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

本文回顾了Myerson和Satterthwaite（1983）对双边贸易机制设计的经典分析，用战略思维的k级模型代替了均衡，并着眼于直接机制。启示原则对k级模型无效，因此在不失去普遍性的情况下，将注意力集中在直接机制上并施加激励相容性是不可行的。但是，如果只有直接的，与k级激励兼容的机制是可行的，并且可以观察到交易者的水平，则Myerson和Satterthwaite对受激励约束的交易者总盈余最大化的机制的定性将定性地归纳为k级模型。如果仅是直接级别，则为k-激励兼容的机制是可行的，但交易者的水平是不可观察的，一般而言，特定的定价机制会在激励约束条件下最大化交易者的总预期盈余。如果直接的，非水平的k激励兼容机制是可行的，并且交易者最好地对它们做出反应，则总的预期盈余最大化机制可能采取完全不同的形式。