In this survey article, we report results on the existence of pure-strategy Nash equilibria in games with an atomless continuum of players, each with an action set that is not necessarily finite. We also discuss purification and symmetrization of mixed-strategy Nash equilibria, and settings in...

In this paper, a generalized version of the Fan-Knaster-Kuratowski-Mazurkiewicz lemma is obtained and used to prove the existence of fixed points for correspondenced defined on a generalized convex spaces. A result on the existence of maximal elements is deduced and is applied to prove the...

The core of an economy consists of those states of the economy which no group of agents (coalition) can "improve upon". A coalition can improve upon a state of the economy if, by using the means available to that group, each member can be made better off. This paper presents the notion of the...

The aim of this paper is to present Arrow's theorem and more generally the common framework of many results which can be called "Arrovian theorems". One begins by recalling the Condorcet majority rules, and why they fail: the "effet Condorcet". These rules are examples of preference aggregation...

This paper studies geometric properties of semi-algebraic economies with (eventually nonconvex) production - a class which includes linear or Cobb-Douglas preferences, polyhedric production sets and indivisible commodities as well. The main departure with the textbook differentiable viewpoint is...

We investigate properties of correlated equilibria in competitive, pure-exchange market games. We prove that: 1) the game defined in Schmeidler (1980) always admits the no-trade issue as mixed equilibrium outcome; 2) non-pure correlated equilibria may exist in every competitive strategic market...

This paper constructs two feasible strategic market games associated to an economy with infinite-dimensional trade space, finitely many traders, and finitely many firms, such that the set of outcomes induced by pure Nash equilibria coincides with the set of competitive equilibria. In both games,...

We consider repeated games of complete information and imperfect monitoring, where the observation structure is given by a directed graph, i.e. all what a player learns are the actions taken by his neighbours on the graph. We prove that a generalized folk theorem holds if and only if the graph...

This paper adapts the methods of Minimax-Hedging developped in Bernis & Giraud [2000] to other models of financial markets, including discontinuous semi-martingale. The measure of the risk is defined as the value of a zero-sum game between the investor and a fictitious player, representing the...