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arXiv · 1505.02847

Minimal conditions for parametric continuity of a utility representation

Patrick H. O'Callaghan
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Abstract

Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on the parameter. The class of parameter spaces where such a representation is guaranteed to exist is also identified. When the parameter is the type or belief of a player, these results have implications for Bayesian and psychological games. When alternatives are discrete, the representation is jointly continuous and an extension of Berge's theorem of the maximum yields a continuous value function. We apply this result to generalise a standard consumer choice problem where parameters are price-wealth vectors. When the parameter space is lexicographically ordered, a novel application to reference-dependent preferences is possible.

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Patrick H. O'Callaghan. 2015-05-12. Minimal conditions for parametric continuity of a utility representation. https://doi.org/10.1016/j.jmateco.2017.07.004

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