Topics on Matching Theory

Transcription

1 Topics on Matching Theory Istanbul Bilgi University. March 2011 Jordi Massó Program and References 1.- Stability and Incentives in Matching Markets Preliminaries (brief reminder) B D. Gale and L. Shapley. College admissions and the stability of marriage, American Mathematical Monthly 69, 9-15 (1962) B A. Roth and M. Sotomayor. Two-sided Matching: A Study in Game-Theoretic Modelling and Analysis. Cambridge University Press, New York (1990) Stability Knuth s Example B D. Knuth. Marriages Stables. Les Presses de l Université de Montréal, Montréal (1976) Paths to Stability B F. Kojima and U. Ünver. Random paths to pairwise stability in many-to-many matching problems: a study in market equilibration, International Journal of Game Theory 36, (2008) B A. Roth and J. Vande Vate. Random paths to stability in two-sided matching, Econometrica 58, (1990) Vacancy Chains B Y. Blum, A. Roth, and U. Rothblum. Vacancy chains and equilibration in seniorlevel labor markets, Journal of Economic Theory 76, (1997) B D. Cantala. Re-stabilizing matching markets at senior level, Games and Economic Behavior 48, 1-17 (2004) B J. Pais. Incentives in decentralized random matching, Games and Economic Behavior 64, (2008) On the Number of Stable Matchings B S. Clark. Uniqueness of stable matchings, Contributions to Theoretical Economics 6, 1-30 (2006) B J. Eeckhout. On the uniqueness of stable marriage matchings, Economics Letters 69, 1-8 (2000) B R. Irving and P. Leather. The complexity of counting stable marriages, SIAM Journal of Computing 15, (1986)

2 B A. Roth and E. Peranson. The redesign of the matching market for american physicians: some engineering aspects of economic design, American Economic Review 89, (1999) Incentives Dominant Strategies Impossibilities B J. Alcalde and S. Barberà. Top dominance and the possibility of strategy-proof stable solutions to matching problems, Economic Theory 4, (1994) B A. Roth. The economics of matching: stability and incentives, Mathematics of Operations Research 7, (1982) Possibilities: Domain Restriction B J. Alcalde and S. Barberà. Top dominance and the possibility of strategy-proof stable solutions to matching problems, Economic Theory 4, (1994) B L. Dubins and D. Freedman. Machiavelli and the Gale-Shapley algorithm, American Mathematical Monthly 88, (1981) B A. Roth. The economics of matching: stability and incentives, Mathematics of Operations Research 7, (1982) Complete Information Nash Implementation B J. Alcalde. Implementation of stable solutions to marriage problems, Journal of Economic Theory 69, (1996) Main Results B D. Gale and M. Sotomayor. Ms Machiavelli and the stable matching problem, American Mathematical Monthly 92, (1985) B A. Roth. Misrepresentation and stability in the marriage problem, Journal of Economic Theory 34, (1984) Incomplete Information Marriage B A. Roth. Two-sided matching with incomplete information about other s preferences, Games and Economic Behavior (1989) Giving Advice B L. Ehlers. In search of advice for participants in matching markets which use the deferred-acceptance algorithm, Games and Economic Behavior 48, (2004) B L. Ehlers. Truncation strategies in matching markets, Mathematics of Operations Research 33, (2008) B J. Pais. Giving advice and perfect equilibria in matching markets, ISEG mimeo (2006) 2

3 B A. Roth and U. Rothblum. Truncation strategies in matching markets of advice for participants, Econometrica 67, (1999) College Admissions in search B C. d Aspremont and B. Peleg. Ordinal Bayesian Incentive Compatibility Representation of Committees, Social Choice and Welfare 5, (1988) B L. Ehlers and J. Massó. Incomplete information and singleton cores in matching markets, Journal of Economic Theory 136, (2007) B L. Ehlers and J. Massó. Matching markets under (in)complete information, Universitat Autònoma de Barcelona mimeo (2011) B D. Gale and L. Shapley. College admissions and the stability of marriage, American Mathematical Monthly 69, 9-15 (1962) B D. Majumdar. Ordinal Bayesian Incentive Compatible Stable Matchings, CORE mimeo (2003) B D. Majumdar and A. Sen. Ordinal Bayesian Incentive Compatible Voting Rules, Econometrica 72, (2004) B A. Roth. The college admissions problem is not equivalent to the marriage problem, Journal of Economic Theory 36, (1985) B A. Roth. Common and con icting interests in two-sided matching markets, European Economic Review 27, (1985) Random Stable Mechanisms B J. Pais. Random matching in the college admissions problem, Economic Theory 35, (2008) 2.- General Many-to-one and Many-to-many Ordinal Matching Models Preliminaries: Many-to-one Ordinal Matching B A. Roth and M. Sotomayor. Two-sided Matching: A Study in Game-Theoretic Modelling and Analysis. Cambridge University Press, New York (1990) Substitutable Preferences B A. Kelso and V. Crawford. Job matching, coalition formation, and gross substitutes, Econometrica 50, (1982) B A. Roth. Stability and polarization of interests in job matching, Econometrica 52, (1984) Quota q-separable Preferences B S. Barberà, H. Sonnenschein, and L. Zhou. Voting by Committees, Econometrica 59, (1991) B C. Blair. The lattice structure of the set of stable matchings with multiple partners, Mathematics of Operations Research 13, (1988) 3

4 B F. Echenique and J. Oviedo. Core many-to-one matchings by xed-point methods, Journal of Economic Theory 115, (2004) B J.H. Hat eld and F. Kojima. Group incentive compatibility for matching with contracts, Games and Economic Behavior 67, (2009) B J.H. Hat eld and P.R. Milgrom. Matching with Contracts, American Economic Review 95, (2005) B R. Martínez, J. Massó, A. Neme, and J. Oviedo. Single agents and the set of many-to-one stable matchings, Journal of Economic Theory 91, (2000) B R. Martínez, J. Massó, A. Neme, and J. Oviedo. On the lattice structure of the set of stable matchings for a many-to-one model, Optimization 50, (2001) B R. Martínez, J. Massó, A. Neme, and J. Oviedo. On group strategy-proof mechanisms for a many-to-one matching model, International Journal of Game Theory 33, (2004) B R. Martínez, J. Massó, A. Neme, and J. Oviedo. A Maximal domain of preferences under which the workers-optimal stable matching mechanism is group strategy-proof for the workers, Universitat Autònoma de Barcelona mimeo (2008) B R. Martínez, J. Massó, A. Neme, and J. Oviedo. The blocking lemma for a manyto-one matching model, Journal of Mathematical Economics 46, (2010) B T. Sönmez. Strategy-proofness in many-to-one matching problems, Economic Design 1, (1996) Many-to-one: The Core B H. Adachi. On a characterization of stable matchings, Economics Letters 68, (2000) B F. Echenique and J. Oviedo. Core many-to-one matchings by xed-point methods, Journal of Economic Theory 115, (2004) On the Invariance of the Set of Core Matchings with Respect to Preferences B R. Martínez, J. Massó, A. Neme, and J. Oviedo. On the invariance of the set of stable matchings with respect to substitutable preference pro les, International Journal of Game Theory 36, (2008) B R. Martínez, J. Massó, A. Neme, and J. Oviedo. On the invariance of the set of Core matchings with respect to preference pro les, Universitat Autònoma de Barcelona mimeo (2009) Preferences over Colleagues B B. Dutta and J. Massó. Stability of matchings when individuals have preferences over colleagues, Journal of Economic Theory 75, (1997) B F. Echenique and M. Yenmez. A solution to matching with preferences over colleagues, Games and Economic Behavior 59, (2007) Many-to-many Matchings 4

5 B F. Echenique and J. Oviedo. A theory of stability in many-to-many matching markets, Theoretical Economics 1, (2006) B H. Konishi and U. Ünver. Credible group-stability in many-to-many matching problems, Journal of Economic Theory 129, (2006) B R. Martínez, J. Massó, A. Neme, and J. Oviedo. An algorithm to compute the full set of many-to-many stable matchings, Mathematical Social Sciences 47, (2004) B M. Sotomayor, Three remarks on the many-to-many stable matching problem, Mathematical Social Sciences 38, (1999) Other solution concepts von Neumann-Morgenstern Stable Sets B L. Ehlers. Von Neumann Morgenstern stable sets in matching problems, Journal of Economic Theory 134, (2007) A Bargaining Set B F. Klijn and J. Massó. A bargaining set for the marriage market, Games and Economic Behavior 42, (2003) B L. Zhou. A new bargaining set of an N person game and endogenous coalition formation, Games and Economic Behavior 6, (1994) 3.- Many-to-many Assignment Games The Assignment Game: Introduction Preliminaries B D. Jaume, J. Massó, and A. Neme. The multiple-partners assignment game with heterogeneous sells and multi-unit demands: competitive equilibria, Universitat Autònoma de Barcelona mimeo (2009) B L. Shapley and M. Shubik. The assignment game I: the Core, International Journal of Game Theory 1, (1972) B E. Camiña. A generalized assignment game, Mathematical Social Sciences 52, (2006) B M. Sotomayor. Connecting the cooperative and competitive structures of the multiple-partners assignment game, Journal of Economic Theory 134, (2007) Optimal Assignments Competitive Equilibria De nition Existence Structure Cartesian Product 5

6 Lattice Core Set-wise Stability Convergence Theorems B J. Massó and A. Neme. On cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria, Universitat Autònoma de Barcelona mimeo (2010) 6