Topics to be covered include the theory of subjective probability, ambi$ guity,
dynamic choice ... D. Kreps. Notes on the theory of choice. Westview Press, 1988.
TOPICS IN DECISION THEORY Winter 2010 Asen Kochov
[email protected] Topics to be covered include the theory of subjective probability, ambiguity, dynamic choice, updating and learning, unforeseen contingencies. There is no exam. Grading will be based on homeworks and a written report on a paper of your choice. Required Books D. Kreps. Notes on the theory of choice. Westview Press, 1988 Recommended Books L. Savage. The Foundations of Statistics. Wiley, New York, NY, 1954 Mathematics C. Aliprantis and K. Border. In…nite Dimensional Analysis. SpringerVerlag, 2 edition, 1999 A number of recent papers o¤er perspectives on decision theory and its connection to behavioral economics F. Gul and W. Pesendorfer. The case for mindless economics. In A. Caplin and A. Schotter, editors, The Foundations of Positive and Normative Economics: A Handbook. Oxford University Press, 2008 W. Pesendorfer. Behavioral economics comes of age. Journal of Economic Literature, 44:712–721, 2006 E. Dekel and B. Lipman. How (not) to do decision theory. forthcoming in Annual Review of Economics, 2009
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EXISTENCE OF A UTILITY REPRESENTATION Kreps: Ch.3 G. Debreu. Representation of a preference ordering by a numerical utility function. In R. Thrall, C. Coombs, and R. Davis, editors, Decision Processes. John Wiley & Sons, 1954 G. Herden. On the existence of utility functions. Mathematical Social Sciences, 17:297–313, 1989
THE MIXTURE SPACE THEOREM Kreps: Ch.5 L. Shapley and M. Baucells. Multiperson utility. UCLA Working paper, 1998
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THE SAVAGE MODEL Savage: Chs. 1-6 P. Fishburn. Utility theory for decision making. John Wiley & Sons, 1970 M. Machina and D. Schmeidler. A more robust de…nition of subjective probability. Econometrica, 60(4):745–780, 1992 M. Machina and D. Schmeidler. A more robust de…nition of subjective probability. Econometrica, 60(4):745–780, 1992 Related Mathematics G. Debreu. Topological methods in cardinal utility theory. In Mathematical Methods in the Social Sciences. Stanford University Press, 1960 W. M. Gorman. The structure of utility functions. Review of Economic Studies, 35:367–390, 1968 SUBJECTIVE PROBABILITY ON SMALL DOMAINS D. Ellsberg. Risk, ambiguity and the Savage axioms. Quarterly Journal of Economics, 75:643–669, 1961 L. Epstein and J. Zhang. Subjective probabilities on subjectively unambiguous events. Econometrica, 69:265–306, 2001 I. Kopylov. Subjective probabilities on "small" domains. Journal of Economic Theory, 133:236–265, 2007 THE ANSCOMBE AUMANN MODEL Kreps: Ch. 7 F. Anscombe and R. Aumann. A de…nition of subjective probability. The Annals of Mathematical Statistics, 34:199–205, 1963
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AMBIGUITY I. Gilboa and D. Schmeidler. Maxmin expected utility with non-unique prior. Journal of Mathematical Economics, 18:141–153, 1989 D. Schmeidler. Subjective probability and expected utility without additivity. Econometrica, 57:571–587, 1989 F. Maccheroni, M. Marinacci, and A. Rustichini. Ambiguity aversion, robustness and the variational representation of preferences. Econometrica, 74:1447–1498, 2006 P. Klibano¤, M. Marinacci, and S. Mukerji. A smooth model of decision making under ambiguity. Econometrica, 73:1849–1892, 2005 K. Seo. Ambiguity and second-order beliefs. Econometrica, 77:1575–1605, 2009 M. Siniscalchi and P. Ghirardato. A more robust de…nition of multiple priors. mimeo, 2010 M. Marinacci and L. Montrucchio. Introduction to the mathematics of ambiguity. In I. Gilboa, editor, Uncertainty in economic theory: a collection of essays in honor of David Schmeidler’s 65th birthday. Routledge, 2004 Criticisms L. Epstein. A paradox for the "smooth ambiguity" model of preference. forthcoming in Econometrica M. Machina. Risk, ambiguity and the rank-dependence axioms. American Economic Review, 99:385–392, 2009 T. Bewley. Knightian decision theory part I. Cowles foundation discussion papers, Yale University, 1986 Applications S. Mukerji and J.-M. Tallon. An overview of economic applications of david schmeidler’s models of decision making under uncertainty. In I. Gilboa, editor, Uncertainty in economic theory: a collection of essays in honor of David Schmeidler’s 65th birthday. Routledge, 2004 J. Dow and S. da Costa Werlang. Uncertainty aversion, risk aversion, and the optimal choice of portfolio. Econometrica, 60(1):197–204, 1992 L. Epstein and M. Schneider. Ambiguity and asset markets. forthcoming in Annual Review of Financial Economics, 2010 4
INTERTEMPORAL MODELS - RECURSIVE UTILITY M. Machina. Dynamic consistency and non-expected utility models of choice under uncertainty. Journal of Economic Literature, 27(4):1622–1668, 1989 D. Kreps and E. Porteus. Temporal resolution of uncertainty and dynamic choice theory. Econometrica, 46(1):185–200, 1978 L. Epstein and S. Zin. Substitution, risk aversion, and the temporal behavior of consumption and asset returns: A theoretical framework. Econometrica, 57(4):937–969, 1989 L. Epstein and M. Schneider. Recursive multiple-priors. Journal of Economic Theory, 113:1–31, 2003 L. Epstein and M. L. Breton. Dynamically consistent beliefs must be bayesian. Journal of Economic Theory, 61:1–22, 1993 Criticisms D. Kreps. Anticipated utility and dynamic choice. In D. Jacobs, E. Kalai, and M. Kamien, editors, Frontiers of Research in Economic Theory. Cambridge University Press, 1995 J. Rust. Do people behave according to bellman’s principle of optimality. mimeo, 1992
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LEARNING AND UPDATING Bayesian Models Kreps: Ch. 11 E. Hewitt and L. J. Savage. Symmetric measures on cartesian products. Transactions of the American Mathematical Society, 80:470–501, 1955 P. Diaconis and D. Freedman. On the consistency of bayes estimates. The Annals of Statistics, 14:1–26, 1986 E. Kalai and E. Lehrer. Weak and strong merging of opinions. Discussion paper, 1993 M. O. Jackson, E. Kalai, and R. Smorodinsky. Bayesian representation of stochastic processes under learning: de …netti revisited. Econometrica, 67: 875–893, 1999 Non-Bayesian Models L. Epstein and M. Schneider. Learning under ambiguity. Review of Economic Studies, 74:1275–1303, 2007 L. Epstein and K. Seo. Symmetry of evidence without evidence of symmetry. Theoretical Economics, 5:313–368, 2010c L. Epstein and K. Seo. A de …netti theorem for capacities: ambiguity about correlation. mimeo, 2010b L. Epstein and K. Seo. Ambiguity with repeated experiments. mimeo, 2010a L. Epstein and K. Seo. Symmetry or dynamic consistency? mimeo, 2010d F. Maccheroni and M. Marinacci. A strong law of large numbers for capacities. Annals of probability, 33:1171–1178, 2005
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MODELING UNAWARENESS / UNFORESEEN CONTINGENCIES Epistemic models B. Lipman, E. Dekel, and A. Rustichini. Standard state-space models preclude unawareness. Econometrica, 66:159–173, 1998 A. Heifetz, M. Meier, and B. C. Schipper. Interactive unawareness. Journal of Economic Theory, 130:78–94, 2006 E. Dekel, B. Lipman, and A. Rustichini. Recent developments in modeling unforeseen contingencies. European Economic Review, 42:523–542, 1998 Choice-theoretic models D. Kreps. A representation theorem for preference for ‡exibility. Econometrica, 47:565–576, 1979 D. Kreps. Static choice in the presence of unforeseen contingencies. In P. Dasgupta, D. Gale, O. Hart, and E. Maskin, editors, Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn, pages 259–281. MIT Press, Cambridge, MA, 1992 E. Dekel, B. Lipman, and A. Rustichini. Representing preferences with a unique subjective state space. Econometrica, 69:891–934, 2001 L. Epstein, M. Marinacci, and K. Seo. Coarse contingencies and ambiguity. Theoretical Economics, 2(4):355–394, 2007 A. Kochov. A model of limited foresight. mimeo, 2010
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