We develop a search model of mergers and acquisitions (M&A), intermediated by private equity (PE) funds which may face pressure to sell. The selling pressure leads to the development of a secondary buyout (SBO) market, enabling PE funds to bail each other out. Interestingly, an increase in the number of PE funds can improve each fund’s value, because the enhanced benefits of SBOs can prevail over the reduction in value from narrower buy-sell spreads due to more intense competition. We calibrate the model using data for the US middle market and find that PE funds could lose 64% of their valuation without SBOs. Moreover, the increase in the number of funds from 2000 to 2017 contributes to a 48% increase in fund valuation due to the complementarity among funds. Nevertheless, our model predicts that this mechanism might have peaked in 2021, and more PE funds could decrease their value.

We investigate the testable implications of the theory of stable matchings. We provide a characterization of the matchings that are rationalizable as stable matchings when agents' preferences are unobserved. The characterization is a simple nonparametric test for stability, in the tradition of revealed preference tests. We also characterize the observed stable matchings when monetary transfers are allowed and the stable matchings that are best for one side of the market: extremal stable matchings. We find that the theory of extremal stable matchings is observationally equivalent to requiring that there be a unique stable matching or that the matching be consistent with unrestricted monetary transfers.