"Regulation under Knightian Uncertainty", 2003
"How do Uncertainty Events (in the Knight sense) Affects Insurance Industry?", 2002

"The Foundations of Non-Cooperative Game Theory", 2003
"An Introduction to Individual Choice under Knightian Uncertainty", 2002

"Integral Representation with Convex Capacities that are Squeeze of (Additive) Probabilities Measures"

   In this paper I will investigate the conditions under which a convex capacity (or a non-additive probability which exhibts uncertainty aversion) can be represented as a squeeze of a(n) (additive) probability measure associate to an uncertainty aversion function. Then I will present two alternative formulations of choquet Integral (and I will extend these formulations to Choquet expected utility) in a parametric approach that will enable me to do comparative static exercises over the uncertainty aversion function in an easy way.

JEL Codes: D81
Keywords: Ellsberg paradox; Knightian uncertainty; capacities (non-additive probabilities); uncertainty aversion; Choquet integral; Choquet expected utility.

(This version: April 2003)

"Nash Equilibrium under Knightian Uncertainty: A Generalization of the Existence Theorem"

   The most well successful definition of Nash equilibrium for two-person normal form games in the presence of Knightian uncertainty is due to Dow-Werlang [1994]. Taking a different definition of support from that of Dow-Werlang’s Nash Equilibrium under Uncertainty paper, Marinacci [2000] extended the proof of the existence for any given uncertainty aversion function.

   The purpose of this paper is to extend the proof of the Dow-Werlang’s existence theorem of Nash equilibrium under uncertainty, using the same definition of support in their paper (the most useful, general notion and has some advantages over the others definitions). I will present a restriction over the set of convex capacities, more specifically, I will work with the class of convex capacities that are squeeze of (additive) probability measure (Coimbra-Lisboa, P.C. [2002] - mimeo) that will enables me to give a parametric approach of the existence result that generalize Dow-Werlang’s existence theorem and will be very useful for comparative static exercises over the uncertainty aversion function.

JEL Codes: C72, D81
Keywords: Ellsberg paradox; Knightian uncertainty; capacities (non-additive probabilities); uncertainty aversion; Choquet integral; equilibrium concepts.

[EPGE Seminars, April 25, 2003] (This version: March 2003)