About an optimum model of market equilibrium

The determination of the equilibrium price within the context of the economic analysis of the supply - demand relation, represents in fact, a particular case of solving the minmax equation from uncooperative games theory. Thus, considering two decision makers and a zero-sum game, we shall have the following problem: max(x)min(y) f(x,y) = min(y) max(x) f(x, y). This papers deals with some optimal properties of the equilibrium price; these properties, which are presented using an original approach, lead us to important economic interpretations. The originality of the paper consists of the modality used in order to determine the equilibrium price starting from the elasticity of supply and demand functions. In case the analytical expressions of the supply and demand functions remain unknown, we specify an original proceeding in order to determine the equation of price dynamics by using a method which is appropriate for higher order linear differential equations.