 2 Road Map ( ⇐ we are here) 3 Model Market Design Goals Applications 4 Our Solution: The Concordance Principle Kominers and Weyl (2010) May 14, 2010 5
Concordance Among Holdouts Introduction Road Map 1 Introduction 2 Road Map ( ⇐ we are here) 3 Model Market Design Goals Applications 4 Our Solution: The Concordance Principle 5 Mechanisms Straightforward Concordance Other Concordance Mechanisms X -plurality Kominers and Weyl (2010) May 14, 2010 5
Concordance Among Holdouts Introduction Road Map 1 Introduction 2 Road Map ( ⇐ we are here) 3 Model Market Design Goals Applications 4 Our Solution: The Concordance Principle 5 Mechanisms Straightforward Concordance Other Concordance Mechanisms X -plurality 6 Conclusion Kominers and Weyl (2010) May 14, 2010 5
Concordance Among Holdouts Model, Design Goals, and Applications Basic Model (in language of land assembly) Kominers and Weyl (2010) May 14, 2010 6
Concordance Among Holdouts Model, Design Goals, and Applications Basic Model (in language of land assembly) Buyer has (private) value b for aggregate plot Kominers and Weyl (2010) May 14, 2010 6
Concordance Among Holdouts Model, Design Goals, and Applications Basic Model (in language of land assembly) Buyer has (private) value b for aggregate plot Each seller i has (private) value v i for her subplot Kominers and Weyl (2010) May 14, 2010 6
Concordance Among Holdouts Model, Design Goals, and Applications Basic Model (in language of land assembly) Buyer has (private) value b for aggregate plot Each seller i has (private) value v i for her subplot Each seller has expected share of total value s i Can be entirely exogenous or determined by buyer s i close to v i / ( � j v j ) = ⇒ better property rights Kominers and Weyl (2010) May 14, 2010 6
Concordance Among Holdouts Model, Design Goals, and Applications Basic Model (in language of land assembly) Buyer has (private) value b for aggregate plot Each seller i has (private) value v i for her subplot Each seller has expected share of total value s i Can be entirely exogenous or determined by buyer s i close to v i / ( � j v j ) = ⇒ better property rights A mechanism is a transaction procedure Kominers and Weyl (2010) May 14, 2010 6
Concordance Among Holdouts Model, Design Goals, and Applications Basic Model (in language of land assembly) Buyer has (private) value b for aggregate plot Submits offer o (recommended o ⋆ ( · )) Each seller i has (private) value v i for her subplot Reports reserve value r i (recommended r ⋆ ( · )) Each seller has expected share of total value s i Can be entirely exogenous or determined by buyer s i close to v i / ( � j v j ) = ⇒ better property rights A mechanism is a transaction procedure Kominers and Weyl (2010) May 14, 2010 6
Concordance Among Holdouts Model, Design Goals, and Applications Basic Model (in language of land assembly) Buyer has (private) value b for aggregate plot Submits offer o (recommended o ⋆ ( · )) Each seller i has (private) value v i for her subplot Reports reserve value r i (recommended r ⋆ ( · )) Each seller has expected share of total value s i Can be entirely exogenous or determined by buyer s i close to v i / ( � j v j ) = ⇒ better property rights A mechanism is a transaction procedure Kominers and Weyl (2010) May 14, 2010 6
Concordance Among Holdouts Model, Design Goals, and Applications The Simple Example Revisited Ten farmers own (privately valued) farms 2 3 4 5 6 7 8 9 10 1 You want to buy the farms and build an airfield (worth 90) All you know is that farmers’ values are uniformly drawn from { 1 , . . . , 10 } (expected total value 55) Kominers and Weyl (2010) May 14, 2010 7
Concordance Among Holdouts Model, Design Goals, and Applications The Simple Example Revisited Ten farmers own (privately valued) farms v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 You want to buy the farms and build an airfield (worth b ) All you know is that farmers’ values are uniformly drawn from { 1 , . . . , 10 } (expected total value 55) Kominers and Weyl (2010) May 14, 2010 7
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