Convergence in games with continua of equilibriaJournal articleSebastian Bervoets et Mathieu Faure, Journal of Mathematical Economics, Volume 90, pp. 25-30, 2020

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.

Learning with minimal information in continuous gamesJournal articleSebastian Bervoets, Mario Bravo et Mathieu Faure, Theoretical Economics, Volume 15, Issue 4, pp. 1471-1508, 2020

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 equilibrium occurs in all locally ordinal potential games as soon as Nash equilibria are isolated.

Stability in games with continua of equilibriaJournal articleSebastian Bervoets et Mathieu Faure, Journal of Economic Theory, Volume 179, Issue C, pp. 131-162, 2019

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.

Intergenerational correlation and social interactions in educationJournal articleSebastian Bervoets et Yves Zenou, European Economic Review, Volume 92, Issue C, pp. 13-30, 2017

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.

Efficient networks in games with local complementaritiesJournal articleMohamed Belhaj, Sebastian Bervoets et Frédéric Deroian, Theoretical Economics, Volume 11, Issue 1, pp. 357-380, 2016

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.

On avoiding vote swappingJournal articleSebastian Bervoets et Vincent Merlin, Social Choice and Welfare, Volume 46, Issue 3, pp. 495-509, 2016

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.

Vote trading and subset sumsJournal articleSebastian Bervoets, Vincent Merlin et Gerhard J. Woeginger, Operations Research Letters, Volume 43, Issue 1, pp. 99-102, 2015

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.

Production Efforts in Large Indian Cities: A Network-based ApproachJournal articleSebastian Bervoets et Frédéric Deroian, Journal of Interdisciplinary Economics, Volume 25, Issue 1-2, pp. 117-145, 2013

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

Gerrymander-proof representative democraciesJournal articleSebastian Bervoets et Vincent Merlin, International Journal of Game Theory, Volume 41, Issue 3, pp. 473-488, 2012

No abstract is available for this item.

An axiomatic approach to predictability of outcomes in an interactive settingJournal articleSebastian Bervoets, Theory and Decision, Volume 68, Issue 3, pp. 311-323, 2010

No abstract is available for this item.