Preference for flexibility and dynamic consistency with incomplete preferences
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Preference for flexibility and dynamic consistency with incomplete preferences Fernanda Senra de Moura1 • Gil Riella2 Accepted: 7 September 2020 Ó Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We generalize a previous result about dynamically consistent menu preferences to the case where preferences are not necessarily complete. We show that, as it is the case when preferences are complete, a subjective state space version of dynamic consistency is linked to a comparative theory of preference for flexibility. In words, an objective signal is interpreted as an event in the agent’s subjective state space and the agent acts in a dynamically consistent way after that if and only if we can attribute all the differences between the agent’s preferences before and after the signal to the fact that the agent values flexibility more before the signal than after. Keywords Flexibility consistency Bayesian update Subjective state space Multiple priors
1 Introduction Consider an individual who usually makes reservations for diner in the morning. For simplicity, suppose that the only thing this person cares in a restaurant are the different meals it offers. In this case, we can model each restaurant simply as a set, or menu, of meals. Dekel et al. (2001)—henceforth DLR—and Dekel et al. (2007) characterize when the decisions of such an individual can be represented by a unique subjective state space and a state-dependent utility function. The idea is that the individual is uncertain about what her tastes will be when she finally arrives at the restaurant in the evening. Given that, the individual maximizes the expected & Gil Riella [email protected] Fernanda Senra de Moura [email protected] 1
Department of Economics, University College London, London, UK
2
Escola de Polı´ticas Pu´blicas e Governo, Getulio Vargas Foundation, Brası´lia, Brazil
123
F. S. de Moura, G. Riella
utility she can derive from each available restaurant, given her state-dependent utility function and her prior over her subjective state space.1 Now suppose that in some days the individual makes her choice only after lunch. It is conceivable that what she eats at lunch affects the likelihood of having one taste or another at the time she arrives at the restaurant in the evening. What she eats at lunch is observable, so we can treat it as an objective signal. However, since the state space is subjective, we have no direct means to understand how the individual interprets this signal in terms of her subjective state space. The main result in Riella (2013) characterizes when the individual interprets the signal as a measurable event in her subjective state space and, given that she has learned this event, acts in a dynamically consistent way. The analysis in Riella (2013) is performed under the assumption that the individual’s preferences admit a finite Positive Additive Expected Utility representation and, consequently, are complete. Although completeness is a prope
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