Against the orthodox view of the Nash equilibrium as “the embodiment of the idea that economic agents are rational” (Aumann, 1985, p 43), some theorists have proposed ‘non-classical’ concepts of rationality in games, arguing that rational agents should be capable of improving upon inefficient equilibrium outcomes. This paper considers some implications of these proposals for economic theory, by focusing on institutional design. I argue that revisionist concepts of rationality conflict with the constraint that institutions should be designed to be incentive-compatible, (...) that is, that they should implement social goals in equilibrium. To resolve this conflict, proponents of revisionist concepts face a choice between three options: (1) reject incentive compatibility as a general constraint, (2) deny that individuals interacting through the designed institutions are rational, or (3) accept that their concepts do not cover institutional design. I critically discuss these options and I argue that a more inclusive concept of rationality, e.g. the one provided by Robert Sugden’s version of team reasoning, holds the most promise for the non-classical project, yielding a novel argument for incentive compatibility as a general constraint. (shrink)