Strategyproofness, Leontief Economies and the Kalai-Smorodinsky Solution

We present new characterizations of the Raiffa and Kalai-Smorodinsky solutions based on strategyproofness of an allocation mechanism for an underlying economy with Leontief preferences. Our first result shows that the 2-player Kalai-Smorodinsky solution is the unique bargaining solution which if Efficient, Symmetric, Scale Invariant and Strategyproof on a Leontief economy. Next we consider the class of weighted DRF mechanisms which are of great practical interest and are group strategyproof. We show that they satisfy and are characterized by a new proportional consistency axiom, Ratio Consistency, and that the multi-player Raiffa solution is the unique unique weighted DRF mechanism that generates a bargaining solution. Finally, we present a result that complements Imai’s characterization of the multi-player lexicographic-Kalai-Smorodinsky solution. We show that strategyproofness, combined with other basic axioms, implies a version of the individually rational individual monotonicity which when combined with the Independence of Irrelevant Alternatives other than Ideal Point axiom characterizes the lexicographic-Kalai-Smorodinsky solution for 3-players and is conjectured to characterize it for an arbitrary number of players. These results shed new light and provide new insights into the study of mechanisms on Leontief economies and bargaining theory as well as having practical applications in the design of modern data-centers and cloud computing platforms.