754 research outputs found
Evaluating a model of global psychophysical judgments for brightness: II. Behavioral properties linking summations and productions
Steingrimsson (Attention, Perception, & Psychophysics, 71, 1916–1930, 2009) outlined Luce’s (Psychological Review, 109, 520–532 2002, 111, 446–454 2004) proposed psychophysical theory and tested, for brightness, behavioral properties that, separately, gave rise to two psychophysical functions, Ψ⊕ and \documentclass[12pt]{minimal}
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\begin{document}\end{document}. The function Ψ⊕ maps pairs of physical intensities onto positive real numbers and represents subjective summation, and the function \documentclass[12pt]{minimal}
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\begin{document}\end{document} represents a form of ratio production. This article, the second in a series expected to consist of three articles, tests the properties linking summation and production such that it forces \documentclass[12pt]{minimal}
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\begin{document}\end{document}. The properties tested are a form of distributivity and, in three experiments, were subjected to an empirical evaluation. Considerable support is provided for the existence of a single function Ψ for both summation and ratio production. The scope of this series of articles is to establish the theory as a descriptive model of binocular brightness perception
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On the origin of utility, weighting, and discounting functions: How they get their shapes and how to change their shapes
We present a theoretical account of the origin of the shapes of utility, probability weighting, and temporal discounting functions. In an experimental test of the theory, we systematically change the shape of revealed utility, weighting, and discounting functions by manipulating the distribution of monies, probabilities, and delays in the choices used to elicit them. The data demonstrate that there is no stable mapping between attribute values and their subjective equivalents. Expected and discounted utility theories, and also their descendants such as prospect theory and hyperbolic discounting theory, simply assert stable mappings to describe choice data and offer no account of the instability we find. We explain where the shape of the mapping comes from and, in describing the mechanism by which people choose, explain why the shape depends on the distribution of gains, losses, risks, and delays in the environment
Nash bargaining in ordinal environments
We analyze the implications of Nash’s (1950) axioms in ordinal bargaining environments; there, the scale invariance axiom needs to be strenghtened to take into account all order-preserving transformations of the agents’ utilities. This axiom, called ordinal invariance, is a very demanding one. For two-agents, it is violated by every strongly individually rational bargaining rule. In general, no ordinally invariant bargaining rule satisfies the other three axioms of Nash. Parallel to Roth (1977), we introduce a weaker independence of irrelevant alternatives axiom that we argue is better suited for ordinally invariant bargaining rules. We show that the three-agent Shapley-Shubik bargaining rule uniquely satisfies ordinal invariance, Pareto optimality, symmetry, and this weaker independence of irrelevant alternatives axiom. We also analyze the implications of other independence axioms
An equivalent formulation for the Shapley value
The final authenticated version is available online at: https://doi.org/10.1007/978-3-662-58464-4_1.An equivalent explicit formula for the Shapley value is provided, its equivalence with the classical one is proven by double induction. The importance of this new formula, in contrast to the classical one, is its capability of being extended to more general classes of games, in particular to j-cooperative games or multichoice games, in which players choose among different levels of participation in the game.Peer ReviewedPostprint (published version
Clustering and the hyperbolic geometry of complex networks
Clustering is a fundamental property of complex networks and it is the
mathematical expression of a ubiquitous phenomenon that arises in various types
of self-organized networks such as biological networks, computer networks or
social networks. In this paper, we consider what is called the global
clustering coefficient of random graphs on the hyperbolic plane. This model of
random graphs was proposed recently by Krioukov et al. as a mathematical model
of complex networks, under the fundamental assumption that hyperbolic geometry
underlies the structure of these networks. We give a rigorous analysis of
clustering and characterize the global clustering coefficient in terms of the
parameters of the model. We show how the global clustering coefficient can be
tuned by these parameters and we give an explicit formula for this function.Comment: 51 pages, 1 figur
Assortment optimisation under a general discrete choice model: A tight analysis of revenue-ordered assortments
The assortment problem in revenue management is the problem of deciding which
subset of products to offer to consumers in order to maximise revenue. A simple
and natural strategy is to select the best assortment out of all those that are
constructed by fixing a threshold revenue and then choosing all products
with revenue at least . This is known as the revenue-ordered assortments
strategy. In this paper we study the approximation guarantees provided by
revenue-ordered assortments when customers are rational in the following sense:
the probability of selecting a specific product from the set being offered
cannot increase if the set is enlarged. This rationality assumption, known as
regularity, is satisfied by almost all discrete choice models considered in the
revenue management and choice theory literature, and in particular by random
utility models. The bounds we obtain are tight and improve on recent results in
that direction, such as for the Mixed Multinomial Logit model by
Rusmevichientong et al. (2014). An appealing feature of our analysis is its
simplicity, as it relies only on the regularity condition.
We also draw a connection between assortment optimisation and two pricing
problems called unit demand envy-free pricing and Stackelberg minimum spanning
tree: These problems can be restated as assortment problems under discrete
choice models satisfying the regularity condition, and moreover revenue-ordered
assortments correspond then to the well-studied uniform pricing heuristic. When
specialised to that setting, the general bounds we establish for
revenue-ordered assortments match and unify the best known results on uniform
pricing.Comment: Minor changes following referees' comment
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