TITLE:
The Solidarity Value as a Probabilistic Solidarity Value
AUTHORS:
Serge B. Nlénd Oum, Lawrence Diffo Lambo
KEYWORDS:
Game Theory, Shapley Value, Solidarity Value, Probabilistic Value, Probabilistic System
JOURNAL NAME:
Theoretical Economics Letters,
Vol.10 No.6,
December
31,
2020
ABSTRACT: Our paper focuses on two evolutions in the Shapley
value: on the one hand, Radzik and Nowak’s solidarity value (in short s-value)
allows the needy to receive solidarity help from privileged players; on the
other hand, Weber’s concept of probabilistic value provides a setting where the probability of
joining a coalition depends both on the player being picked to join and on the
coalition being constituted, unlike for the Shapley value which assumes equal
chance to all players still waiting aside. In a context where the solidarity of
Nowak and Radzik is the guiding policy for profit sharing, what is the meaning
of this Weber’s idea of probabilistic value? We come out with a large class of
values, called Probabilistic solidarity values (ps-values), that comprises the s-value. Our two
main results are a characterization of Radzik-Nowak’s solidarity value as a
specific Probabilistic solidarity value and a characterization of symmetric
ps-values which exhibit a rational intuitive property found in literature on
the per-capita productivity.