Articles scientifiques

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.


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