This paper introduces a family of domains of bargaining problems allowing for non-convexity. For each domain in this family, single-valued bargaining solutions satisfying the Nash axioms are explicitly characterized as solutions of the iterated maximization of Nash products weighted by the row vectors of the associated bargaining weight matrices. This paper also introduces a simple procedure to standardize bargaining weight matrices for each solution into an equivalent triangular bargaining weight matrix, which is simplified and easy to use for applications. Furthermore, the standardized bargaining weight matrix can be recovered from bargaining solutions of simple problems. This recovering result provides an empirical framework for determining the bargaining weights.
Bibliographical noteWe are grateful for comments from Youngsub Chun, Pradeep Dubey, Mamoru Kaneko, Abraham Neyman, Hans Peters, Yair Tauman, Shmuel Zamir, Yongsheng Xu, Junjie Zhou, an anonymous referee, and seminar participants at a number of universities and conferences.
© 2023 Walter de Gruyter GmbH, Berlin/Boston 2023.
- bargaining problem
- Nash product
- iterated solution
- weight matrix