Balancing Bilinearly Interfering Elements

David Carfì, Gianfranco Gambarelli


Many decisions in various fields of application have to take into account the joined effects of two elements that can interfere with each other. This happens for example in Medicine (synergic or antagonistic drugs ), in Agriculture (anti-cryptogamics), in Public Economics (interfering economic policies),  in Industrial Economics (where the demand of an asset can be influenced by the supply of another asset), Zootechnics and so on. When it is necessary to decide about the dosage of such elements, there is sometimes a primary interest for one effect rather than another; more precisely, it may be of interest that the effects of an element are in a certain proportion with respect to the effects of the other. It may be also necessary to take into account minimum quantities that must be assigned.

In Carfì et al (2013) a mathematical model was proposed to solve the above problem in exact form. In this paper we present the solution in closed form for the case in which the function of the effects is bilinear.


Bargaining problems; Game Theory; Antagonist Elements; Interfering Elements; Optimal dosage; Synergies

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