We discuss the mathematical difficulties encountered in Patinkin's classical cartel model. It may be impossible to derive Patinkin's cartel by finding the reciprocal marginal cost functions: it could be impossible for cartel members to compute a solution, unless certain assumptions are made to...

We examine ibn Ezra's procedure (Rabinovitch 1973; O'Neill 1982) historically used to solve the Rights Arbitration problem in the general framework of bankruptcy problems. When the greatest claim is larger than or equal to the estate, the procedure is a maximal game (Aumann 2010). However, when the...

We examine the Talmudic three wives problem, which is a generalization of the Talmudic contested garment problem solved by Aumann and Maschler (1985) using coalitional procedure. This problem has many practical applications. In an attempt to unify all Talmudic methods, Guiasu (2010, 2011)...

After defining biproportion (or RAS) rigorously, we recall two fundamental theorems: unicity of biproportion (any biproportional algorithm leads to the same solution than biproportion, which turns biproportion into a mathematical tool as indisputable than proportion), ineffectiveness of...

In the Supply-Use (or Make-Use) input-output models, “product-technology” (PT) or “fixed-industry-sales-structure” (FISS) assumptions are more widely adopted (SNA, Eurostat) for deriving symmetric input-output tables (SIOT) than “industry-technology” or...

MFA (Minimal Flow Analysis) is a method of qualitative input-output analysis used for identifying national of regional industrial clusters. It is based on the analysis of layers (in an input-output model, flow matrices generated at each iteration toward equilibrium). We show through theory that...

The principle of matrix adjustment methods consists into finding what is the matrix which is the closest to an initial matrix but with respect of the column and row sum totals of a second matrix. In order to help deciding which matrix-adjustment method is the better, the article returns to the...

The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for...

The Talmud Division is a very old method of sharing developed by the rabbis in the Talmud and brought to the fore in the modern area some authors, among them are Aumann and Maschler. One compares the Talmud Division to other methods, mainly here the most popular, Aristotle's Proportional...

This paper returns to de Mesnard's paper of 2000, which has exposed the so-called method of bicausative matrices. This method was created to analyze the structural change between two matrices, as an improvement of the causative method of Jackson and al. (1990). In its 2000 paper, de Mesnard has...