This paper considers multiple principals' competing mechanism design
problems in directed search markets with frictions. It proposes the notion
of a robust DIC-response equilibrium where a principal responds to a
competing principal's deviation with a DIC (dominant-strategy incentive
compatible) direct mechanism and following his deviation to any arbitrary
mechanism a principal cannot gain in every continuation equilibrium. In a
robust DIC-response equilibrium, a principal only needs to know the identity of the deviating principal but not the whole market information that agents have in the market. The robustness can be checked with a principal's deviation to only BIC (Bayesian incentive compatible) direct mechanism. This paper provides a sharp characterization of a robust DIC-response equilibrium allocations where the greatest lower bound of a principal's payoff is expressed in terms of incentive compatible direct mechanisms. It also discusses the implications of how those results can be applied to directed search models including the BIC-DIC equivalence.