Alfred Galichon, Professor of Economics, Sciences Po

Abstract: We consider a model of matching with imperfectly transferable utility, including as special cases both the transferable utility (Monge-Kantorovich) and nontransferable utility (Gale-Shapley) models. Versions of this model capture a number of situations in economics: marriage, the labor market, industrial alliances, school choice, etc. We provide a unified framework for equilibrium characterization and comparative statics in a version of the model where agents have a random utility component which introduces stochasticity in their choice problem. Outside of the transferable utility case, the equilibrium does not have a variational formulation. However, we show that an analytically and computationally tractable solution can be given by using the concept of 'entropy of choice', a generalization of classical entropy linked to the individual optimal choice problems. This method allows the study and the computation of non-variational equilibrium transportation problems which are relevant in Economics, and cannot be tackled using the theory of optimal transportation. We derive implications for identification and comparative statics