Bargaining with a ruler
Let \(G\) be an \(n+1\) player game. Player 0 is called the ruler and plays a special role, in contrast to the remaining \(n\) players, indexed by \(i\), \(i>0\). Players 1 to \(n\) play a noncooperative game among themselves, while each of them plays a 2-person bargaining game with the ruler. Let \(G_{-i}\) be the reduced game which results when player \(i\) refuses to bargain with the ruler. The disagreement point of the bargaining game between player \(i\) and the ruler is determined by the payoff \(i\) gets in \(G_{-i}\). The paper presents a set of axioms for a solution to this game, some in the spirit of the axioms for Nash's bargaining solution, but also including a crucial consistency condition. The main result of the paper is to axiomatize a unique solution for \(G\). This solution is interpreted in terms of monopolist offering a cost-saving innovation to an industry in Cournot competition. Other interesting interpretations of this result are also possible.
scientific article; zbMATH DE number 70154