Matching with Continuous Bidirectional Investment

We develop a one-to-one matching game where men and women (interns and employers, etc.) exert costly efforts to produce benefits for their partners. We prove the existence and Pareto optimality of interior stable allocations, and we characterize the relationship between players’ costs, efforts, benefits, and payoffs in such allocations. We find, for instance, that men and women with lower marginal costs of effort choose to provide their partners with higher benefits by exerting more effort; in return, they receive higher benefits from their partners and attain higher payoffs. ∗Department of Economics, University of Arizona, email: [email protected], copyright 2014. My thanks to Andreas Blume, Federico Echenique, Isa Hafalir, Hans Haller, Asaf Plan, Marek Pycia, Mark Walker, John Wooders, and Bumin Yenmez as well as to seminar participants at the University of Arizona, the University of California Los Angeles, and the 2014 Southwest Economic Theory Conference for many helpful discussions, comments, and suggestions. Comments are welcome! (The most recent version of this paper is available at https://sites.google.com/site/jamescdfisher/research.)