Year: 2015
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: O'Callaghan, Patrick, O'Callaghan, Patrick
Language: English
Subfield: General Decision Sciences
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2203723949