Equilibria of nonatomic anonymous games

We define a new notion of equilibrium for nonatomic anonymous games, termed epsilon-estimated equilibrium, and prove its existence for any positive s. This notion encompasses and brings to nonatomic games recent concepts of equilibrium such as self-confirming, peer-confirming, and Berk-Nash. This augmented scope is our main motivation. Our approach also resolves some conceptual problems present in Schmeidler (1973) pointed out by Shapley

Reasoning about negligibility and proximity in the set of all hyperreals

International audienceWe consider the binary relations of negligibility, comparability and proximity in the set of all hyperreals. Associating with negligibility, comparability and proximity the binary predicates N, C and P and the connectives [N], [C] and [P], we consider a first-order theory based on these predicates and a modal logic based on these connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic