Bargaining Set Solution Concepts in Dynamic Cooperative Games

This paper is concerned with the question of defining the bargaining set, a cooperative game solution, when cooperation takes place in a dynamic setting. The focus is on dynamic cooperative games in which the players face (finite or infinite) sequences of exogenously specified TU-games and receive sequences of imputations against those static cooperative games in each time period. Two alternative definitions of what a ‘sequence of coalitions’ means in such a context are considered, in respect to which the concept of a dynamic game bargaining set may be defined, and existence and non-existence results are studied. A solution concept we term ‘subgame-stable bargaining set sequences’ is also defined, and sufficient conditions are given for the non-emptiness of subgame-stable solutions in the case of a finite number of time periods.