Sebastian Bervoets

Chercheur ,  CNRS

Économétrie, finance et méthodes mathématiques
Bervoets
Statut
Chargé de recherche
Domaine(s) de recherche
Théorie des jeux et réseaux sociaux, Choix social
Thèse
2005, Aix-Marseille Université
Téléchargement
CV
Contact
sebastian.bervoets[at]univ-amu.fr
+33(0)4 13 55 25 29 / +33(0)4 13 94 20 05
Adresse

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

Site
https://perso.amse-aixmarseille.fr/bervoets/
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 propose a dynastic model where individuals are born into an educated or uneducated environment that they inherit from their parents. We study the impact of social interactions on the correlation in parent-child educational status, independently of any parent-child interaction. When the level of social interactions is decided by a social planner, we show that the correlation in education status between generations decreases very fast as social interactions increase. In turn, when the level of social interactions is decided by the individuals themselves, we show that the intergenerational correlation still decreases, although less rapidly than with exogenous social interactions.
Mots clés Education, Intergenerational correlation, Strong and weak ties, Social mobility
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Résumé In this paper we analyse the problem of vote swapping in representative democracies. Vote swapping consists of exchanging votes between two voters from two different jurisdictions in order to beat a candidate that both voters dislike. The recent debates and legal disputes about this manipulation device raise some important ethical issues. We adopt an axiomatic approach, first establishing the relationship between vote swapping and a restricted form of gerrymandering, which is another way of manipulating elections in representative democracies. We then look for voting rules that are immune to such manipulations and show that any such voting rules only exist if either the voters or the candidates are given unreasonable power
Mots clés Democracy, Vote Exchange, Strategic Swaps, Voting, Federalism
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Résumé We address the problem of a planner looking for the efficient network when agents play a network game with local complementarities and links are costly. We show that for general network cost functions, efficient networks belong to the class of Nested-Split Graphs. Next, we refine our results and find that, depending on the specification of the network cost function, complete networks, core-periphery networks, dominant group architectures, quasi-star and quasi-complete networks can be efficient.
Mots clés Strategic complementarity, Network games, Nested split graphs
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Résumé We analyze the complexity of vote trading problems with equal-sized voting districts.For two allied vote-swapping parties, the problem is polynomially solvable.For three parties, the problem is NP-complete.
Mots clés Subset sum problem, Manipulation, Vote trading, Vote swapping
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Résumé In this article we construct a network of roads connecting large Indian cities and we evaluate this network’s overall performance. We consider a model where the production efforts of connected cities are strategic complements, and we relate the equilibrium effort profile to a well known centrality measure, the Katz-Bonacich centrality. We then make use of this result to compute the level of efforts of different cities in the current network and identify which city contributes most to overall efforts, which existing road is the most influential and which new road should be constructed in priority. Our results shed light on the importance of relatively small cities on aggregate efforts. Our exercise illustrates how network details might generate unexpected effects. JEL: C72, D85
Mots clés Strategic complementarity, Network policy, Indian National Roads Network, Aggregate efforts maximization, Aggregate efforts maximiza
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Résumé This article is devoted to the analysis of electoral systems involving two step procedures. It appears that designers are able to manipulate the result of these type of elections by gerrymandering, except in a very few cases. When imposing an unanimity condition on every jurisdiction's voting rule, it is shown that, for any finite number of candidates, a two step voting rule that is gerrymander-proof necessarily gives every voter the power of overruling the unanimity. A characterization of the set of gerrymander proof rules is provided in the case of two candidates.
Mots clés Gerrymandering, Manipulation, Federal voting rules
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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 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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Résumé We consider agents playing a linear network game with strategic complementarities. We analyse the problem of a policy maker who can change the structure of the network in order to increase the aggregate efforts of the individuals and/or the sum of their utilities, given that the number of links of the network has to remain fixed. We identify some link reallocations that guarantee an improvement of aggregate efforts and/or aggregate utilities. With this comparative statics exercise, we then prove that the networks maximising both aggregate outcomes (efforts and utilities) belong to the class of Nested-Split Graphs.
Mots clés Network, Linear interaction, Bonacich Centralities, Strategic complementarity, Nested split graphs
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Résumé We propose a dynastic model in which individuals are born in an educated or uneducated environment that they inherit from their parents. We study the role of social networks on the correlation in the parent-child educational status independent of any parent-child interaction. We show that the network reduces the intergenerational correlation, promotes social mobility and increases the average education level in the population. We also show that a planner that encourages social mobility also reduces social welfare, hence facing a trade off between these two objectives. When individuals choose the optimal level of social mobility, those born in an uneducated environment always want to leave their environment while the reverse occurs for individuals born in an educated environment.
Mots clés Intergenerational correlation, Social mobility, Strong and weak ties, Education
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