STOCHASTIC CHOICE AND REVEALED PERTURBED UTILITY BY DREW FUDENBERG,

Perturbed utility functions—the sum of expected utility and a nonlinear perturbation function—provide a simple and tractable way to model various sorts of stochastic choice. We provide two easily understood conditions each of which characterizes this representation: One condition generalizes the acyclicity condition used in revealed preference theory, and the other generalizes Luce’s IIA condition. We relate the discrimination or selectivity of choice rules to properties of their associated perturbations, both across different agents and across decision problems. We also show that these representations correspond to a form of ambiguity-averse preferences for an agent who is uncertain about her true utility.

[1]  Pietro Ortoleva,et al.  Stochastic Choice and Preferences for Randomization , 2015, Journal of Political Economy.

[2]  Mira Frick.  Monotone threshold representations , 2016 .

[3]  William H. Sandholm,et al.  Learning in Games via Reinforcement and Regularization , 2014, Math. Oper. Res..

[4]  Drew Fudenberg,et al.  Stochastic Choice and Revealed Perturbed Utility , 2015 .

[5]  Kota Saito,et al.  Savage in the Market , 2015 .

[6]  Kota Saito,et al.  Preferences for Flexibility and Randomization under Uncertainty , 2015 .

[7]  D. Fudenberg,et al.  Dynamic Logit with Choice Aversion , 2015 .

[8]  A. Palma,et al.  Demand systems for market shares , 2015 .

[9]  Yuichi Noguchi.  Bayesian Learning, Smooth Approximate Optimal Behavior, and Convergence to ε-Nash Equilibrium , 2015 .

[10]  Faruk Gul,et al.  Random Choice as Behavioral Optimization , 2014 .

[11]  Ryota Iijima.  Deterministic Equilibrium Selection Under Payoff-Perturbed Dynamics , 2014 .

[12]  Philip J. Reny,et al.  A Characterization of Rationalizable Consumer Behavior , 2014 .

[13]  Georg Weizsacker,et al.  Flipping a Coin: Theory and Evidence , 2012, SSRN Electronic Journal.

[14]  H. Peyton Young,et al.  Fast convergence in evolutionary equilibrium selection , 2013, Games Econ. Behav..

[15]  Felix Kubler,et al.  Asset Demand Based Tests of Expected Utility Maximization , 2013 .

[16]  J. Swait,et al.  Probabilistic Choice (Models) as a Result of Balancing Multiple Goals , 2013 .

[17]  Paola Manzini,et al.  Stochastic Choice and Consideration Sets , 2012, SSRN Electronic Journal.

[18]  A. Chernev.  Product Assortment and Consumer Choice: An Interdisciplinary Review , 2012 .

[19]  Drew Fudenberg,et al.  Heterogeneous beliefs and local information in stochastic fictitious play , 2011, Games Econ. Behav..

[20]  Per Olov Lindberg,et al.  Extreme values, invariance and choice probabilities , 2011 .

[21]  D. Blackwell.  Controlled Random Walks , 2010 .

[22]  Massimo Marinacci,et al.  Coarse contingencies and ambiguity , 2007 .

[23]  Mark Voorneveld,et al.  Better May be Worse: Some Monotonicity Results and Paradoxes in Discrete Choice Under Uncertainty , 2006 .

[24]  Mark Voorneveld.  Probabilistic Choice in Games: Properties of Rosenthal’s t-Solutions , 2006, Int. J. Game Theory.

[25]  J. M. Bilbao,et al.  Contributions to the Theory of Games , 2005 .

[26]  Faruk Gul,et al.  Random Expected Utility , 2005 .

[27]  A. Rustichini,et al.  Ambiguity Aversion, Robustness, and the Variational Representation of Preferences , 2006 .

[28]  William H. Sandholm,et al.  ON THE GLOBAL CONVERGENCE OF STOCHASTIC FICTITIOUS PLAY , 2002 .

[29]  Lars-Göran Mattsson,et al.  Probabilistic choice and procedurally bounded rationality , 2002, Games Econ. Behav..

[30]  Eric van Damme,et al.  Evolution in Games with Endogenous Mistake Probabilities , 2002, J. Econ. Theory.

[31]  M. Lepper,et al.  The Construction of Preference: When Choice Is Demotivating: Can One Desire Too Much of a Good Thing? , 2006 .

[32]  M. Hirsch,et al.  Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games , 1999 .

[33]  R. McKelvey,et al.  Quantal Response Equilibria for Normal Form Games , 1995 .

[34]  D. Fudenberg,et al.  Consistency and Cautious Fictitious Play , 1995 .

[35]  C. Leake.  Discrete Choice Theory of Product Differentiation , 1995 .

[36]  L. Thurstone.  A law of comparative judgment. , 1994 .

[37]  A game-theoretic approach to the binary stochastic choice problem , 1992 .

[38]  Peter C. Fishburn,et al.  Induced binary probabilities and the linear ordering polytope: a status report , 1992 .

[39]  Itzhak Gilboa,et al.  A necessary but insufficient condition for the stochastic binary choice problem , 1990 .

[40]  Stephen A. Clark.  A concept of stochastic transitivity for the random utility model , 1990 .

[41]  Robert W. Rosenthal,et al.  A bounded-rationality approach to the study of noncooperative games , 1989 .

[42]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[43]  Mark J. Machina,et al.  Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries , 1985 .

[44]  박상용.  [경제학] 현시선호이론(Revealed Preference Theory) , 1980 .

[45]  David M. Kreps.  A REPRESENTATION THEOREM FOR "PREFERENCE FOR FLEXIBILITY" , 1979 .

[46]  Jean-Claude Falmagne,et al.  A representation theorem for finite random scale systems , 1978 .

[47]  J. Harsanyi.  Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points , 1973 .

[48]  J. Harsanyi.  Oddness of the number of equilibrium points: A new proof , 1973 .

[49]  A. Tversky.  Choice by elimination , 1972 .

[50]  D. McFadden.  Conditional logit analysis of qualitative choice behavior , 1972 .

[51]  S. Afriat.  THE CONSTRUCTION OF UTILITY FUNCTIONS FROM EXPENDITURE DATA , 1967 .

[52]  D. Scott.  Measurement structures and linear inequalities , 1964 .

[53]  C. Kraft,et al.  Intuitive Probability on Finite Sets , 1959 .

[54]  J. Marschak.  Binary Choice Constraints on Random Utility Indicators , 1959 .

[55]  G. Debreu,et al.  Stochastic Choice and Cardinal Utility , 1958 .

[56]  J. Marschak,et al.  Experimental Tests of Stochastic Decision Theory , 1957 .

[57]  R. Luce.  Semiorders and a Theory of Utility Discrimination , 1956 .

[58]  H. Houthakker.  Revealed Preference and the Utility Function , 1950 .