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.

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