Efficient mechanisms for level-k bilateral trading

This paper revisits Myerson and Satterthwaite's (1983) classic analysis of mechanism design for bilateral trading, replacing equilibrium with a level-k model strategic thinking focusing on direct mechanisms. The revelation principle fails models, so restricting attention to mechanisms imposing incentive-compatibility are not without loss generality. If, however, only direct, level-k-incentive-compatible feasible traders' levels observable, characterization that maximize total surplus subject incentive constraints generalizes qualitatively models. If but generically particular posted-price maximizes expected constraints. non-level-k-incentive-compatible traders best respond them, surplus-maximizing may take completely different forms.