On the Structural Stability of Values for Cooperative Games

• Published in: Journal of optimization theory and applications Vol. 189; no. 3; pp. 873 - 888
• Main Authors: Li, Xianghui, Li, Yang
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Cooperation; Engineering; Equilibrium; Game theory; Games; Graphs; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Stability criteria; Structural stability; Theory of Computation; 91A12; 05C65; Level structure; 91A43; Stability; Coalition formation; Strong equilibrium
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-021-01863-6

It is generally assumed that any set of players can form a feasible coalition for classical cooperative games. But, in fact, some players may withdraw from the current game and form a union, if this makes them better paid than proposed. Based on the principle of coalition split, this paper presents an endogenous procedure of coalition formation by levels and bargaining for payoffs simultaneously, where the unions formed in the previous step continue to negotiate with others in the next step as “individuals,” looking for maximum share of surplus by organizing themselves as a partition. The structural stability of the induced payoff configuration is discussed, using two stability criteria of core notion for cooperative games and strong equilibrium notion for noncooperative games.