Tópicos en Microeconomía Modelos de asignación bilateral. Juegos de asignación uno-a-uno. Juegos de asignación muchos-a-uno y muchos-a-muchos

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1 Tópicos en Microeconomía Modelos de asignación bilateral. Juegos de asignación uno-a-uno. Modelo Formal y Definición de asignaciones. Asignación Estable. Distintos modelos y Propiedades. Teorema de existencia y optimalidad. Reticulados. Teorema del hospital rural. Juegos de asignación muchos-a-uno y muchos-a-muchos. Preferencias. Distintos conceptos de estabilidad. Relaciones entre conceptos de estabilidad. Teoremas de existencia. Optimalidad. Reticulados. Juegos de asignación uno-a-uno con indiferencias. Modelo Formal. Distintos conceptos de estabilidad. Relaciones entre conceptos de estabilidad. Optimalidad. Reticulado. Profesor Jorge Oviedo (8 horas) Bibliografía Gusfield. D. M. y R. W. Irving. The Stable Marriage Problem: Structure and Algorithms. MIT Press, Knuth, D. E. Stable marriage and its relation to other combinatorial problems CRM Proceedings and Lecture Notes, Vol. 10 American Mathematical Society, 1997 Roth, A. E. y M. A. Oliveira Sotomayor. Two sided Matching: A Study in game theoretic Modelling and Analysis. Econometric Society Monograph No. 18 Cambridge University Press, Mercados de Asignación Descentralizados Caminos hacia la estbilidad: Optimalidad débil. Caminos hacia la estabilidad. Ejemplo de Knuth. Teorema de Roth and Vande Vate. Algoritmo secuencial. Cadenas de vacancia. Algoritmo de aceptación diferida partiendo de una asignación arbitraria. Asignaciones cuasi estables. Aspectos dinámicos. Re-estabilización después de vacancias. Extensiones. Incentivos: Mecanismos estables optimales. Mecanismos estables no manipulables. Teorema de imposibilidad de Roth. Mecanismos estables no manipulables: Restricción de dominio. Parcial no manipulabilidad. Equilibrios de Nash y estabilidad. Parcial estabilidad por grupos. Equilibrios de Nash información incompleta. Bibliografía Libro: Alvin E. Roth and Marilda A. Oliveira Sotomayor. Two sided Matching: A Study in game theoretic Modelling and Analysis. Econometric Society Monograph No. 18 Cambridge University Press, Blum Y., A. Roth, y U. Rothblum (1997), "Vacancy chains and equilibration in senior-level labor markets", J. Econom. Theory, 76, Boyle E.y F. Echenique (2009), "Sequential entry in Many-to-one Matching Markets ", Social Choice and Welfare, 33, Cantala D. (2003), "Restabilizing matching markets at senior level ", J. Econom. Theory, 103, McVitie and L. Wilson..The stable marriage problem, Communications of the ACM 14, (1971).

2 Martinez R., Massó J., Neme A., Oviedo J. (2003) An Algorithm to Compute the Full Set of Many to Many Stable Matching. Mathematical Social Sciences, Elsevier, vol. 47(2), pg Martinez R., Massó J., Neme A., Oviedo J. (2001) On the Lattice Structure of the Set of Stable Matchings for a Many to One Model. Optimization; vol 50; pg Roth. A. "The economics of matching: stability and incentives," Mathematics of Operations Research 7, (1982). Roth A. and J. Vande Vate. "Random paths to stability in two-sided matching," Econometrica 58, (1990). Artìculos optativos: Abeledo H. y U. G. Rothblum (1995), "Paths to Marriange Stability", Discrete Applied Mathematics, 63, Alcalde J. and S. Barberà. "Top dominance and the possibility of strategy-proof stable solutions to matching problems," Economic Theory 4, (1994). Biró P., K. Cechlárová, y T. Fleiner (2006), "The dynamics of stable matching markets and half-matchings for the stable marriage and roommates problems", Int J. Game Theory, 36, Boyle E.y F. Echenique (2009), "Sequential entry in Many-to-one Matching Markets ", Social Choice and Welfare, 33, Diamantoudi E., E. Miyagawa y L. Xue (2004), "Random paths to Stability in the Roommate Problem", Games and Economic Behavior, 48, Dubins L. and D. Freedman. "Machiavelli and the Gale-Shapley algorithm," American Mathematical Monthly 88, (1981). Gale D. and M. Sotomayor. "Ms Machiavelli and the stable matching problem," American Mathematical Monthly 92, (1985). Hatfield J., Milgrom P. (2005) Matching with contracts. The American Economic Review; Vol. 95 Nro. 4 ; pg Klaus B. and F. Klijn. "Corrigendum to `On randomized matching mechanisms' [Economic Theory 8(1996) ," Economic Theory 32, (2007). Kojima F., Ünver U. (2008) Ramdom Paths to Pairwise Stability in Many to Many Matching Problems: a Study on Market Equilibration Int J Game Theory 36: Ma J.. "On randomized matching mechanisms," Economic Theory 8, (1996). Pais J...Random matching in the college admisssions problem,.economic Theory 35, (2008). Roth. A. "The economics of matching: stability and incentives," Mathematics of Operations Research 7, (1982). Sotomayor, Marilda, "Implementation in the many-to-many matching market," Games and Economic Behavior, Elsevier, vol. 46(1), pages , January Juegos de Asignación Modelo de asignación uno-a-uno con dinero. Juego cooperativo asociado. El "Core" del juego. Aspectos estratégicos. Juegos de asignación, descripción formal del modelo. El Core. Mecanismo de subasta multi-objetivo. Estructura del Core. Equilibrio competitivo: definición y existencia. Estructura del conjunto de Equilibrios competitivos. Incentivos.

3 Diferentes juegos de asignación generalizados. Equilibrio competitivo asociado. Juego cooperativo asociado. Diferentes conceptos de solución cooperativa. Modelo replicado. Teoremas de convergencia. Bibliografia: Libro: Alvin E. Roth and Marilda A. Oliveira Sotomayor. Two sided Matching: A Study in game theoretic Modelling and Analysis. Econometric Society Monograph No. 18 Cambridge University Press, Camiña..A generalized assignment game,.mathematical Social Sciences 52, (2006). Debreu, G. and Scarf, H. "A limit theorem on the Core of an economy," International Economic Review 4, (1963). Jaume D., J. Massó y A. Neme "The Multiple-partners Assignment Game with Heterogeneous Sells and Multi-unit Demands: Competitive Equilibria". Forthcoming in Mathematical Methods of Operations Research. (2012) Massó J. y A. Neme. "On Cooperative Solutions of a Generalized Assignment Game: Limit Theorems to the Set of Competitive Equilibria," mimeo (2012). Shapley L. and H. Scarf..On cores and indivisibilities,.journal of Mathematical Economics 1, 2328 (1974). Shapley L. and M. Shubik..The assignment game I: the core,.international Journal of Game Theory 1, (1972). Sotomayor, M. "Correlating the competitive and cooperative structures of the time-sharing assignment game under rigid agreements," mimeo (2011). Artículos optativos: Edgeworth, F.Y. Mathematical Psychics. London: Kegan Paul (1881). Fagebaume A., D. Gale, and M. Sotomayor. "A note on the multiple partners assignment game," Journal of Mathematical Economics 46, (2010). Klaus, B and M. Walzl. "Stable Many-to-Many Matchings with Contracts," Journal of Mathematical Economics, 45, (2009). Ma..Strategyproofness and the strict core in a market with indivisibilities,.international Journal of Game Theory 23, 7583 (1994). Milgrom, P. "Assignment messages and exchanges," American Economic Review: Micro 1, (2009). Owen1975 : Owen, G. "On the Core of linear production games," Mathematical Programming 9, (1975). Roth..Incentive compatibility in a market with indivisible goods,.economics Letters 9, (1982). Sotomayor, M. "The multiple partners game," in Majumdar, M. (editor) Equilibrium and dynamics: Essays in honor to David Gale. Macmillian, (1992). Sotomayor, M. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory 28, (1999). Sotomayor M.,.Three remarks on the manytomany stable matching prob lem,.mathematical Social Sciences 38, 5570 (1999). Sotomayor M...Connecting the cooperative and competitive structures of the multiplepartners assignment game,. Journal of Economic Theory 134,

4 (2007). Sotomayor, M. "Correlating new cooperative and competitive concepts in the time-sharing assignment game," mimeo (2009). Juegos Cooperativos Juegos cooperativos con utilidad transferible. Función característica. Juegos en forma normal. Pagos factibles o imputaciones. Juegos equivalentes. Normalización. Pagos dominados. Núcleo (Core). Ejemplos. Colecciones balanceadas y caracterización del núcleo. Mercados con pagos transferibles. Equilibrio competitivo y núcleo. Juegos convexos, Núcleo y conjuntos de Weber. Otras soluciones de juegos cooperativos: Conjuntos estables de von Neummann- Morgenstern. Objeciones, contraobjeciones. Conjuntos de regateo (bargaining). Excesos. Núcleo (kernel). Nucleolo (nucleolus), propiedades. Valor de Shapley. Axiomas que definen el Valor de Shapley. Extensiones multilaterales. Índice de poder de Banzhaff-Coleman. Juegos Cooperativos con utilidad no transferible. Ejemplos. Núcleo (Core) Profesor: Jorge Oviedo (8 horas) Bibliografía Gilles, R. P. The Cooperative Game Theory of Networks and Hierarchies. Springer Osborne M. J. y A. Rubinstein. A course in Game Theory. MIT Press Peters H. Game Theory: A Multi-Leveled Approach. Springer Funciones de Eleccion Social Funciones de elección social. Manipulabilidad. Teoremas de imposibilidad en dominios irrestrictos. Teoremas de Gibbard-Satterthwaite. Estructura de juego asociado e implementación. Principio de revelación para estrategias dominantes. Conexión con el Teorema de agregación de preferencias de Arrow. Los conjuntos de opciones individuales, una prueba simple del teorema de imposibilidad. Dominios restringidos. Preferencias unimodales. Mecanismos de votación. Principio del votante mediano. Teoremas de posibilidad. Métodos de votación por comités. Teoremas de posibilidad. Métodos de voto por comités bajo restricciones. Teoremas de posibilidad. Dominios maximales. Bibliografia: Libros: Arrow, K. (1951):.Social Choice and Individual Values., Cowles Foundation Monograph, Yale University Press. 2nd edition Wiley New York Salvador Barberà. Strategy-proof Social Choice. MOVE, Universitat Autònoma de Barcelona and Barcelona GSE. January 29, Farquharson, R. (1969): Theory of Voting, Yale University Press: New Haven. Moulin, H. (1983): The Strategy of Social Choice, Amsterdam: North-Holland. Peleg, B. (1984): Game Theoretic Analysis of Voting in Committees. Cambridge: Cambridge University Press. Barberà, S. and B. Peleg (1990):.Strategy-Proof Voting Schemes with Continuous Preferences., Social Choice and Welfare 7, Barberà, S.; F. Gul, and E. Stacchetti (1993):.Generalized Median Voter Schemes and Committees., Journal of Economic Theory 61,

5 Barberà, S.; H. F. Sonnenschein and L. Zhou (1991):.Voting by Committees., Econometrica 59, Barberà, S.; J. Massó and A. Neme (1997):.Voting under Constraints., Journal of Economic Theory 76(2), Barberà, S.; J. Massó and A. Neme (1998):.Maximal Domains of Preferences Preserving Strategy-Proofness for Generalized Median Voter Schemes., Social Choice and Welfare 16, Barberà, S.; J. Massó and A. Neme (2005):.Voting by Committees under Constraints., Journal of Economic Theory 122, Berga D.; G. Bergantiños; J. Massó and A. Neme (2006):.On Exiting After Voting., International Journal of Game Theory 34(1), Gibbard, A. (1973):.Manipulation of Voting Schemes: A General Result., Econometrica 41, Moulin, H. (1980a):.On Strategyproofness and Single-peakedness. Public Choice 35(4), Satterthwaite, M. A. (1973): Ph.D. Dissertation,.The Existence of Strategy Proof Voting Procedures., University of Wisconsin-Madison. Artículos optativos: Barberà, S. (1977b):.Manipulation of Social Decision Functions. Journal of Economic Theory 15(2), Barberà, S. (1980a):.Pivotal Voters: A New Proof of Arrow.s Theorem., Economics Letters 6, Barberà, S. (1983a):.Strategy-Proofness and Pivotal Voters: A Direct Proof of the Gibbard-Satterthwaite Theorem., International Economic Review 24(2), Barberà, S. and M. O. Jackson (1995):.Strategy-Proof Exchange. Econometrica 63, Barberà, S.; J. Massó and S. Serizawa (1998):.Strategy-Proof Voting on Compact Ranges., Games and Economic Behavior 25, Cantalá, D. (2004):.Choosing the level of a public good when agents have an outside option., Social Choice and Welfare 22(3), Gibbard, A. (1973):.Manipulation of Voting Schemes: A General Result., Econometrica 41, Gibbard, A. (1977):.Manipulation of Schemes That Mix Voting with Chance., Econometrica 45(3), Kalai, E. and E. Muller (1977):.Characterization of Domains Admitting Nondictatorial Social Welfare Functions and Nonmanipulable Voting Procedures., Journal of Economic Theory 16(2), Massó, J. and A. Neme (2004):.A Maximal Domain of Preferences for Strategyproof, Eficient, and Simple Rules in the Division Problem. Social Choice and Welfare 23(2), Maus, S.; H. Peters and T. Storcken (2007):.Anonymous Voting and Minimal Manipulability., Journal of Economic Theory 135(1), Moulin, H. (1980b):.Implementing E cient, Anonymous and Neutral Social Choice Functions., Journal of Mathematical Economics 7(3) Satterthwaite, M. A. (1973): Ph.D. Dissertation,.The Existence of Strategy Proof Voting Procedures., University of Wisconsin-Madison.

6 Satterthwaite, M. A. (1975):.Strategy-Proofness and Arrow.s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions., Journal of Economic Theory 10, Satterthwaite, M. A. (2001):.Strategy-proofness and Markets., Social Choice and Welfare 18(1), Schmeidler, D. and H. Sonnenschein (1978):.Two Proofs of the Gibbard- Satterthwaite Theorem on the Possibility of a Strategy-proof Social Choice Function., in Gottinger and Leinfellner (Eds.), Decision Theory and Social Ethics, Reidel Publishing Company: Dordrecht. Bienes Privados: Reglas No-Manipulables Descripción del modelo de bienes privados. Definición de no-manipulabilidad. Teorema de imposibilidad. Conexión con el Teorema de Gibbard-Sattethwaite. Restricción de dominio. Preferencias unimodales. Teorema de existencia de reglas no manipulables, Pareto eficiente, anónimas y simétricas. Caracterización. Diferentes conceptos de simetría. Reglas secuenciales. Caracterizaciones. Reglas a prueba de soborno. Dominios maximales. Reglas no manipulables con participación voluntaria. Modelo de bienes privados con recursos individuales. Reglas no manipulables. Bibliografia: Libros: Progresos enteoría de los Juegos y sus Aplicaciones. Bienes Privados: Reglas no Manipulables. Neme Alejandro Ed. Asociación Argentina de Economía Política. Barberà, S., M. Jackson y A. Neme (1997)..Strategy-proof allotment rules. Games and Economic Behavour 18, Ching, S. (1992)..A simple characterization of the uniform rule.. Economic. Letters 40, Ching, S. y S. Serizawa (1998)..A maximal domain for the existence of strategy-proof rules.. Journal of Economic Theory 78 (1), Massó, J. y A. Neme (2000)..Maximal domain of preferences in the division problem.. En prensa en Games and Economic Behavour. Moulin H. y W. Thomson (1996)..Axiomatic analysis of resource allocation problems.. En Social Choice Re-examined Vol 2. Editado por K. Arrow, A. Sen y K. Suzumura, McMillan. Sprumont, Y. (1991)..The division problem with single-peaked preferences: a characterization of the uniform allocation rule.. Econometrica 59, Artículos optativos: Berga, D. y S. Serizawa (2000)..Maximal domain for strategy-proof rules with one public good.. Journal of Economic Theory 90, Ching, S. (1994)..An alternative characterization of the uniform rule. Social Choice and Welfare 11, Ching, S. y S. Serizawa (1998)..A maximal domain for the existence of strategy-proof rules.. Journal of Economic Theory 78 (1), De Frutos, M.A y J. Massó (1995)..More on the Uniform allocation rule: equity and consistency.. Working Paper Universitat Autònoma de Barcelona.

7 Massó, J. y A. Neme (2001)..A maximal domain of preferences for tops-only rules in the division problem.. Mimeo. Universitat Autònoma de Barcelona y Universidad Nacional de San Luís. Schummer, J. (2000)..Manipulation through bribes.. Journal of Economic Theory 91 (2), Schummer, J. y W. Thomson (1996)..Two derivations of the uniform rule and an application to bankruptcy.. Economic Letters 55 (3), Sen, A. K. (1970)..The impossibility of a Paretian liberal.. Journal of Political Economy 78, Serizawa, S. (1998)..Pairwise strategy-proofness.. Mimeo. Tohoku University. S onmez, T Consistency, Monotonicity, and the Uniform Rule,. Econ. Lett. 46, 229]235. Sprumont, Y. (1995)..Strategy-proof collective choice in economic and political environments.. Canadian Journal of Economics 28, Thomson, W The Replacement Principle in Economies with Single- Peaked Preferences,.J. Econ. Theory, forthcoming. Thomson, W. 1994a...Consistent Solutions to the Problem of Fair Division when Preferences are Single-Peaked,.J. Econ. Theory 63, 219]245. Thomson, W. 1994b...Resource Monotonic Solutions to the Problem of Fair Division when Preferences are Single-Peaked,.Social Choice and Welfare 63, Thomson,W PopulationMonotonic Solutions to the Problem of Fair Division when Preferences are Single-Peaked,.Econ. Theory 5, 229]246. Thomson, W. (1997)..The replacement domination principle in economies with single-peaked preferences.. Journal of Economic Theory 76 (1), Young, P On Dividing an Amount According to Individual Claims or Liabilities,.Math. Oper. Res. 12, 398]414. Zhou, L. (1991a)..Impossibility of strategy-proof mechanisms in economies with pure public goods.. Review of Economic Studies 58, Zhou, L. (1991b)..Inefficiency of strategy-proof allocation mechanisms in pure exchange economies.. Social Choice and Welfare 8,