A finite decentralized marriage market with bilateral search

I study a model in which a finite number of men and women look for future spouses via random pairwise meetings. The central question is whether equilibrium marriage outcomes are stable matchings when search frictions are small. The answer is they can but need not be. For any stable matching there is an equilibrium leading to it almost surely. However there may also be equilibria leading to an unstable matching almost surely. A restriction to simpler strategies or to markets with aligned preferences rules out such equilibria. However unstable-even Pareto-dominated-matchings may still arise with positive probability under those two restrictions combined. In addition, inefficiency due to delay may remain significant despite vanishing search frictions. Finally, a condition is identified under which all equilibria are outcome equivalent, stable, and efficient.