### Discussion Paper

## Abstract

In recent years economics agents and systems have become more and more interacting and juxtaposed, therefore the social sciences need to rely on the studies of physical sciences to analyze this complexity in the relationships. According to this point of view the authors rely on the geometrical model of the Möbius strip used in the electromagnetism which analyzes the moves of the electrons that produce energy. They use a similar model in a Corporate Social Responsibility context to devise a new cost function in order to take into account of three positive crossed effects on the efficiency: i) cooperation among stakeholders in the same sector; ii) cooperation among similar stakeholders in different sectors and iii) the stakeholders' loyalty towards the company. By applying this new cost function to a firm's decisional problem the authors find that investing in Corporate Social Responsibility activities is ever convenient depending on the number of sectors, the stakeholders' sensitivity to these investments and the decay rate to alienation. The work suggests a new method of analysis which should be developed not only at a theoretical but also at an empirical level.

## Comments and Questions

I am afraid, I could not follow the main idea of the paper at all. The presentation is certainly very confusing.

In section 2, the authors describe the Hamiltonian (expression 1) of non-interacting electrons on a general N X 2M rectangular strip

(lattice) (Moebius or not). As mentioned, the ...[more]

... external field phase kinetic term could accommodate the changes in the electron spin states, without the twist on the strip. (and can be introduced with the twist without the field term). More importantly, the fermion operators (denoted here by a or a-dagger) here act on the many electron states and change the (dynamic) states accordingly.

After presenting this formalism, the authors go to section 3, where for N stakeholders and 2M 'activities', a "Hamiltonian"

like cost function is formulated in eqn (2) (in page 11), where the a's are now (real) numbers (and no longer operators, with real eigenvalues), with some superficial similarity with Hamiltonian

(1) (in page 8).

How does it help to map? Is there any connection of section 3 with section 2? In any case, the optimization of the cost function in (2) can be done independently, as has been done here, essentially without any reference to electron spin state

changes: the algebra are quite different: how are the operator algebra required to deal with the Hamiltonian (1) in section 2 (which is not discussed here of course) useful for the real number algebra and optimization of the cost function (2) in section 3?

There seems to be some serious flaws in the design of the paper, or I am missing perhaps something important. The presentation in the paper needs to be much more clear and straightforward before the merit of the paper can be judged.

Answer to comment 1

see attached file

see attached file

see attached file

Answer_to_referee2_by_the authors

Revised paper