Balancing Bilinearly Interfering Elements

David Carfì, Gianfranco Gambarelli

Abstract


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.

Keywords


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

Full Text:

PDF

References


Battaggion M. R., Grieco D., 2009. R&D Competition with Radical and Incremental Innovation, Rivista Italiana degli Economisti, 2

Carfì, D., 2009. Payoff space in C1-games, Applied Sciences (APPS), vol.11, pp.1-16, ISSN 1454-5101

Carfì, D. G. Gambarelli and A. Uristani, 2013. Balancing pairs of interfering elements, Financial management, measurement of performance and evaluation of investment appraisal (Zarządzanie finansami. Mierzenie wyników przedsiębiorstw i ocena efektywności inwestycji), Zeszyty Naukowe Uniwersytetu Szczecińskiego, No. 760, Szczecin University Press, Szczecin, 435-442. ISSN 1640-6818, 1733-2842.

Chandy R. K., Tellis G. J., 1998. Organizing for Radical Product Innovation: The Overlooked Role of Willingness to Cannibalize, Journal of Marketing Research, Vol. XXXV, 474-487.

Fragnelli V. and Gambarelli, G. (eds.), 2013a. Open Problems in the Theory of Cooperative Games, Special Issue of International Game Theory Review, 15(2).

Fragnelli V. and Gambarelli, G. (eds.), 2013b. Open Problems in the Applications of Cooperative Games, Special Issue of International Game Theory Review 15(3).

Gambarelli, G., 1990. “A new approach for evaluating the Shapley value”. Optimization, 21, 3, 445-452.

Nijssen E. J., Hillebrand B., Vermeulen P. A. M., Kemp R., 2004. Understanding the Role of Willingness to Cannibalize in New Service Development, Scales Research Reports H200308, EIM Business and Policy Research




DOI: https://doi.org/10.7494/dmms.2015.9.1.27

Refbacks

  • There are currently no refbacks.