Solidarity and monotonicity in cooperative game theory

• Applicant: Professor Dr. André Casajus, since 11/2015
• Subject Area: Economic Theory ; Accounting and Finance
• Term: from 2014 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 261749485

Recently, the reconciliation of solidarity and performance orientation attracted a lot of attention in the literature of cooperative game theory. Our project contributes to this research program. The Shapley value (Shapley 1953) probably is the most important single-valued solution concept of cooperative game theory. Young (1985) shows that the Shapley solution is characterized by three economically sound axioms: efficiency, symmetry, and strong monotonicity. While efficiency and symmetry are rather "innocuous" standard axioms, strong monotonicity reflects the strict performance orientation of the Shapley value. Instead of the strong monotonicity axiom, van den Brink et al. (2013) consider a weak monotonicity axiom. This weak monotonicity axiom allows to combine performance orientation on the one hand and solidarity considerations on the other hand. However, the implications of the weak monotonicity axiom have not sufficiently been explored so far. To do this is the first aim of this project. The formation of groups within the society is an important question in social sciences. In cooperative game theory, attempts have been made to explain the formation of groups by help of stability considerations. Within these attempts, solidarity among the players has not yet been taken into account. In this project, we examine whether and to what extent solidarity promotes the formation of groups. Finally, the Shapley solution and its characterizations form the basis for many other applications and allocation rules as well as their foundations. In this project, we look at established applications through the lens of solidarity.

• DFG Programme: Research Grants
• International Connection: France, Japan, Netherlands, South Korea
• Participating Persons: Professor Johannes René van den Brink, Ph.D.; Professor Sylvain Béal, Ph.D.; Professor Youngsub Chun, Ph.D.; Professor Yukihiko Funaki, Ph.D.; Amandine Ghintran, Ph.D.
• Ehemaliger Antragsteller: Dr. Frank Hüttner, until 11/2015