On a class of linear-state differential games with subgame individually rational and time consistent bargaining solutions

• Main Author: Simon Hoof
• Format: Article
• Language: English
• Published: Society for the Promotion of Mechanism and Institution Design 2020-12-01
• Series: Journal of Mechanism and Institution Design
• Subjects: differential games; bargaining solutions; time consistency
• Online Access: http://www.mechanism-design.org/arch/v005-1/p_03.pdf

We consider n-person pure bargaining games in which the space of feasible payoffs is constructed via a normal form differential game. At the beginning of the game the agents bargain over strategies to be played over an infinite time horizon. An initial cooperative solution (a strategy tuple) is called subgame individually rational (SIR) if it remains individually rational throughout the entire game and time consistent (TC) if renegotiating it at a later time instant yields the original solution. For a class of linear-state differential games we show that any solution which is individually rational at the beginning of the game satisfies SIR and TC if the space of admissible cooperative strategies is restricted to constants. An application drawn from environmental economics illustrates the results.