Strategically Analogous Mechanisms

This paper studies when strategic understanding acquired in one mechanism can be transferred to another. We introduce a framework in which agents' knowledge is represented as a set of payoff comparisons they can make, and use it to formalize what it means to understand that a strategy profile is an equilibrium. We first apply this framework to mechanisms that are strategically equivalent-that is, share the same game form up to relabeling of actions-and show that agents' understanding of equilibrium transfers across such mechanisms once the relevant action correspondences are explained to them. We then define strategic analogy, a weaker notion that allows not only actions but also types to be remapped, and show that understanding of equilibrium transfers across strategically analogous mechanisms once agents recognize how actions and types correspond. Applications include single-item auctions, scoring auctions, and nonlinear pricing with capacity constraints.