An economic agent (player) sometimes fails to correct hypothetical (contingent) thinking, which may increase the occurrence of anomalies in various economic situations. This paper demonstrates a method to encourage such a boundedly rational player to practice correct hypothetical thinking in strategic situations with imperfect information. We introduce a concept termed “frame” as a description of a synchronized cognitive procedure, through which a player decides multiple actions in a step-by-step manner, shaping his (or her) strategy selection as a whole. We could regard a frame as a supposedly irrelevant factor from the viewpoint of full rationality. However, this paper theoretically shows that in a multi-unit auction with private values, the ascending proxy auction has a significant advantage over the second-price auction in terms of the boundedly rational players' incentive to practice correct hypothetical thinking, because of the difference, not in physical rule, but in background frame, between these auction formats. By designing frames appropriately, we generally show that any static game that is solvable in iteratively undominated strategies is also solvable even if players cannot practice correct hypothetical thinking without the help of a well-designed frame.