A good reference is Microeconomic Foundations I: Choice and Competitive Markets, by David Kreps (K), Princeton University Press 2012.

Maskin E, Roberts K. On the Fundamental Theorems of General Equilibrium. Economic Theory. 2008;35(2): 233-240.

Roth A. Misrepresentation and stability in the marriage problem. Journal of Economic Theory, 1984, 383-387.

Zhou L. Stable matchings and equilibrium outcome of the Gale-Shapley's algorithm for the marriage problem. Economics Letters, 1991, 25-29.

Chade H, Eeckhout J. and Smith L. Sorting through search and matching models in economics. Journal of Economic Literature 2017, 493-544. The beginning of the article is required, the rest is good to peruse to get the idea where further research goes.

TerviÃ¶ M. The difference that CEOs make: An assignment model approach. American Economic Review 2008, 642-668. The first, theoretical, part is required reading.

Virag G. High Profit Equilibria in Directed Search Models. Games and Economic Behavior, (71/1) 2011, 224-234.