Monotonicity of bargaining solutions in relative disagreement utility

Does a party benefit from taking an action which worsens the disagreement point for all parties, but relatively less for themselves? This question has important applications to areas including antitrust, household bargaining, trade negotiations and conflict. I define and study a desirable property of bargaining solutions, which I call “monotonicity in relative disagreement utility” (MRDU). MRDU requires that, if a party’s disagreement utility increases (decreases) more (less) than any other player’s, then their bargaining outcome must strictly improve. The Egalitarian solution is the only cooperative bargaining solution which guarantees MRDU. Other solutions, including the Nash, Kalai-Smorodinsky and non-Egalitarian Proportional solutions, may violate this property under a general bargaining set. Under transferable utility, a solution guarantees MRDU if and only if it belongs to a class of solutions which satisfies four widely used axioms. This class includes the Egalitarian, Nash and Kalai-Smorodinsky solutions.