Existence of Nash Equilibria on Convex Sets

We analyze a non-cooperative game in which the set of feasible strategy profiles is compact and convex but possibly non-rectangular. Thus, a player's feasible strategies may depend on the strategies used by others, as in Debreu's (1952,1982) generalized games. In contrast to the model of Debreu, we do not require preferences to be defined over infeasible strategy profiles, and we do not require a player's feasible strategy correspondence to have non-empty values. We prove existence of Nash equilibria under a lower hemicontinuity condition, and we give examples of classes of games in which this condition is satisfied

Tax avoidance and the political appeal of progressivity

Empiriquement, on observe que la majorité des Etats a fait le choix d'un système d'imposition progressif. Pourtant, le fondement théorique de ce choix n'est pas évident. Si l'on interprète le système d'imposition appliquée comme le résultat d'un jeu entre deux partis politiques Downsiens, le fait que la majorité de la population soit relativement pauvre permet de conforter l'observation empirique. Cependant, des résultats théoriques récents montrent que, à l'équilibre, des électeurs purement égoïstes ne font pas toujours ce choix-là. Cet article tente de raffiner ces derniers modèles théoriques pour proposer une autre explication au choix d'un système progressif. Notre thèse est la suivante : la présence d'évasion fiscale – caractéristique importante des systèmes d'imposition sur le revenu – a des effets sur l'équilibre du jeu politique en modifiant les préférences des individus les plus riches de la société. Dans un premier temps, l'ensemble des équilibres en stratégies mixtes du jeu est caractérisé (pour des systèmes d'imposition de type quadratique), et on montre alors que l'évasion fiscale renforce l'élection de systèmes progressifs d'imposition. Dans un deuxième temps, on analyse un cas de système d'imposition de type “wiggling" en montrant que l'évasion fiscale mène, quand elle est suffisamment importante, à l'élection de systèmes progressifs d'imposition avec certitude.Compétition électorale;Taxtation du revenu progressive;Evasion fiscale;Equilibre en stratégies mixtes

Ambiguity in electoral competition.

L'article propose une théorie de la compétition électorale ambigüe. Une plate-forme est ambigüe si les votants peuvent l'interpréter de différentes manières. Une telle plate-forme met plus ou moins de poids sur sur les différentes options possibles de sorte qu'elle est plus ou moins facilement interprétée comme une politique ou une autre. On fait l'hypothèse que les partis politiques peuvent contrôler exactement leurs plate-formes mais ne peuvent pas cibler celles-ci vers les votants individuellement. Chaque électeur vote d'après son interprétation des plate-formes des partis mais est averse à l'ambiguité. On montre que ce jeu de compétition électorale n'a pas d'équilibre de Nash. Cependant ses stratégies max-min sont les stratégies optimales du jeu Downsien en stratégies mixtes. De plus, si les partis se comportent de manière suffisament prudente par rapport à l'aversion pour l'ambiguité des électeurs, ces mêmes stratégies forment un équilibre.Compétition électorale;Ambigüité;Comportement prudent;Jeux à somme nulle

Existence of Nash Equilibria on Convex Sets

We analyze a non-cooperative game in which the set of feasible strategy profiles is compact and convex but possibly non-rectangular. Thus, a player's feasible strategies may depend on the strategies used by others, as in Debreu's (1952,1982) generalized games. In contrast to the model of Debreu, we do not require preferences to be defined over infeasible strategy profiles, and we do not require a player's feasible strategy correspondence to have non-empty values. We prove existence of Nash equilibria under a lower hemicontinuity condition, and we give examples of classes of games in which this condition is satisfied

Political Competition over Distortionary Taxation

Political parties compete over income tax functions, and voters vote and decide whether to pay full taxes or to make an e®ort to modify their tax bur- den. We show that political parties only propose e±cient income tax func- tions, in a similar manner to the probabilistic voting theory. Regarding the shape of income tax functions, it need not be the case that the majority of vot- ers prefer progressive taxation to regressive taxation as a consequence of the distortions. Nevertheless, we prove that the political appeal for progressivity is restored under mild conditions.Income taxation, Distortions, Efficiency, Progressivity, Political competition

Bargaining Foundations of the Median Voter Theorem

We provide game-theoretic foundations for the median voter theorem in a one-dimensional bargaining model based on Baron and Ferejohn’s (1989) model of distributive politics. We prove that, as the agents become arbitrarily patient, the set of proposals that can be passed in any subgame perfect equilibrium collapses to the median voter’s ideal point. While we leave the possibility of some delay, we prove that the agents’ equilibrium continuation payoffs converge to the utility from the median, so that delay, if it occurs, is inconsequential. We do not impose stationarity or any other refinements. Our result counters intuition based on the folk theorem for repeated games, and it contrasts with the known result for the distributive bargaining model that, as agents become patient, any division of the dollar can be supported as a subgame perfect equilibrium outcome.

Stuck in the middle: Ideology, valence and the electoral failures of centrist parties

In recent years centrist-liberal parties, such as the German Free Democratic Party (FDP) in 2013 and the British Liberal Democrats in 2015 and 2017, suffered enormous electoral defeats. These defeats highlight a prominent puzzle in the study of party competition and voting behavior; the empty center phenomenon. That is, empirical evidence suggests that most parties do not converge to the median voter's position, despite the centripetal force of the voters’ preference distribution. Using survey data from Canada, Finland, Germany and the United Kingdom, this article shows that deterioration of centrist parties’ valence image is followed by a collapse of their vote shares. Using mathematical simulations, this article shows that centrist parties have limited strategic opportunities to regain their support. Differently from other parties, centrist parties cannot alter their policy platforms to compensate for their deteriorated valence image. These results have important implications for political representation and voters–elite linkages

Modelling Politics

Formal models of elections have emphasized the convergence of party leaders towards the center of the electoral distribution. This paper discusses various political episodes in British and US history to suggest that political divergence is generic. This leads to the inference that political choice involves electoral judgment as well as preference. The stochastic electoral model is extended to incorporate the basis of judgment, namely valence. The model suggests that when the electoral system is based on proportional electoral methods, then there will be numerous parties with very di¤erent valences, adopting very divergent positions. Under plurality rule, on the other hand, the role of activists appears to restrict the number of parties to two, and to cause a slow political rotation in the policy space.

A Theory of Voting in Large Elections

This paper provides a game-theoretic model of probabilistic voting and then examines the incentives faced by candidates in a spatial model of elections. In our model, voters’ strategies form a Quantal Response Equilibrium (QRE), which merges strategic voting and probabilistic behavior. We first show that a QRE in the voting game exists for all elections with a finite number of candidates, and then proceed to show that, with enough voters and the addition of a regularity condition on voters’ utilities, a Nash equilibrium profile of platforms exists when candidates seek to maximize their expected margin of victory. This equilibrium (1) consists of all candidates converging to the policy that maximizes the expected sum of voters’ utilities, (2) exists even when voters can abstain, and (3) is unique when there are only 2 candidates