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# Bervoets

## Publications

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.

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.

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.

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.

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.

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

No abstract is available for this item.

No abstract is available for this item.

This paper is devoted to the analysis of two tiers voting rules. First, one candidate is elected in every jurisdiction and next, an aggregation procedure collects the results from the jurisdictions in order to designate the final winner. It appears that whenever individuals are allowed to change jurisdiction when casting their ballot, it is possible that they can manipulate the result of the election, except when the voting rule is the Priority rule, which assigns a priority order to the candidates. Classification JEL : D71, D72

This paper provides an axiomatic characterization of two rules for comparing alternative sets of objects on the basis of the diversity that they offer. The framework considered assumes a finite universe of objects and a priori given ordinal quadernary relation that compares alternative pairs of objects on the basis of their ordinal dissimilarity. Very few properties of this quadernary relation are assumed (beside completeness, transitivity and a very natural form of symmetry). The two rules that we characterize are the maxi max criterion and the lexi-max criterion. The maxi max criterion considers that a set is more diverse than another if and only if the two objects that are the most dissimilar in the former are weakly as dissimilar as the two most dissimilar objects in the later. The lexi-max criterion is defined as usual as the lexicographic extension of the maximax criterion.

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.