Framing Game Theory

A real player sometimes fails to practice hypothetical thinking, which increases the occurrence of anomalies in various situations. This study incorporates psychology into game theory and demonstrates a cognitive method to encourage bounded-rational players to practice correct hypothetical thinking in strategic interactions with imperfect information. We introduce a concept termed "frame" as a description of a synchronized cognitive procedure through which each player decides multiple actions in a step-by-step manner, shaping his (or her) strategy selection. We could regard a frame as the supposedly irrelevant factors from the viewpoint of full rationality. However, this paper theoretically shows that in a multi-unit trading with private values, the ascending proxy auction has a significant advantage over the second-price auction in terms of the bounded-rational players' incentive to practice hypothetical thinking, because of the difference, not in physical rule, but in background frame. By designing a frame appropriately, we generally show that any static game that is solvable in iteratively undominated strategies is also solvable, even if players cannot practice hypothetical thinking without the help of a well-designed frame. We further investigate the possibility that even a detail-free frame design serves to overcome the difficulty of hypothetical thinking. We extend this investigation to the Bayesian environments.