A simple status quo that ensures participation (with application to efficient bargaining)

We consider Bayesian incentive-compatible mechanisms with independent types and either private values or interdependent values that satisfy a form of "congruence." We show that in these settings, interim participation constraints are satisfied when the status quo is the randomized allocation that has the same distribution as the equilibrium allocation in the mechanism. Moreover, when utilities are convex in the allocation, we can instead satisfy participation constraints with the deterministic status quo equal to the expected equilibrium allocation in the mechanism. For quasilinear settings, these observations imply the possibility of efficient bargaining when the status quo specifies the expected efficient decision provided that the total surplus is convex in the decision.