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...

We introduce here zero-sum games, which represent the strategic interactions where two agents have totally opposed interests. The concept of rational solution for such interactions is then defined by the notions of value and optimal strategies. These quantities always exist if the information is...

We introduce here extensive form games which are the most accurate way of describing a strategic situation. We show how this model finds its place in the hallmark of strategic games. We give a proof of Kuhn's fundamental theorem for games of perfect recall, that is: every mixed strategy is...

In order to get rid of the condition X=Y, we introduce an extension of the Dynkin game by allowing for an extended set of strategies, namely the set of mixed strategies. The main result of the paper is that the extended Dynkin game has a value when the processes X and Y are only restricted to be...

We consider two-player repeated games with lack of information on one side: first, payoff matrices are chosen according to a known probability, and are only announced to one of the players called the informed player. Then, the game with the selected payoffs is infinitely repeated. We prove here...

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...