A class of non-cooperative constrained games is analyzed for which the Ky Fan function is convex-concave. Nash equilibria of such games correspond to diagonal saddle points of the said function. This feature is exploited in designing computational algorithms for finding such equilibria.

This paper deals with on-line computation—or step-wise learning—of Pareto optimal insurance contracts. Our approach tolerates that the loss distribution might be unknown, intractable, or not well specified. Thus we accommodate fairly inexperienced parties. Losses are here simulated or...

So-called potential functions are important, prominent, and common to many diverses fields, including optimization, dynamic processes, and physics. Monderer and Shapley have recently added a class of noncooperative games to that list. We extend their notion and consider repeated play of games...

This note deals with on-line computatin of learning of Pareto optimal insurance contracts. We account for the fact that the loss distribution often is unknown, unavailable, or intractable. Alternatively, the contracting parties could be inexperienced. In both cases losses must be simulated of...

Owners of stochastic assets can pool their endowments to smoothen and insure individual payoffs across outcomes and time. We explore, in such a setting, how contingent shadow prices on aggregate resources can be used for three purposes: first, to design mutual contracts for risk averse agents;...