Fair division in Shaplay sense - case studies

Abstract

Objectives The aim of the work is to determine the Shapley value for the considered cases, important from the point of view of financial management. Material and methods Case descriptions, game theory, Shapley value Results In the examples considered regarding the construction of a private common road and the division of profits between the company owner and his employees, the Shapley value represents a fair division, but contrary to the social sense of justice. In the first example, a pre-imposed, equal or proportional division of costs could only satisfy one of the considered players, while in the second, although the example is idealized (e.g. it does not take into account competition on the market), the result allows to justify why the boss (company owner, president) earns incomparably more than his employees. Conclusions The work shows that even in a very simplified situation, various division concepts are possible, which may contradict each other and other requirements for decision-making methods.

Keywords

• shapley value
• fair division
• n-person games
• game theory
• cost sharing