The reactive bargaining set: Structure, dynamics and extension to NTU games

The reactive bargaining set (Granot [1994]) is the set of outcomes for which no justified objection exists. Here, in a justified objection the objector first watches how the target tries to act (if he has such an option), and then reacts by making a profit and ruining the target's attempt to maintain his share. In this paper we explore properties of the reactive bargaining set, set up the system of inequalities that defines it, and construct a dynamic system in the sense of Stearns' transfer scheme that leads the players to this set. We also extend the definition of the reactive bargaining set to NTU games in a way that keeps it nonempty. To shed light on its nature and its relative ease of computation, we compute the reactive bargaining set for games that played important role in the game theory literature.