Distortion through modeling asymmetric bargaining power

We study the consequences of modeling asymmetric bargaining power in two- person bargaining problems. Comparing the application of an asymmetric version of a bargaining solution to an upfront modification of the disagreement point, the resulting distortion crucially depends on the bargaining solution concept. While for the Kalai-Smorodinsky solution a weak player benefits from modifying the disagreement point, the situation is reversed for the Nash bargaining solution. There, weaker players are better o in the asymmetric bargaining solution. When comparing the application of the asymmetric versions of the Nash and the Kalai-Smorodinsky solutions, we demonstrate that there is an upper bound for the weight of a player, so that she is better o with the Nash bargaining solution. This threshold is ultimately determined by the relative utilitarian bargaining solution. From a mechanism design perspective, our results provide valuable information for a social planner, when implementing a bargaining solution for unequally powerful players.