On convexity and supermodularity.

Concavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members are concave whenever they are supermodular. We show that for some important Riesz spaces both the class of positively homogeneous functionals and the class of translation invariant functionals have the Choquet property. We extend in this way the results of Choquet [1] and Konig [4].

Unique Solutions of Some Recursive Equations in Economic Dynamics

We study unique and globally attracting solutions of a general nonlinear equation that has as special cases some recursive equations widely used in Economics.Recursive equations, Intertemporal consumption

Mas-Colell Bargaining Set of Large Games

We study the equivalence between the MB-set and the core in the general context of games with a measurable space of players. In the first part of the paper, we study the problem without imposing any restriction on the class of games we consider. In the second part, we apply our findings to specific classes of games for which we provide new equivalence results. These include non-continuous convex games, exact non-atomic market games and non-atomic non-exact games. We also introduce, and characterize, a new class of games, which we call thin games. For these, we show not only that the MB-set is equal to the core, but also that it is the unique stable set in the sense of von Neumann and Morgenstern. Finally, we study the relation between thin games, market games and convex games.Mas-Colell Bargaining Set, maximal excess game, core-equivalence, thin games, market games, convex games.

On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type.

In this paper we study the existence of bubbles for pricing equilibria in a pure exchange economy à la Lucas, with infinitely lived homogeneous agents. The model is analyzed under fairly general assumptions: no restrictions either on the stochastic process governing dividends’ distribution or on the utilities (possibly unbounded) are required. We prove that the pricing equilibrium is unique as long as the agents exhibit uniformly bounded relative risk aversion. A generic uniqueness result is also given regardless of agent’s preferences. A few ”pathological” examples of economies exhibiting pricing equilibria with bubble components are constructed. Finally, a possible relationship between our approach and the theory developed by Santos and Woodford on ambiguous bubbles is investigated. The whole discussion sheds more insight on the common belief that bubbles are a marginal phenomenon in such models.

On Concavity and Supermodularity

Concavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members are concave whenever they are supermodular. We show that for some important Riesz spaces both the class of positively homogeneous functionals and the class of translation invariant functionals have the Choquet property. We extend in this way the results of Choquet [2] and Konig [5].Concavity, Supermodularity

Refinement Derivatives and Values of Games

A definition of set-wise differentiability for set functions is given through refining the partitions of sets. Such a construction is closely related to the one proposed by Rosenmuller (1977) as well as that studied by Epstein (1999) and Epstein and Marinacci (2001). We present several classes of TU games which are differentiable and study differentiation rules. The last part of the paper applies refinement derivatives to the calculation of value of games. Following Hart and Mas-Colell (1989), we define a value operator through the derivative of the potential of the game. We show that this operator is a truly value when restricted to some appropriate spaces of games. We present two alternative spaces where this occurs: the spaces pM( ) and POT2. The latter space is closely related to Myerson's balanced contribution axiom.TU games; large games; non-additive set functions; value; derivatives

Subcalculus for set functions and cores of TU games.

This paper introduces a subcalculus for general set functions and uses this framework to study the core of TU games. After stating a linearity theorem, we establish several theorems that characterize mea- sure games having finite-dimensional cores. This is a very tractable class of games relevant in many economic applications. Finally, we show that exact games with Þnite dimensional cores are generalized linear production games.TU games; non-additive set functions; subcalculus; cores

Cores and stable sets of finite dimensional games.

In this paper we study exact TU games having finite dimensional non-atomic cores, a class of games that includes relevant economic games. We first characterize them by showing that they are a particular type of market games. Using this characterization, we then show that in such a class the cores are their unique von Neumann- Morgenstern stable sets.