Abstract
We study a finite decision model where the utility function is an additive combination of a personal valuation component and an interaction component. Individuals are characterized according to these two components (their valuation type and externality type), and also according to their crowding type (how they influence others). We study how positive externalities lead to typo symmetries euillbrIn, while negative externalities allow the existence of equillibria that are not type-symmetric. In particular, we show that positive elides lead to euilibria having a unique partition into a minimum number of societies (simi individuals using the same strategy, see 1271); and negat ve externalities I to equilibria with multiple societal partitions, some with the maximum number of societies

Abstract

Abstract
We consider the problem faced by a wage-earner with an uncertain lifetime having to reach decisions concerning consumption and life-insurance purchase, while investing his savings in a financial market comprised of one risk-free security and an arbitrary number of risky securities whose prices are determined by diffusive linear stochastic differential equations. We assume that life-insurance is continuously available for the wage-earner to buy from a market composed of a fixed number of life insurance companies offering pairwise distinct life-insurance contracts. We characterize the optimal consumption, investment and life-insurance selection and purchase strategies for the wage-earner with an uncertain lifetime and whose goal is to maximize the expected utility obtained from his family consumption, from the size of the estate in the event of premature death, and from the size of the estate at the time of retirement. We use dynamic programming techniques to obtain an explicit solution in the case of discounted constant relative risk aversion (CRRA) utility functions.

Abstract
We study the effects of product differentiation in a Stackelberg model with demand uncertainty for the first mover. We do an ex-ante and ex-post analysis of the profits of the leader and of the follower firms in terms of product differentiation and of the demand uncertainty. We show that even with small uncertainty about the demand, the follower firm can achieve greater profits than the leader, if their products are sufficiently differentiated. We also compute the probability of the second firm having higher profit than the leading firm, subsequently showing the advantages and disadvantages of being either the leader or the follower firm.

Abstract
We consider a toral Anosov automorphism G(gamma) : T-gamma --> T-gamma given by G(gamma) (x, y) = (ax + y, x) in the < v, w > base, where , a is an element of N\{1}, gamma = 1/(a + 1/(a + 1/...)), v = (gamma, 1) and w = (-1, gamma) in the canonical base of R-2 and T-gamma = R-2 / (vZ x wZ). We introduce the notion of gamma-tilings to prove the existence of a one-to-one correspondence between (i) marked smooth conjugacy classes of Anosov diffeomorphisms, with invariant measures absolutely continuous with respect to the Lebesgue measure, that are in the isotopy class of G(gamma); (ii) affine classes of gamma-tilings; and (iii) gamma-solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences.

Abstract