Bayesian-Nash vs dominant-strategy implementation with countervailing incentives: the two-type case

We extend the principal/one-agent model with countervailing incentives to a framework in which the principal deals with two agents behaving non-cooperatively and protected by limited liability. Focusing on the two-type case, we show that, beside the situation in which first best is effected even without relying on type correlation, dominant-strategy implementation yields no penalty to the principal, with respect to Bayesian-Nash implementation, when the principal faces, on the opposite, very tight constraints.