In the case of an economy with production, we unify McKenzie-Debreu's and Arrow-Hahn's concepts of irreductibility by a generalization of the Bergstrom-irreductibility. This, together with existence of a quasi-equilibrium, will be shown to imply existence of a Walras equilibrium.

We present the model of games with incomplete information first introduced by Harsanyi and show the link with extensive form games with imperfect information. We provide then a construction of the universal type space of Mertens and Zamir together with some properties.

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 present and prove the equality between the core and the set of Walras allocations for a pure exchange economy with l goods and a continuum of consumers, represented by an atomless measure space.

We study a class of exchange economies where the characteristics of the agent are fixed but the initial endowments. We define a notion of regular economies which encompasses the different approach of the literature. We then prove that a regular exchange economy has a finite odd number of...

In this chapter, we derive Yaari's model of decision under risk in connection with Schmeidler's model of decision under uncertainty. The model is illustrated with two applications in insurance theory. Final comments concern the general Rank Dependent Expected Utility (RDEU) model.

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...

Since some Nash equilibria can be considered as irrational, we are interested here in refinements of Nash equilibria, i.e. concepts of solutions associating to each game a subset of Nash equilibria of this game. Considering only finite games with normal form, we first define the most desirable...