Learning to make risk neutral choices in a symmetric world

Given their reference point, most people tend to be risk averse over gains and risk seeking over losses. Therefore, they exhibit a dual risk attitude which is reference dependent. This paper studies an adaptive process for choice under risk where, while maintaining reference-dependent preferences in the short run, the agent eventually learns to make risk neutral choices. The agent repeatedly faces a choice problem over monetary lotteries. At each period, she picks a lottery that maximizes the probability of meeting the current target. Right after, she plays the lottery and adjusts her reference point for the next period in the direction of the actually experienced payoff. In the long-run, the reference point settles down to a specific value and the choice behavior converges to maximization of the expected value. However, at each period the agent maintains a dual risk attitude. Therefore, learning to make risk neutral choices takes place without the agent ever learning to be risk neutral.

[1]  J. Blum.  Approximation Methods which Converge with Probability one , 1954 .

[2]  Jeffrey C. Ely,et al.  Evolution of Preferences , 2007 .

[3]  G. Pflug,et al.  Stochastic approximation and optimization of random systems , 1992 .

[4]  H. Levy,et al.  The Efficiency Analysis of Choices Involving Risk1 , 1975 .

[5]  Jack Meyer,et al.  Two Moment Decision Models And Expected Utility Maximization: Some Implications For Applied Research , 1988 .

[6]  H. Levy.  Two-Moment Decision Models and Expected Utility Maximization: Comment , 1989 .

[7]  Marco Li Calzi.  A language for the construction of preferences under uncertainty , 1999 .

[8]  David M. Kreps,et al.  Advances In Economics and Econometrics: Theory And Applications: Seventh World Congress , 1997 .

[9]  D. Kahneman,et al.  Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias , 1991 .

[10]  J. March.  Learning to be risk averse. , 1996 .

[11]  G. Gigerenzer.  On Narrow Norms and Vague Heuristics: A Reply to Kahneman and Tversky (1996) , 1996 .

[12]  R. Marimon.  Learning from learning in economics , 1996 .

[13]  A. Dvoretzky.  On Stochastic Approximation , 1956 .

[14]  T. Sargent.  Bounded rationality in macroeconomics , 1993 .

[15]  Tilman Börgers,et al.  Naive Reinforcement Learning With Endogenous Aspirations , 2000 .

[16]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[17]  Itzhak Gilboa,et al.  Case-Based Optimization , 1996 .

[18]  T. M. Williams,et al.  Optimizing Methods in Statistics , 1981 .

[19]  Arthur J. Robson,et al.  The Evolution of Attitudes to Risk: Lottery Tickets and Relative Wealth , 1996 .

[20]  L. J. Savage,et al.  The Utility Analysis of Choices Involving Risk , 1948, Journal of Political Economy.

[21]  Daniel Kahneman,et al.  Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias , 1991 .

[22]  P. Fishburn,et al.  TWO‐PIECE VON NEUMANN‐MORGENSTERN UTILITY FUNCTIONS* , 1979 .

[23]  Chip Heath,et al.  Psychological Factors and Stock Option Exercise , 1998 .

[24]  Paul H. Rubin,et al.  AN EVOLUTIONARY MODEL OF TASTE FOR RISK , 1979 .

[25]  H. Robbins,et al.  A Convergence Theorem for Non Negative Almost Supermartingales and Some Applications , 1985 .

[26]  H. Markowitz.  The Utility of Wealth , 1952, Journal of Political Economy.

[27]  Erio Castagnoli,et al.  Expected utility without utility , 1996 .

[28]  Robert F. Bordley,et al.  Decision analysis using targets instead of utility functions , 2000 .