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Externality effects in the formation of societies
Finding all stable matchings with couples
1.  Department of Economics, Stanford University, 579 Serra Mall, Stanford, CA 94305, United States 
References:
[1] 
A. Abdulkadiroglu, Y.K. Che and Y. Yasuda, Resolving conflicting preferences in school choice: The 'boston' mechanism reconsidered, American Economic Review, (2009), 399410. doi: 10.2139/ssrn.1465293. 
[2] 
A. Abdulkadiroglu, P. A. Pathak and A. E. Roth, Strategyproofness versus efficiency in matching with indifferences: Redesigning the new york city high school match, American Economic Review, 99 (2009), 19541978. 
[3] 
A. Abdulkadiroǧlu and T. Sönmez, School choice: A mechanism design approach, American Economic Review, 93 (2003), 729747. 
[4] 
H. Adachi, On a characterization of stable matchings, Economics Letters, 68 (2000), 4349. doi: 10.1016/S01651765(99)002414. 
[5] 
I. Ashlagi, M. Braverman and A. Hassidim, Stability in large matching markets with complementarities, Operations Research, 62 (2014), 713732. doi: 10.1287/opre.2014.1276. 
[6] 
E. M. Azevedo and J. W. Hatfield, Complementarity and multidimensional heterogeneity in matching markets, 2012,, Mimeo., (). 
[7] 
M. Balinski and T. Sönmez, A tale of two mechanisms: student placement, Journal of Economic Theory, 84 (1999), 7394. doi: 10.1006/jeth.1998.2469. 
[8] 
P. Biró, T. Fleiner, R. W. Irving and D. F. Manlove, The college admissions problem with lower and common quotas, Theoretical Computer Science, 411 (2010), 31363153. doi: 10.1016/j.tcs.2010.05.005. 
[9] 
P. Biró, T. Fleiner and R. Irving, Matching couples with scarf's algorithm,, Institute of Economics, (). 
[10] 
P. Biró, R. W. Irving and I. Schlotter, Stable matching with couples: an empirical study, Journal of Experimental Algorithmics (JEA), 16 (2011), Article 1.2, 27 pp. doi: 10.1145/1963190.1963191. 
[11] 
P. Biró and F. Klijn, Matching with couples: A multidisciplinary survey, International Game Theory Review, 15 (2013), 1340008, 18 pp. doi: 10.1142/S0219198913400082. 
[12] 
P. Biró, D. F. Manlove and I. McBride, The hospitals/residents problem with couples: Complexity and integer programming models, in Experimental Algorithms, Springer, 2014, 1021. 
[13] 
Y.K. Che, J. Kim and F. Kojima, Stable Matching in Large Economies, Technical report, mimeo, 2013. 
[14] 
Y.K. Che and F. Kojima, Asymptotic equivalence of probabilistic serial and random priority mechanisms, Econometrica, 78 (2010), 16251672. doi: 10.3982/ECTA8354. 
[15] 
B. Dutta and J. Masso, Stability of matchings when individuals have preferences over colleagues, Journal of Economic Theory, 75 (1997), 464475. doi: 10.1006/jeth.1997.2291. 
[16] 
F. Echenique, Finding all equilibria in games with strategic complements, Journal of Economic Theory, 135 (2007), 514532. doi: 10.1016/j.jet.2006.06.001. 
[17] 
F. Echenique and J. Oviedo, Core manytoone matchings by fixed point methods, Journal of Economic Theory, 115 (2004), 358376. doi: 10.1016/S00220531(04)000421. 
[18] 
F. Echenique and J. Oviedo, A theory of stability in manytomany matching, Theoretical Economics, 1 (2006), 233273. doi: 10.2139/ssrn.691443. 
[19] 
F. Echenique and M. B. Yenmez, A solution to matching with preferences over colleagues, Games and Economic Behavior, 59 (2007), 4671. doi: 10.1016/j.geb.2006.07.003. 
[20] 
A. Erdil and H. Ergin, What's the matter with tiebreaking? improving efficiency in school choice, American Economic Review, 98 (2008), 669689. doi: 10.1257/aer.98.3.669. 
[21] 
T. Fleiner, A fixedpoint approach to stable matchings and some applications, Mathematics of Operations Research, 28 (2003), 103126. doi: 10.1287/moor.28.1.103.14256. 
[22] 
D. Fragiadakis and P. Troyan, Market design under distributional constraints: Diversity in school choice and other applications, 2014,, Mimeo., (). 
[23] 
D. Fragiadakis, A. Iwasaki, P. Troyan, S. Ueda and M. Yokoo, Strategyproof matching with minimum quotas,, mimeo., (). 
[24] 
D. Gale and L. S. Shapley, College admissions and the stability of marriage, American Mathematical Monthly, 69 (1962), 915. doi: 10.2307/2312726. 
[25] 
D. Gale and M. A. O. Sotomayor, Ms. machiavelli and the stable matching problem, American Mathematical Monthly, 92 (1985), 261268. doi: 10.2307/2323645. 
[26] 
D. Gale and M. A. O. Sotomayor, Some remarks on the stable matching problem, Discrete Applied Mathematics, 11 (1985), 223232. doi: 10.1016/0166218X(85)900745. 
[27] 
M. Goto, N. Hashimoto, A. Iwasaki, Y. Kawasaki, S. Ueda, Y. Yasuda and M. Yokoo, Strategyproof matching with regional minimum quotas, in AAMAS2014, 2014. 
[28] 
M. Goto, A. Iwasaki, Y. Kawasaki, Y. Yasuda and M. Yokoo, Improving fairness and efficiency in matching markets with regional caps: Prioritylist based deferred acceptance mechanism,, Mimeo (the latest version is available at , (). 
[29] 
J. Hatfield and P. Milgrom, Matching with contracts, American Economic Review, 95 (2005), 913935. doi: 10.1257/0002828054825466. 
[30] 
J. W. Hatfield and F. Kojima, Matching with contracts: Comment, American Economic Review, 98 (2008), 11891194. doi: 10.1257/aer.98.3.1189. 
[31] 
J. W. Hatfield and S. D. Kominers, Contract design and stability in matching markets,, Harvard University and Stanford University working paper., (). 
[32] 
N. Immorlica and M. Mahdian, Marriage, honesty, and stability, Proceedings of the Sixteenth Annual ACMSIAM Symposium on Discrete Algorithms, (electronic), ACM, New York, (2005), 5362. 
[33] 
Y. Kamada and F. Kojima, Stability and strategyproofness for matching with constraints: A problem in the japanese medical match and its solution, American Economic Review P&P, 102 (2012), 366370. doi: 10.1257/aer.102.3.366. 
[34] 
Y. Kamada and F. Kojima, General theory of matching under distributional constraints, 2014,, Mimeo., (). 
[35] 
Y. Kamada and F. Kojima, Stability concepts in matching with distributional constraints, 2014,, Mimeo., (). 
[36] 
Y. Kamada and F. Kojima, Efficient matching under distributional constraints: Theory and applications, American Economic Review, 105 (2015), 6799. doi: 10.1257/aer.20101552. 
[37] 
O. Kesten, School choice with consent, The Quarterly Journal of Economics, 125 (2010), 12971348. doi: 10.1162/qjec.2010.125.3.1297. 
[38] 
B. Klaus and F. Klijn, Stable matchings and preferences of couples, Journal of Economic Theory, 121 (2005), 75106. doi: 10.1016/j.jet.2004.04.006. 
[39] 
B. Klaus, F. Klijn and J. Masso, Some things couples always wanted to know about stable matchings (but were afraid to ask), Review of Economic Design, 11 (2007), 175184. doi: 10.1007/s1005800600179. 
[40] 
F. Kojima and P. A. Pathak, Incentives and stability in large twosided matching markets, American Economic Review, 99 (2009), 608627. doi: 10.1257/aer.99.3.608. 
[41] 
F. Kojima, P. A. Pathak and A. E. Roth, Matching with couples: Stability and incentives in large markets, Quarterly Journal of Economics, 128 (2013), 15851632. doi: 10.1093/qje/qjt019. 
[42] 
F. Kojima, A. Tamura and M. Yokoo, Designing matching mechanisms under constraints: An approach from discrete convex analysis, 2015,, Mimeo., (). 
[43] 
H. Konishi and U. Unver, Credible group stability in multipartner matching problems, Journal of Economic Theory, 129 (2006), 5780. doi: 10.1016/j.jet.2005.02.001. 
[44] 
E. J. McDermid and D. F. Manlove, Keeping partners together: algorithmic results for the hospitals/residents problem with couples, Journal of Combinatorial Optimization, 19 (2010), 279303. doi: 10.1007/s1087800992572. 
[45] 
D. G. McVitie and L. Wilson, Stable marriage assignments for unequal sets, BIT, 10 (1970), 295309. doi: 10.1007/BF01934199. 
[46] 
T. Nguyen and R. Vohra, Near feasible stable matchings with complementarities, PIER Working Paper, 2014. doi: 10.2139/ssrn.2500824. 
[47] 
M. Ostrovsky, Stability in supply chain networks,, American Economic Review, (): 897. 
[48] 
P. A. Pathak and T. Sönmez, Leveling the playing field: Sincere and sophisticated players in the boston mechanism, The American Economic Review, 98 (2008), 16361652. doi: 10.1257/aer.98.4.1636. 
[49] 
P. A. Pathak and T. Sönmez, School admissions reform in chicago and england: Comparing mechanisms by their vulnerability to manipulation, American Economic Review, 103 (2013), 80106. doi: 10.1257/aer.103.1.80. 
[50] 
M. Pycia, Stability and preference alignment in matching and coalition formation, Econometrica, 80 (2012), 323362. doi: 10.3982/ECTA7143. 
[51] 
E. Ronn, Npcomplete stable matching problems, Journal of Algorithms, 11 (1990), 285304. doi: 10.1016/01966774(90)900072. 
[52] 
A. E. Roth, The evolution of the labor market for medical interns and residents: A case study in game theory, Journal of Political Economy, 92 (1984), 9911016. doi: 10.1086/261272. 
[53] 
A. E. Roth, On the allocation of residents to rural hospitals: A general property of twosided matching markets, Econometrica, 54 (1986), 425427. doi: 10.2307/1913160. 
[54] 
A. E. Roth, A natural experiment in the organization of entrylevel labor markets: regional markets for new physicians and surgeons in the united kingdom,, The American economic review, (): 415. 
[55] 
A. E. Roth and E. Peranson, The redesign of the matching market for american physicians: Some engineering aspects of economic design, American Economic Review, 89 (1999), 748780. doi: 10.1257/aer.89.4.748. 
[56] 
A. E. Roth and M. A. Sotomayor, Twosided Matching: A Study in GameTheoretic Modeling and Analysis, Econometric Society monographs, Cambridge, 1990. doi: 10.1017/CCOL052139015X. 
[57] 
T. Sönmez and M. U. Ünver, Course bidding at business schools, International Economic Review, 51 (2010), 99123. doi: 10.1111/j.14682354.2009.00572.x. 
[58] 
M. A. O. Sotomayor, A nonconstructive elementary proof of the existence of stable marriages, Games and Economic Behavior, 13 (1996), 135137. doi: 10.1006/game.1996.0029. 
[59] 
M. A. O. Sotomayor, Three remarks on the manytomany stable matching problem, Mathematical social sciences, 38 (1999), 5570. doi: 10.1016/S01654896(98)000481. 
[60] 
M. A. O. Sotomayor, Implementation in the manytomany matching market, Games and Economic Behavior, 46 (2004), 199212. doi: 10.1016/S08998256(03)000472. 
show all references
References:
[1] 
A. Abdulkadiroglu, Y.K. Che and Y. Yasuda, Resolving conflicting preferences in school choice: The 'boston' mechanism reconsidered, American Economic Review, (2009), 399410. doi: 10.2139/ssrn.1465293. 
[2] 
A. Abdulkadiroglu, P. A. Pathak and A. E. Roth, Strategyproofness versus efficiency in matching with indifferences: Redesigning the new york city high school match, American Economic Review, 99 (2009), 19541978. 
[3] 
A. Abdulkadiroǧlu and T. Sönmez, School choice: A mechanism design approach, American Economic Review, 93 (2003), 729747. 
[4] 
H. Adachi, On a characterization of stable matchings, Economics Letters, 68 (2000), 4349. doi: 10.1016/S01651765(99)002414. 
[5] 
I. Ashlagi, M. Braverman and A. Hassidim, Stability in large matching markets with complementarities, Operations Research, 62 (2014), 713732. doi: 10.1287/opre.2014.1276. 
[6] 
E. M. Azevedo and J. W. Hatfield, Complementarity and multidimensional heterogeneity in matching markets, 2012,, Mimeo., (). 
[7] 
M. Balinski and T. Sönmez, A tale of two mechanisms: student placement, Journal of Economic Theory, 84 (1999), 7394. doi: 10.1006/jeth.1998.2469. 
[8] 
P. Biró, T. Fleiner, R. W. Irving and D. F. Manlove, The college admissions problem with lower and common quotas, Theoretical Computer Science, 411 (2010), 31363153. doi: 10.1016/j.tcs.2010.05.005. 
[9] 
P. Biró, T. Fleiner and R. Irving, Matching couples with scarf's algorithm,, Institute of Economics, (). 
[10] 
P. Biró, R. W. Irving and I. Schlotter, Stable matching with couples: an empirical study, Journal of Experimental Algorithmics (JEA), 16 (2011), Article 1.2, 27 pp. doi: 10.1145/1963190.1963191. 
[11] 
P. Biró and F. Klijn, Matching with couples: A multidisciplinary survey, International Game Theory Review, 15 (2013), 1340008, 18 pp. doi: 10.1142/S0219198913400082. 
[12] 
P. Biró, D. F. Manlove and I. McBride, The hospitals/residents problem with couples: Complexity and integer programming models, in Experimental Algorithms, Springer, 2014, 1021. 
[13] 
Y.K. Che, J. Kim and F. Kojima, Stable Matching in Large Economies, Technical report, mimeo, 2013. 
[14] 
Y.K. Che and F. Kojima, Asymptotic equivalence of probabilistic serial and random priority mechanisms, Econometrica, 78 (2010), 16251672. doi: 10.3982/ECTA8354. 
[15] 
B. Dutta and J. Masso, Stability of matchings when individuals have preferences over colleagues, Journal of Economic Theory, 75 (1997), 464475. doi: 10.1006/jeth.1997.2291. 
[16] 
F. Echenique, Finding all equilibria in games with strategic complements, Journal of Economic Theory, 135 (2007), 514532. doi: 10.1016/j.jet.2006.06.001. 
[17] 
F. Echenique and J. Oviedo, Core manytoone matchings by fixed point methods, Journal of Economic Theory, 115 (2004), 358376. doi: 10.1016/S00220531(04)000421. 
[18] 
F. Echenique and J. Oviedo, A theory of stability in manytomany matching, Theoretical Economics, 1 (2006), 233273. doi: 10.2139/ssrn.691443. 
[19] 
F. Echenique and M. B. Yenmez, A solution to matching with preferences over colleagues, Games and Economic Behavior, 59 (2007), 4671. doi: 10.1016/j.geb.2006.07.003. 
[20] 
A. Erdil and H. Ergin, What's the matter with tiebreaking? improving efficiency in school choice, American Economic Review, 98 (2008), 669689. doi: 10.1257/aer.98.3.669. 
[21] 
T. Fleiner, A fixedpoint approach to stable matchings and some applications, Mathematics of Operations Research, 28 (2003), 103126. doi: 10.1287/moor.28.1.103.14256. 
[22] 
D. Fragiadakis and P. Troyan, Market design under distributional constraints: Diversity in school choice and other applications, 2014,, Mimeo., (). 
[23] 
D. Fragiadakis, A. Iwasaki, P. Troyan, S. Ueda and M. Yokoo, Strategyproof matching with minimum quotas,, mimeo., (). 
[24] 
D. Gale and L. S. Shapley, College admissions and the stability of marriage, American Mathematical Monthly, 69 (1962), 915. doi: 10.2307/2312726. 
[25] 
D. Gale and M. A. O. Sotomayor, Ms. machiavelli and the stable matching problem, American Mathematical Monthly, 92 (1985), 261268. doi: 10.2307/2323645. 
[26] 
D. Gale and M. A. O. Sotomayor, Some remarks on the stable matching problem, Discrete Applied Mathematics, 11 (1985), 223232. doi: 10.1016/0166218X(85)900745. 
[27] 
M. Goto, N. Hashimoto, A. Iwasaki, Y. Kawasaki, S. Ueda, Y. Yasuda and M. Yokoo, Strategyproof matching with regional minimum quotas, in AAMAS2014, 2014. 
[28] 
M. Goto, A. Iwasaki, Y. Kawasaki, Y. Yasuda and M. Yokoo, Improving fairness and efficiency in matching markets with regional caps: Prioritylist based deferred acceptance mechanism,, Mimeo (the latest version is available at , (). 
[29] 
J. Hatfield and P. Milgrom, Matching with contracts, American Economic Review, 95 (2005), 913935. doi: 10.1257/0002828054825466. 
[30] 
J. W. Hatfield and F. Kojima, Matching with contracts: Comment, American Economic Review, 98 (2008), 11891194. doi: 10.1257/aer.98.3.1189. 
[31] 
J. W. Hatfield and S. D. Kominers, Contract design and stability in matching markets,, Harvard University and Stanford University working paper., (). 
[32] 
N. Immorlica and M. Mahdian, Marriage, honesty, and stability, Proceedings of the Sixteenth Annual ACMSIAM Symposium on Discrete Algorithms, (electronic), ACM, New York, (2005), 5362. 
[33] 
Y. Kamada and F. Kojima, Stability and strategyproofness for matching with constraints: A problem in the japanese medical match and its solution, American Economic Review P&P, 102 (2012), 366370. doi: 10.1257/aer.102.3.366. 
[34] 
Y. Kamada and F. Kojima, General theory of matching under distributional constraints, 2014,, Mimeo., (). 
[35] 
Y. Kamada and F. Kojima, Stability concepts in matching with distributional constraints, 2014,, Mimeo., (). 
[36] 
Y. Kamada and F. Kojima, Efficient matching under distributional constraints: Theory and applications, American Economic Review, 105 (2015), 6799. doi: 10.1257/aer.20101552. 
[37] 
O. Kesten, School choice with consent, The Quarterly Journal of Economics, 125 (2010), 12971348. doi: 10.1162/qjec.2010.125.3.1297. 
[38] 
B. Klaus and F. Klijn, Stable matchings and preferences of couples, Journal of Economic Theory, 121 (2005), 75106. doi: 10.1016/j.jet.2004.04.006. 
[39] 
B. Klaus, F. Klijn and J. Masso, Some things couples always wanted to know about stable matchings (but were afraid to ask), Review of Economic Design, 11 (2007), 175184. doi: 10.1007/s1005800600179. 
[40] 
F. Kojima and P. A. Pathak, Incentives and stability in large twosided matching markets, American Economic Review, 99 (2009), 608627. doi: 10.1257/aer.99.3.608. 
[41] 
F. Kojima, P. A. Pathak and A. E. Roth, Matching with couples: Stability and incentives in large markets, Quarterly Journal of Economics, 128 (2013), 15851632. doi: 10.1093/qje/qjt019. 
[42] 
F. Kojima, A. Tamura and M. Yokoo, Designing matching mechanisms under constraints: An approach from discrete convex analysis, 2015,, Mimeo., (). 
[43] 
H. Konishi and U. Unver, Credible group stability in multipartner matching problems, Journal of Economic Theory, 129 (2006), 5780. doi: 10.1016/j.jet.2005.02.001. 
[44] 
E. J. McDermid and D. F. Manlove, Keeping partners together: algorithmic results for the hospitals/residents problem with couples, Journal of Combinatorial Optimization, 19 (2010), 279303. doi: 10.1007/s1087800992572. 
[45] 
D. G. McVitie and L. Wilson, Stable marriage assignments for unequal sets, BIT, 10 (1970), 295309. doi: 10.1007/BF01934199. 
[46] 
T. Nguyen and R. Vohra, Near feasible stable matchings with complementarities, PIER Working Paper, 2014. doi: 10.2139/ssrn.2500824. 
[47] 
M. Ostrovsky, Stability in supply chain networks,, American Economic Review, (): 897. 
[48] 
P. A. Pathak and T. Sönmez, Leveling the playing field: Sincere and sophisticated players in the boston mechanism, The American Economic Review, 98 (2008), 16361652. doi: 10.1257/aer.98.4.1636. 
[49] 
P. A. Pathak and T. Sönmez, School admissions reform in chicago and england: Comparing mechanisms by their vulnerability to manipulation, American Economic Review, 103 (2013), 80106. doi: 10.1257/aer.103.1.80. 
[50] 
M. Pycia, Stability and preference alignment in matching and coalition formation, Econometrica, 80 (2012), 323362. doi: 10.3982/ECTA7143. 
[51] 
E. Ronn, Npcomplete stable matching problems, Journal of Algorithms, 11 (1990), 285304. doi: 10.1016/01966774(90)900072. 
[52] 
A. E. Roth, The evolution of the labor market for medical interns and residents: A case study in game theory, Journal of Political Economy, 92 (1984), 9911016. doi: 10.1086/261272. 
[53] 
A. E. Roth, On the allocation of residents to rural hospitals: A general property of twosided matching markets, Econometrica, 54 (1986), 425427. doi: 10.2307/1913160. 
[54] 
A. E. Roth, A natural experiment in the organization of entrylevel labor markets: regional markets for new physicians and surgeons in the united kingdom,, The American economic review, (): 415. 
[55] 
A. E. Roth and E. Peranson, The redesign of the matching market for american physicians: Some engineering aspects of economic design, American Economic Review, 89 (1999), 748780. doi: 10.1257/aer.89.4.748. 
[56] 
A. E. Roth and M. A. Sotomayor, Twosided Matching: A Study in GameTheoretic Modeling and Analysis, Econometric Society monographs, Cambridge, 1990. doi: 10.1017/CCOL052139015X. 
[57] 
T. Sönmez and M. U. Ünver, Course bidding at business schools, International Economic Review, 51 (2010), 99123. doi: 10.1111/j.14682354.2009.00572.x. 
[58] 
M. A. O. Sotomayor, A nonconstructive elementary proof of the existence of stable marriages, Games and Economic Behavior, 13 (1996), 135137. doi: 10.1006/game.1996.0029. 
[59] 
M. A. O. Sotomayor, Three remarks on the manytomany stable matching problem, Mathematical social sciences, 38 (1999), 5570. doi: 10.1016/S01654896(98)000481. 
[60] 
M. A. O. Sotomayor, Implementation in the manytomany matching market, Games and Economic Behavior, 46 (2004), 199212. doi: 10.1016/S08998256(03)000472. 
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