Elementy modelowania ekonomicznego opartego na teorii uczenia się w grach populacyjnych

• Autorzy: Michał Ramsza
• Języki publikacji: PL

Abstrakty

Celem pracy jest przedstawienie metody modelowania procesów społecznych i ekonomicznych opartej na teorii uczenia się w grach populacyjnych. Omówiono podstawy teoretyczne zastosowanej metody: pojęcie gry w postaci normalnej i ekstensywnej, pojęcie równowagi Nasha i równowagi doskonałej, ogólny model ewolucji, klasę procedur porównań, klasyczną procedurę gry fikcyjnej, modele powstałe w wyniku zastosowania procedur porównań, zachowania populacji graczy używających procedur gry fikcyjnej oraz narzędzia matematyczne najbardziej istotne z punktu widzenia modelowania procesów społeczno-ekonomicznych. Zaprezentowano następnie zastosowanie omówionych metod w modelowaniu procesów społeczno-ekonomicznych.

Słowa kluczowe

PL

Modelowanie ekonometryczne; Teoria gier; Uczenie się; Modelowanie procesów gospodarczych; Przegląd literatury

EN

Econometric modeling; Game theory; Studying; Economic process modeling; Literature review

• Czasopismo: Monografie i Opracowania / Szkoła Główna Handlowa
• Rocznik: 2010
• Numer: nr 576
• Strony: 140

Twórcy

autor

Michał Ramsza

Bibliografia

• Aliprantis CD., Border K.C., Infinite dimensional analysis, Springer, 2006.
• Arnold W.I., Równania różniczkowe zwyczajne, Państwowe Wydawnictwo Naukowe, 1975.
• Aubin J.P., Optima and equilibria, Springer, 1991.
• Aubin J. P., Frankowska H., Set-Valued Analysis, Birkhauser, 1990.
• Aumann R., Subjectivity and correlation in randomized strategies, "Journal of Mathematical Economics", 1974, vol. 1, s. 67-96.
• Bar-Hillel M., Wagenaar W.A., The perception of randomness, "Advances in Applied Mathematics", 1991, vol. 12, s. 428-454.
• Becker G.S., A theory of marriage: part I, "Journal of Political Economy", 1973, vol. 81, s. 813-846.
• Becker G.S., A theory of marriage: part II, "Journal of Political Economy",1974, vol. 82, s. S11-S26.
• Benaim M., Weibull J.W., Deterministic approximation of stochastic evolution in games, "Econometrica", 2003, vol. 71, s. 873-903.
• Berger U., Fictitious play in 2 x n games, "Journal of Economic Theory", 2005, vol. 120, s. 139-154.
• Berger U., Two more classes of games with the continuous-time fictitious play property, "Games and Economic Behavior", 2007, vol. 60, s. 247-261.
• Bergstrom T.C., The algebra of assortative encounters and the evolution of cooperation, "International Game Theory Review", 2003, vol. 5, s. 1-18.
• Bertrand J., Theorie mathematique de la richesse sociale, "Journal des Savants", 1883, vol. 67, s. 499-508.
• Binmore K., Samuelson L., Muddling through: Noisy equilibrium selection, "Journal of Economic Theory", 1997, vol. 74, s. 235-265.
• Binmore K., Samuelson L., Vaughan R., Musical chairs: Modelling noisy evolution, "Games and Economic Behavior", 1995, vol. 11, s. 1-35.
• Binmore K., Shaked A., Sutton J., Testing noncooperative bargaining theory: a preliminary study, "The American Economic Review", 1985, vol.75, s. 1178-1180.
• Bjornerstedt J., Weibull J.W., Nash equilibrium and evolution by imitation, w: Arrow K.J., Colombatto E., Perlman M., Schmidt C. (red.), The rational foundations of economic behavior, St. Martin's Press, 1996.
• Bolton G.E., A comparative model of bargaining: Theory and evidence, "American Economic Review", 1991, vol. 81, s. 1096-1136.
• Bolton G.E., Zwick R., Anonymity versus punishment in ultimatum bargaining, "Games and Economic Behavior", 1995, vol. 10, s. 95-121.
• Borgers T., Sarin R., Learning through reinforcement and replicator dynamics, "Journal of Economic Theory", 1997, vol. 77, s. 1-14.
• Boylan R.T., Continuous approximation of dynamica systems with randomly matched individuals, "Journal of Economic Theory", 1995, vol. 66, s. 615-625.
• Boylan R.T., Laws of large numbers for dynamical systems with randomly matched individuals, "Journal of Economic Theory", 1992, vol. 57, s. 473-506.
• Brown G., Iterative solutions of games by fictitous play, w: Koopmans T.C (red.), Activity Analysis of Production and Allocation, Wiley, 1951.
• Cannning D., Average behavior in learning models, "Journal of Economic Theory", 1992, vol. 57, s. 442-472.
• Conley C.C., Isolated invariant sets and the Morse index, "Regional Conference Series in Mathematics", 1978, vol. 38, American Mathematical Society.
• Corradi V., Sarin R., Continuous approximations of stochastic evolutionary game dynamics, "Journal of Economic Theory", 2000, vol. 94, s. 163-191.
• Cournot A., Recherches sur les Principes Mathematiques de la Theorie des Richesses, 1838, wersja angielska: Bacon N. (red.), Researches into the Mathematical Principles of the Theory of Wealth, Macmillan, 1897.
• Debreu D., A social equilibrium existence theorem, "Proceedings of the National Academy of Science", 1952, vol. 38, s. 886-893.
• Durlauf S.N., Blume L.E., The new Palgrave dictionary of economics, Pal grave Macmillan, 2008.
• Edgeworth F.Y., Mathematical Psychics: An essay on the application of mathematics to the moral sciences, C. Kegan & Co., 1881.
• Fan K., Fixed point and minimax theorems in locally convex topological linear spaces, "Proceedings of the National Academy of Science", 1952. vol. 38, s. 121-126.
• Fehr E., Schmidt K., A theory of fairness, competition and cooperation, "Quarterly Journal of Economics", 1999, vol. 114, s. 817-868.
• Fehr E., Schmidt K., Theories of fairness and reciprocity: Evidence and economic applications, w: Dewatripont S., Hansen L. (red.), Advances in Economic theory: Eight World Congress, Cambdridge University Press, 2003.
• Forsythe R., Horowitz J.L., Savin N.E., Sefton M., Fairness in simple bargaining experiments, "Games and Economic Behavior", 1994, vol. 6, s. 347-369.
• Foster D.P., Peyton Young H., Regret testing: learning to play Nash equilibrium without knowing you have an opponent, "Theoretical Economics", 2006, vol. l, s. 341-367.
• Fudenberg D., Kreps D.M., Learning mixed equilibria, "Games and Economic Behavior", 1993, vol. 5, s. 320-367.
• Fudenberg D., Tirole J., Game theory, The MIT Press, 1991.
• Gale J., Binmore K.G., Samuelson L., Learning to be imperfect: the ultimatum game, "Games and Economic Behavior", 1995, vol. 8, s. 56-90.
• Gilboa I., Matsui A., Social stability and equilibrium, "Econometrica", 1991, vol. 59, s. 859-867.
• Glicksberg I.L., A further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points, "Proceedings of the National Academy of Science", 1952, vol. 38, s. 170-174.
• Guth W., Schmittberger R., Schwarze B., An experimental analysis of ultimatum bargaining, "Journal of Economic Behavior and Organization", 1982, vol. 3, s. 367-388.
• Guth W., Tietze R., Ultimatum bargaining behavior: A survey and comparison of experimental results, "Journal of Economic Psychology", 1990, vol. 11, s. 417-449.
• Guth W., Yaari M., An evolutionary approach to explaining reciprocal behavior in a simple strategic game, Working paper, 1990.
• Guth W., Yaari M., Incomplete information about reciprocal incentives: An evolutionary approach to explaining cooperative behavior, Working paper, 1990.
• Hahn S., The convergence of fictitious play in 3 x 3 games with strategic complementarities, "Economics Letters", 1999, vol. 64, s. 57-60.
• Harberger A.C., Efficiency effects of taxes on income from capital, w: Krzyżaniak M. (red.), Effects of corporation income tax, Wayne State University Press, 1966.
• Hofbauer J., Imitation dynamics for games, Working paper, 1995.
• Hofbauer J., Stability for the best response dynamics, Working paper, 1995.
• Hofbauer J., Sigmund K., Adaptive dynamics and evolutionary stability, "Applied Mathematics Letters", 1990, vol. 3, s. 75-79.
• Hopkins E., Learning, matching, and aggregation, "Games and Economic Behavior", 1999, vol. 26, s. 79-110.
• Huck S., Oechssler J., The indirect evolutionary approach to explaining fair allocations, "Games and Economic Behavior", 1999, vol. 28, s. 13-24.
• Jordan J.S., Three problems in learning mixed-strategy Nash equilibria, "Games and Economic Behavior", 1993, vol. 5, s. 368-386.
• Kahneman D., Knetsch J.L., Thaler R.H., Fairness and the assumptions of Economics, "The Journal of Business", 1986, vol. 59, s. S285-S300.
• Kandori M., Mailath G.J., Rob R., Learning, mutation and long run equilibria in games, "Econometrica", 1993, vol. 61, s. 29-56.
• Kohlberg E., Mertens J.-F., On the strategic stability of equilibria, "Econometrica", 1986, vol. 54, s. 1003-1037.
• Krishna V., Learning in games with strategic complementarities, Working paper, 1992.
• Kuhn H., Extensive games and the problem of information, "Annals of Mathematics Studies", 1953, vol. 28, s.193-216.
• Markus L., Yamabe H., Global stability criteria for differential systems, "Osaka Mathematical Journal", 1960, vol. 12, s. 305-317.
• Mas-Collel A., The theory of general economic equilibrium: a differentiable approach, Cambridge University Press, 1985.
• Mas-Colell A., Whinston M.D., Green J.R., Microeconomic Theory, Oxford University Press, 1995.
• Matsui A., Best response dynamics and socially stable strategies, "Journal of Economic Theory", 1991, vol. 57, s. 343-362.
• Maynard Smith J., Evolution and the theory of games, Cambridge University Press, 1982.
• Maynard Smith J., Price G.R., The logic of animal conflict, "Nature", 1973, vol. 246, s. 15-18.
• McFadden D., Econometric models of probabilistic choice, w: Manski C.E, McFadden D. (red.), Structural analysis of discrete data with econometric applications, MIT Press, 1981.
• Miękisz J., Ramsza M., Sampling through the ultimatum game, Working paper, 2009.
• Miekisz J., Ramsza M, Symmetric ultimatum game, Working paper, 2009.
• Milgorm R, Roberts J., Adaptive and sophisticated learning in normal form games, "Games and Economic Behavior", 1991, vol. 3, s. 82-100.
• Miyasawa K., On the convergence of learning processes in a 2 x2 non-zero game, Working paper, 1961.
• Monderer D., Shapley L., Fictitious play property for games with identical interests, "Journal of Economic Theory", 1996, vol. 68, s. 258-265.
• Nash J., Equilibrium points in n-person games, "Proceedings of the National Academy of Sciences", 1950, vol. 36, s. 48-49.
• Nash J., Non-cooperative games, PhD, Princeton University, 1950.
• Nash J., Non-cooperative games, "The Annals of Mathematics", 1951, vol. 54, s. 286-295.
• Ochs J., Roth A.E., An experimental study of sequential bargaining, "American Economic Review", 1989, vol. 79, s. 355-384.
• O'Neill B., Semi-riemannian geometry, Academic Press, 1983.
• Osborne M., Rubinstein A., Games with procedurally rational players, "American Economic Review", 1998, vol. 88, s. 834-847.
• Peyton Young H., The evolution of conventions, "Econometrica", 1993, vol. 61, s. 57-84.
• Peyton Young H., An evolutionary model of bargaining, "Journal of Economic Theory", 2003, vol. 59, s. 145-168.
• Pietrzak B., Polański Z., Woźniak B. (red.), System finansowy w Polsce, Wydawnictwo Naukowe PWN, 2006.
• Prasnikar V., Roth A.E., Considerations of fairness and strategy: Experimental data from sequential games, "Quarterly Journal of Economics", 1992, vol. 107, s. 865-888.
• Ramsza M., Krzywa Laffera - podejście ewolucyjne, "Roczniki Kolegium Analiz Ekonomicznych SGH", 2002, vol. 10, s. 91-98.
• Ramsza M., Extending sampling dynamics, badania statutowe SGH, 2009.
• Ramsza M., Innovation and bargaining, Working paper, 2009.
• Ramsza M., Taxing boundedly rational entrepreneurs, badania statutowe SGH, 2010.
• Ramsza M., Seymour R.M., Fictitious play in an evolutionary environment., "Games and Economic Behavior", 2010, vol. 68, s. 303-324.
• Richeson D., Wiseman J., A fixed point theorem for bounded dynamical systems, "Illinois Journal of Mathematics", 2002, vol. 46, s. 491-495.
• Richeson D., Wiseman J., Addendum to "A fixed point theorem for bounded dynamical systems", "Illinois Journal of Mathematics", 2004, vol. 48, s. 1079-1080.
• Robinson J., An iterative method of solving a game, "The Annals of Mathematics", 1951, vol. 54, s. 296-301.
• Roth A.E., Bargaining experiments, w: red. J. Kagel, A.E. Roth, Handbook of Experimental Economics, Princeton University Press, 1995.
• Roth A.E., Erev I., Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term, "Games and Economic Behavior", 1995, vol. 8, s. 164-212.
• Rubistein A., Perfect equilibrium in a bargaining model, "Econometrica", 1982, vol. 50, s. 97-109.
• Sachs J.D., Larrain F.B., Macroeconomics in the global economy, Harvester Wheatsheaf, 1993.
• Salop S., Monopolistic competition with outside goods, "Bell Journal of Economics", 1979, vol. 10, s. 141-156.
• Sandholm W.H., Markov evolution with inexact information, Working paper, 1999.
• Sandholm W.H., Pairwise comparison dynamics and evolutionary foundations for Nash equilibrium, "Games", 2010, vol. 1, s. 3-17.
• Schumpeter J.A., The crisis of the tax state, w: International Economic Papers, Macmillan, 1954.
• Schumpeter J.A., The theory of economic development, Harvard University Press, 1911, wydanie polskie: Teoria rozwoju gospodarczego, Państwowe Wydawnictwo Naukowe, 1960.
• Shapley L.S., Some topics in two-person games, w: Drescher M., Shapley L.S., Tucker W. (red.), Advances in Game Theory, Princeton University Press, 1964.
• Shirata Y., The evolution of fairness under an assortative matching rule in the ultimatum game, Working paper, 2008.
• Spiegler R., Competition over agents with boundedly rational expectations, "Theoretical Economics", 2006, vol. 1, s. 207-231.
• Sydseater K., Hammond P., Seierstad A., Strom A., Further Mathematics for Economic Analysis, Prentice Hall, 2008.
• Taylor C, Nowak M.A., Evolutionary game dynamics with non-uniform interaction rates, "Theoretical Population Biology", 2006, vol. 69, s. 243-252.
• Taylor P.D., Jonker L.B., Evolutionary stable strategies and games dynamics, "Mathematical Bioscience", 1978, vol. 40, s. 145-156.
• Varian H.R., Microeconomic Analysis, W. W. Norton & Co., 1992.
• Weg E., Rapaport A., Felsenthal D.S., Two-person bargaining behavior in fixed discounting factors games with infinite horizon, "Games and Economic Behavior", 1990, vol. 2, s. 76-95.
• Weibull J.W., Evolutionary Game Theory, The MIT Press, 1997.