An Approximate Law of One Price in Random Assignment Games

Assignment games represent a tractable model of two-sided mar- kets with transfers. We study the likely properties of the core of randomly generated assignment games. When the joint productivity of every firm and worker has a noise element with a bounded dis- tribution, with high probability all workers who have approximately the same human capital level are paid roughly equal wages, and all firms of similar quality make similar profits. This implies that core allocations vary significantly in balanced markets, but that there is core convergence in even slightly unbalanced markets. The same phe- nomenon occurs when firms’ quality and workers’ human capital level are complementary factors in productivity. When the noise element is unbounded, there may be a large variation in payoffs.