Assignment Games with Externalities And Matching-Based Competition

We develop a model of assignment games with pairwise-identity-dependent externalities. A concept of conjectural equilibrium is proposed, and the universal conjecture is shown to be the necessary and sufficient condition for the general existence of equilibrium. We then apply the solution concept to a matching-based Cournot model in which the unit production cost of a firm depends on both the technology of the firm and the human capital of the manager hired, and show that if technology and human capital are complementary, the positive assortative matching (PAM) is a stable matching under rational expectations, or even if firm technology and human capital are substitutable yet the substitutive effect is dominated by the marginal effects of technology and human capital, the PAM is still a rational stable matching.However, if the substitutive effect on the unit production cost is sufficiently strong or the market demand is sufficiently high, the negative assortative matching is a rational stable matching.