Mathieu Faure

Chercheur ,  Aix-Marseille Université , Faculté d'économie et de gestion (FEG)

Économétrie, finance et méthodes mathématiques
Faure
Statut
Professeur des universités
Domaine(s) de recherche
Théorie des jeux et réseaux sociaux
Thèse
2002, University of Marne-la-Vallée
Téléchargement
CV
Contact
mathieu.faure[at]univ-amu.fr
+33(0)4 13 55 25 48
Adresse

AMU - AMSE
5-9 Boulevard Maurice Bourdet, CS 50498
​13205 Marseille Cedex 1

Site
https://sites.google.com/site/matfaure/home?authuser=0
Résumé This article establishes an equivalence between four incomplete rankings of distributions of income among agents who are vertically differentiated with respect to some nonincome characteristic (health, household size, etc.). The first ranking is the possibility of going from one distribution to the other by a finite sequence of income transfers from richer and more highly ranked agents to poorer and less highly ranked ones. The second ranking is the unanimity among utilitarian planners who assume that agents' marginal utility of income is decreasing with respect to both income and the source of vertical differentiation. The third ranking is the Bourguignon (Journal of Econometrics, 42 (1989), 67–80) Ordered Poverty Gap dominance criterion. The fourth ranking is a new dominance criterion based on cumulative lowest incomes.
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Résumé While payoff-based learning models are almost exclusively devised for finite action games, where players can test every action, it is harder to design such learning processes for continuous games. We construct a stochastic learning rule, designed for games with continuous action sets, which requires no sophistication from the players and is simple to implement: players update their actions according to variations in own payoff between current and previous action. We then analyze its behavior in several classes of continuous games and show that convergence to a stable Nash equilibrium is guaranteed in all games with strategic complements as well as in concave games, while convergence to Nash occurs in all locally ordinal potential games as soon as Nash equilibria are isolated.
Mots clés Stochastic approximation, Continuous games, Payoff-based learning
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Résumé In game theory, the question of convergence of dynamical systems to the set of Nash equilibria has often been tackled. When the game admits a continuum of Nash equilibria, however, a natural and challenging question is whether convergence to the set of Nash equilibria implies convergence to a Nash equilibrium. In this paper we introduce a technique developed in Bhat and Bernstein (2003) as a useful way to answer this question. We illustrate it with the best-response dynamics in the local public good game played on a network, where continua of Nash equilibria often appear.
Mots clés Convergence, Continua of Nash equilibria, Best-response dynamics
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Résumé The stability of Nash equilibria has often been studied by examining the asymptotic behavior of the best-response dynamics. This is generally done in games where interactions are global and equilibria are isolated. In this paper, we analyze stability in contexts where interactions are local and where there are continua of equilibria. We focus on the public good game played on a network, where the set of equilibria is known to depend on the network structure (Bramoullé and Kranton, 2007), and where, as we show, continua of equilibria often appear. We provide necessary and sufficient conditions for a component of Nash equilibria to be asymptotically stable vis-à-vis the best-response dynamics. Interestingly, we demonstrate that these conditions relate to the structure of the network in a simple way. We also provide corresponding results for several dynamical systems related to the best response.
Mots clés Stability, Public good games, Best-response dynamics
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Résumé We study one of the main concept of online learning and sequential decision problem known as regret minimization. We investigate three different frameworks, whether data are generated accordingly to some i.i.d. process, or when no assumption whatsoever are made on their generation and, finally, when they are the consequences of some sequential interactions between players. The overall objective is to provide a comprehensive introduction to this domain. In each of these main setups, we define and analyze classical algorithms and we analyze their performances. Finally, we also show that some concepts of equilibria that emerged in game theory are learnable by players using online learning schemes while some other concepts are not learnable.
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Résumé Generalized Polya urn models have been used to model the establishment dynamics of a small founding population consisting of k di?erent genotypes or strategies. As population sizes get large, these population processes are well-approximated by a mean limit ordinary di?erential equation whose state space is the k simplex. We prove that if this mean limit ODE has an attractor at which the temporal averages of the population growth rate is positive, then there is a positive probability of the population not going extinct (i.e. growing without bound) and its distribution converging to the attractor. Conversely, when the temporal averages of the population growth rate is negative along this attractor, the population distribution does not converge to the attractor. For the stochastic analog of the replicator equations which can exhibit non-equilibrium dynamics, we show that verifying the conditions for convergence and non-convergence reduces to a simple algebraic problem. We also apply these results to selection-mutation dynamics to illustrate convergence to periodic solutions of these population genetics models with positive probability.
Mots clés Economie quantitative
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Résumé Consider a two-player normal-form game repeated over time. We introduce an adaptive learning procedure, where the players only observe their own realized payoff at each stage. We assume that agents do not know their own payoff function and have no information on the other player. Furthermore, we assume that they have restrictions on their own actions such that, at each stage, their choice is limited to a subset of their action set. We prove that the empirical distributions of play converge to the set of Nash equilibria for zero-sum and potential games, and games where one player has two actions.
Mots clés Economie quantitative
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Résumé We analyze quasi-stationary distributions \μ ε \ ε\textgreater0 of a family of Markov chains \X ε \ ε\textgreater0 that are random perturbations of a bounded, continuous map F:M→M , where M is a closed subset of R k . Consistent with many models in biology, these Markov chains have a closed absorbing set M 0 ⊂M such that F(M 0 )=M 0 and F(M∖M 0 )=M∖M 0 . Under some large deviations assumptions on the random perturbations, we show that, if there exists a positive attractor for F (i.e., an attractor for F in M∖M 0 ), then the weak* limit points of μ ε are supported by the positive attractors of F . To illustrate the broad applicability of these results, we apply them to nonlinear branching process models of metapopulations, competing species, host-parasitoid interactions and evolutionary games.
Mots clés Economie quantitative
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Résumé We discuss consistency of vanishingly smooth fictitious play, a strategy in the context of game theory, which can be regarded as a smooth fictitious play procedure, where the smoothing parameter is time dependent and asymptotically vanishes. This answers a question initially raised by Drew Fudenberg and Satoru Takahashi.
Mots clés Economie quantitative
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Résumé no abstract
Mots clés Economie quantitative
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Résumé In contrast to standard economic models, recent empirical evidence suggests that agents often operate based on subjective and divergent views of the competitive landscape. We develop a novel framework in which such imperfections are explicitly modeled through subjective perception networks, and introduce the concept of perception-consistent equilibrium (PCE), in which agents' actions and conjectures respond to the feedback generated by perceived competition. We establish the existence of equilibrium in broad classes of aggregative games. The model typically yields multiple equilibria, including outcomes that feature patterns of localized exclusion. Remarkably, heterogeneity in beliefs induces perceived competition rents-payoff differentials that arise purely from subjective misperceptions. We further show that PCE actions correspond to ordinal centrality measures, with eigenvector centrality emerging as a behavioral benchmark in separable payoff environments. Finally, a graph-theoretic taxonomy of PCEs reveals a hierarchical structure that ranks perceived competition rents. We also give conditions under which a unique stable equilibrium exists.
Mots clés Eigenvector centrality, Perceived competition rent, Ordinal centrality, Bounded rationality, Exclusionary equilibria, Perception-consistent equilibrium, Competition
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Résumé Deviations from Bayesian updating are traditionally categorized as biases, errors, or fallacies, thus implying their inherent "sub-optimality." We offer a more nuanced view. In learning problems with misspecified models, we show that some non-Bayesian updating can outperform Bayesian updating.
Mots clés Learning, Bayesian, Consistency
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Résumé A set of agents is aware of the existence of an economic opportunity, and compete for the associated prize. We study incentives to communicate about the existence of this economic opportunity to uninformed agents when the winner of the prize shares it with others, through some exogenous sharing rule. Communicating about the opportunity has two conflicting effects: it increases competition, but it can also increase the likelihood of receiving a large share of the prize. We find that, for any sharing rule, there is a minimum equilibrium, which Pareto dominates all other equilibria. We also find that under bilaterally symmetric sharing, more sharing generates more communication. We then discuss these results along several extensions.
Mots clés Investment, Communication, Sharing Network, Rival Opportunity
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Résumé This paper provides a robust criterion for evaluating the allocation of opportunities among various groups. We envisage the problem of comparing these allocations from the view point of an ethical observer placed behind a veil of ignorance with respect to the group in which he/she could end up. We give justi…cation for such an ethical observer to evaluate these allocations of opportunities on the basis of an expected valuation of the expected utility of being in a group assuming an equal probability of falling in every group. We identify a criterion for comparing societies that is agreed upon by all such ethical observers who exhibit aversion to inequality of opportunities. The criterion happens to be a conic extension of zonotope inclusion criterion. We provide various interpretations of this criterion as well as some illustrations of its possible use, notably in the Indian context where we evaluate the inequalities of educational opportunities among castes and genders o¤ered by Indian states.
Mots clés Education, Gender, Zonotopes, Groups, Equalizing opportunities
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Résumé This paper establishes an equivalence between three incomplete rankings of distributions of income among agents that are vertically differentiated with respect to some other non-income characteristic (health, household size, etc.). The first ranking is that associated with the possibility of going from one distribution to the other by a finite sequence of income transfers from richer and more highly ranked agents to poorer and less highly ranked ones. The second ranking is the unanimity of all comparisons of two distributions made by a utilitarian planer who assumes that agents convert income into utility by the same function exhibiting a marginal utility of income that is decreasing with respect to both income and the source of vertical differentiation. The third ranking is the Bourguignon (1989) ordered poverty gap dominance criterion.
Mots clés Equalization, Transfers, Heterogenous agents, Poverty gap, Dominance, Utilitarianism
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Résumé In rank-order tournaments, players have incentives to cheat in order to increase their probability of winning the prize. Usually, cheating is seen as a technology that allows individuals to illegally increase their best potential performances. This paper argues that cheating can alternatively be seen as a technology that ensures that the best performances are reached more often. We call this technology recovery doping and show that it yields new insights on the effects of cheating: recovery doping lowers performance uncertainty, thereby changing the outcome of the contest in favour of the best players. We develop this theory in a game with player heterogeneity and performance uncertainty and then study the results of the cross-country skiing World Cup between 1987 and 2006. In line with our theoretical predictions, race-specific rankings were remarkably stable during the 1990s, subsequently becoming more volatile. This pattern reflects the rise and fall of synthetic EPO and the emergence of blood testing and profiling.
Mots clés Game Theory, Recovery doping, Rank correlation
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