Jekyll and Hyde

Abstract

Jekyll and Hyde were in fact two people inside the same person – an obviously dynamically-inconsistent person. In the book and in the movie, the dynamic inconsistency was resolved in a rather dramatic way. We investigate its resolution in the laboratory.

Notes

¹Alternatively, it can be considered an infinite horizon problem with discount factor ρ.

²A proof can be found in a Technical Appendix, available upon request.

³Alternatively, uses a different discount rate in odd periods from that in the even periods.

⁴We do not enquire into how this resolute behaviour may be implemented.

⁵A proof can be found in a Technical Appendix, available on request.

⁶This is so even if one uses deception: one tells the subject in the first period that his or her objective function is one function and then in the second period one tells the subject ‘now you have a different function’, as it is crucial that a dynamically inconsistent person has two functions, and, in the case of sophisticated and resolute subjects, that they know that this is so. Nor can one tell the subjects that, in odd periods the continuing probability is ρ₁ while in even periods it is ρ₂ because by so doing one induces on them the preference function u(c₁) + ρ1 u(c₂) + ρ₁ ρ₂ u(c₃) + ρ_1² ρ₂ u(c₄) + ρ_1² ρ_2² u(c₅) + · · · which is not the preference function of a dynamically inconsistent person.

⁷Obviously the continuing probabilities have to take into account the earthquake.

⁸The latter determined by the computer.

⁹And, indeed, whether they are told whether the computer is playing naïvely, resolutely or sophisticatedly – which may, in itself, change the behaviour of the human subjects.