Time Lotteries and Stochastic Impatience

Patrick DeJarnette, David Dillenberger, Daniel Gottlieb, Pietro Ortoleva

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We study preferences over lotteries in which both the prize and the payment date are uncertain. In particular, a time lottery is one in which the prize is fixed but the date is random. With Expected Discounted Utility, individuals must be risk seeking over time lotteries (RSTL). In an incentivized experiment, however, we find that almost all subjects violate this property. Our main contributions are theoretical. We first show that within a very broad class of models, which includes many forms of nonexpected utility and time discounting, it is impossible to accommodate even a single violation of RSTL without also violating a property we termed Stochastic Impatience, a risky counterpart of standard Impatience. We then present two positive results. If one wishes to maintain Stochastic Impatience, violations of RSTL can be accommodated by keeping Independence within periods while relaxing it across periods. If, instead, one is willing to forego Stochastic Impatience, violations of RSTL can be accommodated with a simple generalization of Expected Discounted Utility, obtained by imposing only the behavioral postulates of Discounted Utility and Expected Utility.

Original languageEnglish (US)
Pages (from-to)619-656
Number of pages38
Issue number2
StatePublished - Mar 1 2020

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Time lotteries
  • expected discounted utility
  • risk and time preferences
  • stochastic impatience


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