A Minority Game with Bounded Recall


Mathematics of Operations Research

novembre 2007, vol. 32, n°4, pp.873-889

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Mots clés : Folk theorem, de Bruijn sequence, Imperfect monitoring, Uniform equilibrium, Public equilibrium, Private equilibrium

This paper studies a repeated minority game with public signals, symmetric bounded recall, and pure strategies. We investigate both public and private equilibria of the game with fixed recall size. We first show how public equilibria in such a repeated game can be represented as colored subgraphs of a de Bruijn graph. Then we prove that the set of public equilibrium payoffs with bounded recall converges to the set of uniform equilibrium payoffs as the size of the recall increases. We also show that private equilibria behave badly: A private equilibrium payoff with bounded recall need not be a uniform equilibrium payoff

Eliciting Gul's theory of disappointment aversion by the tradeoff method

M. ABDELLAOUI, H. Bleichrodt

Journal of Economic Psychology

décembre 2007, vol. 28, n°6, pp.631-645

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Mots clés : Disappointment aversion; Tradeoff method; Nonexpected utility; Probability weighting; Sign-dependence

Gul's theory of disappointment aversion (DA) has several attractive features, being intuitive, analytically tractable, and parsimonious. In spite of this, the DA model has received little attention in practical applications, which may be partly due to the absence of a procedure to elicit the model. We show how the tradeoff method, developed by Wakker and Deneffe can be used to elicit DA. Our elicitation method is parameter-free: it requires no assumption about utility and/or disappointment aversion. Quantitative tests of DA in three outcome domains, monetary gains, monetary losses, and life-years, suggest that the DA model is too parsimonious. Of the other models of disappointment aversion that have been proposed in the literature, our data are most consistent with the model of Loomes and Sugden

Improved second-order bounds for prediction with expert advice

N. Cesa-Bianchi, Y. Mansour, G. STOLTZ

Machine Learning

mars 2007, vol. 66, n°2, pp.321-352

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Mots clés : Individual sequences, Prediction with expert advice, Exponentially weighted averages

This work studies external regret in sequential prediction games with both positive and negative payoffs. External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. In this setting, we derive new and sharper regret bounds for the well-known exponentially weighted average forecaster and for a second forecaster with a different multiplicative update rule. Our analysis has two main advantages: first, no preliminary knowledge about the payoff sequence is needed, not even its range; second, our bounds are expressed in terms of sums of squared payoffs, replacing larger first-order quantities appearing in previous bounds. In addition, our most refined bounds have the natural and desirable property of being stable under rescalings and general translations of the payoff sequence.

Indirect robust estimation of the short-term interest rate process

V. CZELLAR, G. Andrew Karolyi, E. Ronchetti

Journal of Empirical Finance

septembre 2007, vol. 14, n°4, pp.546-563

Départements : Economie et Sciences de la décision

We propose Indirect Robust Generalized Method of Moments (IRGMM), a simulation-based estimationmethodology, to model short-term interest rate processes. The primary advantage of IRGMM relative toclassical estimators of the continuous-time short-rate diffusion processes is that it corrects both the errorsdue to discretization and the errors due to model misspecification. We apply this approach to monthly USrisk free rates and to various monthly Eurocurrency rates and provide extensive evidence of its predictiveperformances in a variety of settings.

Inference and model choice for sequentially ordered hidden Markov models


Journal of the Royal Statistical Society: Series B - Statistical Methodology

mars 2007, vol. 69, n°2, pp.269-284

Départements : Economie et Sciences de la décision

Mots clés : Hidden Markov models, Label switching, Particle filtering, Sequential Monte Carlo sampling, Time ordering

The system equation of a hidden Markov model is rewritten to label the components by order of appearance, and to make explicit the random behaviour of the number of components, m<sub> t</sub>. We argue that this reformulation is often a good way to achieve identifiability, as it facilitates the interpretation of the posterior density, and the estimation of the number of components that have appeared in a given sample. We develop a sequential Monte Carlo algorithm for estimating the reformulated model, which relies on particle filtering and Gibbs sampling. Our algorithm has a computational cost that is similar to that of a Markov chain Monte Carlo sampler and is much less likely to be affected by label switching, i.e. the possibility of becoming trapped in a local mode of the posterior density. The extension to transdimensional priors is also considered. The approach is illustrated by two real data examples.

Influence of skin colour on the detection of cutaneous erythema and tanning phenomena using reflectance spectrophotometry

J. Latreille, S. Gardinier, L. Ambroisine, E. Mauger, M. TENENHAUS, S. Guéhenneux, F. Morizot, E. Tschachler, C. Guinot

Skin Research and Technology

août 2007, vol. 13, n°3, pp.236-241

Départements : Economie et Sciences de la décision

Mots clés : Erythema, Individual typological angle, Partial least squares discriminant analysis, Skin colour;spectrophotometer, Tanning

Background/purpose:Background/purpose: This research aims at assessing the influence of baseline skin colour on the ability of reflectance spectrophotometry to detect cutaneous erythema induced by a low concentration of methyl nicotinate (2.5 mM) (first objective), and to detect tanning induced by ultraviolet rays (UVA+UVB) at infra-erythemal doses (second objective).Methods: Two independent studies were conducted to reach their respective objectives, on 27 women for the first study and on 12 women for the second study. Skin colour measurements were expressed in two different ways: percentages of reflected light at increasing wavelengths ¿ (400 nm<¿<700 nm, at 10 nm intervals), and chromametric coordinates of the CIELab 1976 system and individual typological angle (ITA°). Partial least squares discriminant analysis was performed to identify percentages of reflected light that allow the discrimination of the observations obtained after methyl nicotinate application from those obtained after water application (control). The same method was used for the discrimination of the measurements obtained after UV irradiation from those obtained before UV irradiation (control).Results and discussion: The cutaneous erythema induced by a low concentration of methyl nicotinate was detected only in subjects with fair to very fair skin defined by ITA=40°. The assumption is that in the darkest skins, the emitted light is mainly absorbed by the melanin in the epidermis. Otherwise, after UV irradiation, the tanning was detectable only for individuals with fair to dark skin defined by ITA <50°. This can be explained by the fact that UV stimulation of the fairest skin subjects, known to be melano-compromised individuals, can only produce a weak tanning that our study did not succeed in detecting

L'a priori et l'a posteriori en économie


Recherches Economiques de Louvain

2007, vol. 73, n°1, pp.5-53

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Un article précédent étudiait la distinction sémantique de l'analytique et du synthétique et l'appliquait à la micro-économie; celui-ci confronte les propositions micro-économiques fondamentales à la distinction épistémologique de l'a priori et de l'a posteriori (ou de l'empirique), tout en s'efforçant de systématiser les quatre concepts. Après avoir repris la définition kantienne de l'a priori et le problème célèbre du synthétique a priori, on met n place deux grandes interprétations des propositions fondamentales, l'empirisme (illustré par l'école classique anglaise) et l'apriorisme (illustré par von Mises au sein de l'école néo-classique autrichienne). On récuse les deux interprétations ' la seconde avec plus de détail que la première. On conclut que les propositions fondamentales sont synthétiques, mais ni a priori, ni a posteriori; cette catégorie échappe aux découpages ordinaires. On défend l'interprétation nouvelle en étudiant la loi des rendements décroissants et l'hypothèse de convexité des ensembles de production.

Large newsvendor games

L. Montrucchio, M. SCARSINI

Games and Economic Behavior

février 2007, vol. 58, n°2, pp.316-337

Départements : Economie et Sciences de la décision

We consider a game, called newsvendor game, where several retailers, who face a random demand, can pool their resources and build a centralized inventory that stocks a single item on their behalf. Profits have to be allocated in a way that is advantageous to all the retailers. A game in characteristic form is obtained by assigning to each coalition its optimal expected profit. We consider newsvendor games with possibly an infinite number of newsvendors. We prove in great generality results about balancedness of the game, and we show that in a game with a continuum of players, under a nonatomic condition on the demand, the core is a singleton. For a particular class of demands we show how the core shrinks to a singleton when the number of players increasesKeywords: Newsvendor games; Nonatomic games; Core; Balanced games

Learning correlated equilibria in games with compact sets of strategies

G. STOLTZ, G. Lugosi

Games and Economic Behavior

avril 2007, vol. 59, n°1, pp.187-208

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Mots clés : Correlated equilibrium, Repeated games, Regret minimization, Internal regret

Hart and Schmeidler's extension of correlated equilibrium to games with infinite sets of strategies is studied. General properties of the set of correlated equilibria are described. It is shown that, just like for finite games, if all players play according to an appropriate regret-minimizing strategy then the empirical frequencies of play converge to the set of correlated equilibria whenever the strategy sets are convex and compact.

Loss Aversion Under Prospect Theory: A Parameter-Free Measurement


Management Science

octobre 2007, vol. 53, n°10, pp.1659-1674

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

A growing body of qualitative evidence shows that loss aversion, a phenomenon formalized in prospect theory, can explain a variety of field and experimental data. Quantifications of loss aversion are, however, hindered by the absence of a general preference-based method to elicit the utility for gains and losses simultaneously. This paper proposes such a method and uses it to measure loss aversion in an experimental study without making any parametric assumptions. Thus, it is the first to obtain a parameter-free elicitation of prospect theory's utility function on the whole domain. Our method also provides an efficient way to elicit utility midpoints, which are important in axiomatizations of utility. Several definitions of loss aversion have been put forward in the literature. According to most definitions we find strong evidence of loss aversion, at both the aggregate and the individual level. The degree of loss aversion varies with the definition used, which underlines the need for a commonly accepted definition of loss aversion*DEMAND (Economic theory)*UTILITY theory*UTILITY theory -- Mathematical models*VALUE*EXPECTED utilityLOSS aversionPROSPECT theory