This paper considers equilibrium directed search with a finite number of heterogeneous workers and firms, where firms compete in direct mechanisms. Unlike previous findings, Nash equilibrium here does solve the problem of coordination failure. Restricting the match value function to be supermodular, and that firms use truthful strategies also imply positive assortative matching and decentralized trading prices which are consistent with the stable (cooperative equilibrium) outcome. The equilibrium mechanism is not an auction. Instead, to attract better skilled workers, firms post a fixed wage rule and hire the most skilled applicant who applies.