A Two-Sided Discrete-Concave Market with Possibly Bounded Side Payments: An Approach by Discrete Convex Analysis

References

• Abraham D. J., Irving R. W., Manlove D. F. Two algorithms for the student-project allocation problem. J. Discrete AlgorithmsForthcomingGoogle Scholar
• Alkan A., Gale D. Stable schedule matching under revealed preference. J. Econom. Theory (2003) 112:289–306Crossref, Google Scholar
• Crawford V. P., Knoer E. M. Job matching with heterogeneous firms and workers. Econometrica (1981) 49:437–450Crossref, Google Scholar
• Danilov V., Koshevoy G., Lang C. Gross substitution, discrete convexity, and submodularity. Discrete Appl. Math. (2003) 131:283–298Crossref, Google Scholar
• Eguchi A., Fujishige S., Tamura A., Ibaraki T., Katoh N., Ono H. A generalized Gale-Shapley algorithm for a discrete-concave stable-marriage model. Algorithms and Comput.: 14th Internat. Sympos., ISAAC2003, Lecture Notes in Computer Science (2003) 2906(Springer-Verlag, Berlin, Germany) 495–504Google Scholar
• Eriksson K., Karlander J. Stable matching in a common generalization of the marriage and assignment models. Discrete Math. (2000) 217:135–156Crossref, Google Scholar
• Farooq R., Shioura A. A note on the equivalence between substitutability and M♮-convexity. Pacific J. Optim. (2005) 1:243–252Google Scholar
• Farooq R., Tamura A. A new characterization of M♮-convex set functions by substitutability. J. Oper. Res. Soc. Japan (2004) 47:18–24Google Scholar
• Fleiner T., Gerards B., Aardal K. A matroid generalization of the stable matching polytope. Integer Programming and Combin. Optim.: 8th Internat. IPCO Conf., Lecture Notes in Computer Science (2001) 2081(Springer-Verlag, Berlin, Germany) 105–114Google Scholar
• Fleiner T. A fixed point approach to stable matchings and some applications. Math. Oper. Res. (2003) 28:103–126Link, Google Scholar
• Fujishige S.Submodular Functions and Optimization, 2nd ed. Annals of Discrete Mathematics 58 (2005) (Elsevier, Amsterdam, The Netherlands) Google Scholar
• Fujishige S., Tamura A. A general two-sided matching market with discrete concave utility functions. Discrete Appl. Math. (2006) 154:950–970Crossref, Google Scholar
• Fujishige S., Yang Z. A note on Kelso and Crawford’s gross substitutes condition. Math. Oper. Res. (2003) 28:463–469Link, Google Scholar
• Gale D., Shapley L. S. College admissions and the stability of marriage. Amer. Math. Monthly (1962) 69:9–15Crossref, Google Scholar
• Gul F., Stacchetti F. Walrasian equilibrium with gross substitutes. J. Econom. Theory (1999) 87:95–124Crossref, Google Scholar
• Iwata S., Moriguchi S., Murota K. A capacity scaling algorithm for M-convex submodular flow. Math. Programming (2005) 103:181–202Crossref, Google Scholar
• Kaneko M. The central assignment game and the assignment markets. J. Math. Econom. (1982) 10:205–232Crossref, Google Scholar
• Kelso J. A. S., Crawford V. P. Job matching, coalition formation, and gross substitutes. Econometrica (1982) 50:1483–1504Crossref, Google Scholar
• Moriguchi S., Murota K. Capacity scaling algorithm for scalable M-convex submodular flow problems. Optim. Methods Software (2003) 18:207–218Crossref, Google Scholar
• Murota K. Convexity and Steinitz’s exchange property. Adv. Math. (1996) 124:272–311Crossref, Google Scholar
• Murota K. Discrete convex analysis. Math. Programming (1998) 83:313–371Crossref, Google Scholar
• Murota K.Discrete Convex Analysis (2003) (Society for Industrial and Applied Mathematics, Philadelphia, PA) Crossref, Google Scholar
• Murota K., Shioura A. M-convex function on generalized polymatroid. Math. Oper. Res. (1999) 24:95–105Link, Google Scholar
• Murota K., Shioura A. Relationship of M-/L-convex functions with discrete convex functions by Miller and by Favati–Tardella. Discrete Appl. Math. (2001) 115:151–176Crossref, Google Scholar
• Murota K., Tamura A. New characterizations of M-convex functions and their applications to economic equilibrium models with indivisibilities. Discrete Appl. Math. (2003) 131:495–512Crossref, Google Scholar
• Roth A. E., Sotomayor M. A. O.Two-Sided Matching—A Study in Game-Theoretic Modeling and Analysis (1990) (Cambridge University Press, Cambridge, UK) Google Scholar
• Roth A. E., Sotomayor M. A. O. Stable outcomes in discrete and continuous models of two-sided matching: A unified treatment. Rev. Econom. (1996) 16:1–24Google Scholar
• Shapley L. S., Shubik M. The assignment game I: The core. Internat. J. Game Theory (1972) 1:111–130Crossref, Google Scholar
• Shioura A. Fast scaling algorithms for M-convex function minimization with application to the resource allocation problem. Discrete Appl. Math. (2004) 134:303–316Crossref, Google Scholar
• Sotomayor M. Three remarks on the many-to-many stable matching problem: Dedicated to David Gale on his 75th birthday. Math. Soc. Sci. (1999) 38:55–70Crossref, Google Scholar
• Sotomayor M. Existence of stable outcomes and the lattice property for a unified matching market. Math. Soc. Sci. (2000) 39:119–132Crossref, Google Scholar
• Tamura A. Coordinatewise domain scaling algorithm for M-convex function minimization. Math. Programming (2005) 102:339–354Crossref, Google Scholar