A Deeper Look at Hyperbolic Discounting

We conduct an experiment to investigate the degree to which deviations from exponential discounting can be accounted for by the hypothesis of hyperbolic discounting. Subjects are asked to choose between an earlier or later payoff in a series of 40 choice questions. Each question consists of a pair of monetary amounts determined by com- pounding a given base amount at a constant rate per period. Two bases (8 and 20 dollars), three compounding rates (low, medium and high) and three delays (2, 4, and 6 weeks) are each used. There are also 2 initial periods (Today and 2 weeks) and there are two separate questionnaires, one with lower “realistic” compounding rates and the other with higher compounding rates, typical of those used in previous studies. We ana- lyze the detailed patterns of choice in 6 groups of 6 related questions each (in which the base and rate is fixed but the initial period and delay varies), documenting the frequency of patterns consistent with exponen- tial discounting and with hyperbolic discounting. We find that exponen- tial discounting is the clear modal choice pattern in virtually all cases. Hyperbolic discounting is never the modal pattern (except in the sense that constant discounting is a special case of hyperbolic discounting). We also estimate a linear probability model that takes account of individual heterogeneity. The estimates show substantial increases in the probabil- ity of choosing the later option when the compounding rate increases, as one would expect. There are small, sometimes significant, increases in this probability when the delay is increased or the initial period is in the future. Such behavior is consistent with hyperbolic discounting, but can account for only a small proportion of choices. Overall, deviations from exponential discounting appear to be due to error, or to other effects not accounted for by hyperbolic discounting. Principal among these is an increase in later choices when the base is larger.

Learning in Tournaments with Inter-Generational Advice

We study learning in a simulated tournament using an inter-generational framework. Here a group of subjects are recruited into the lab and play the stage game for 10 rounds. After his participation is over, each player is replaced by another player, his laboratory descendant, who then plays the game for another 10 rounds as a member of a fresh group of subjects. A particular player in generation t+1 can (1) see the history of choices by his generation t predecessor and (2) receive advice from that predecessor via free-form messages that generation t players leave for their generation t+1 successors. We find that the presence of advice makes a difference in that the experimental groups who get advice perform better – their decisions are closer to the Nash equilibrium – compared to a control group of subjects that plays the game with no recourse to such advice.Advice

Bargaining and the Joint-Cost Theory of Strikes: An Experimental Study.

This article reports on an experiment that is designed to test predictions about the frequency of disagreement (strikes) in games with complete information. An empirical test of the "joint-cost" theory, which relates strike activity to the marginal cost of striking, is based on a set of "shrinking pie" games in which subjects bargain in consecutive periods over how to divide a sum of money. Strike activity is a frequent occurrence in these games and, moreover, does not disappear over time. The joint-cost theory receive some support, indicating that further tests may be useful. Copyright 1990 by University of Chicago Press.

A Service of zbw Leibniz-Informationszentrum Wirtschaft Leibniz Information Centre for Economics Consistency and Aggregation in Individual Choice Under Uncertainty

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A DEEPER LOOK AT HYPERBOLIC DISCOUNTING

ABSTRACT. We conduct an experiment to investigate the degree to which deviations from exponential discounting can be accounted for by the hypothesis of hyperbolic discounting. Subjects are asked to choose between an earlier or later payoff in a series of 40 choice questions. Each question consists of a pair of monetary amounts determined by compounding a given base amount at a constant rate per period. Two bases (8 and 20 dollars), three compounding rates (low, medium and high) and three delays (2, 4, and 6 weeks) are each used. There are also 2 initial periods (Today and 2 weeks) and there are two separate questionnaires, one with lower “realistic ” compounding rates and the other with higher compounding rates, typical of those used in previous studies. We analyze the detailed patterns of choice in 6 groups of 6 related questions each (in which the base and rate is fixed but the initial period and delay varies), documenting the frequency of patterns consistent with exponential discounting and with hyperbolic discounting. We find that exponentia