Quantity-setting competition with differentiated goods under uncertain demand

We consider a quantity-setting duopoly model, and we study the decision to move first or second, by assuming that the firms produce differentiated goods and that there is some demand uncertainty. The competitive phase consists of two periods, and in either period, the firms can make a production decision that is irreversible. As far as the firms are allowed to choose (non-cooperatively) the period they make the decision, we study the circumstances that favour sequential rather than simultaneous decisions.

Desirable role in a price-setting international mixed duopoly

In this paper, we study the order of moves in a mixed international duopoly for differentiated goods, where firms choose whether to set prices sequentially or simultaneously. We discuss the desirable role of the public firm by comparing welfare among three games. We find that, in the three possible roles, the domestic public firm put a lower price, and then produces more than the foreign private firm.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.