Abstract
On a symmetric differentiated Stackelberg duopoly model in which there is asymmetric demand information owned by leading and follower firms, we show that the leading firm does not necessarily have advantage over the following one. The reason for this is that the second mover can adjust its output level after observing the realized demand, while the first mover chooses its output level only with the knowledge of demand distribution.

Abstract
In the paper, we discuss two questions about degree d smooth expanding circle maps, with d >= 2. (i) We characterize the sequences of asymptotic length ratios which occur for systems with Holder continuous derivative. The sequences of asymptotic length ratios are precisely those given by a positive Holder continuous function s (solenoid function) on the Cantor set C of d-adic integers satisfying a functional equation called the matching condition. In the case of the 2-adic integer Cantor set, the functional equation is s(2x + 1) = s(x)/s(2x) 1 + 1s(2x-1) -1. We also present a one-to-one correspondence between solenoid functions and affine classes of exponentially fast d-adic tilings of the real line that are fixed points of the d-amalgamation operator. (ii) We calculate the precise maximum possible level of smoothness for a representative of the system, up to diffeomorphic conjugacy, in terms of the functions s and cr(x) = (1 + s(x))/(1 + (s(x + 1))(-1)). For example, in the Lipschitz structure on C determined by s, the maximum smoothness is C1+alpha for 0 < alpha <= 1 if and only if s is alpha-Holder continuous. The maximum smoothness is C2+alpha for 0 < alpha <= 1 if and only if cr is (1 + alpha)-Holder. A curious connection with Mostow type rigidity is provided by the fact that s must be constant if it is alpha-Holder for alpha > 1.

Abstract
In this paper, we consider a Stackelberg duopoly competition with differentiated goods and with unknown costs. The firms' aim is to choose the output levels of their products according to the well-known concept of perfect Bayesian equilibrium. There is a firm (F(1)) that chooses first the quantity q(1) of its good; the other firm (F(2)) observes q(1) and then chooses the quantity g(2) of its good. We suppose that each firm has two different technologies, and uses one of them following a probability distribution. The use of either one or the other technology affects the unitary production cost. We show that there is exactly one perfect Bayesian equilibrium for this game. We analyse the advantages, for firms and for consumers, of using the technology with the highest production cost versus the one with the cheapest cost.

Abstract
We study the optimal consumption, investment and life-insurance purchase and selection strategies for a wage-earner with an uncertain lifetime with access to a financial market comprised of one risk-free security and one risky-asset whose prices evolve according to linear diffusions modulated by a continuous-time stochastic process determined by an additional diffusive nonlinear stochastic differential equation. The process modulating the linear diffusions may be regarded as an indicator describing the state of the economy in a given instant of time. Additionally, we allow the Brownian motions driving each of these equations to be correlated. The life-insurance market under consideration herein consists of a fixed number of providers offering pairwise distinct contracts. We use dynamic programming techniques to characterize the solutions to the problem described above for a general family of utility functions, studying the case of discounted constant relative risk aversion utilities with more detail.

Abstract
We consider a continuous lifetime model for investor whose lifetime is a random variable. We assume the investor has an access to the social welfare system, the financial market and the life insurance market. The investor aims to find the optimal strategies that maximize the expected utility obtained from consumption, investing in the financial market, buying life insurance, registering in the social welfare system, the size of his estate in the event of premature death and the size of his fortune at time of retirement if he lives that long. We use dynamic programming techniques to derive a second-order nonlinear partial differential equation whose solution is the maximum objective function. We use special case of discounted constant relative risk aversion utilities to find an explicit solutions for the optimal strategies. Finally, we have shown a numerical solution for the problem under consideration and study some properties for the optimal strategies.

Abstract
We show that in finite settings with identical firms and consumers, asymmetric pure price equilibria with positive profits exist. We consider a price competition duopoly for a homogeneous product. Demand stems from a second-stage consumption game at posted prices, with consumers' behavior impacted by negative network effects. We characterize equilibrium prices and demand. In all subgame-perfect pure price equilibria, both firms have positive profits, and in some, firms charge different prices.