The Impossibility of Individually Rational, Pareto-efficient, and Strategy-proof rules for Fractional Matching Markets

The Impossibility of Individually Rational, Pareto-efficient, and Strategy-proof rules for Fractional Matching Markets

For a model of fractional two-sided matching, we show that strategy-proofness, Pareto-efficiency, and individual rationality are incompatible. This result is robust to whether, or to what extent, transfers are possible. Since we prove this impossibility for the domain of preferences with linear utility representations, a natural interpretation of the model is of probabilistic matching. We show that even the weaker ex post Pareto-efficiency is incompatible with strategy-proofness and individual rationality.