In real life, people rarely think endlessly about what others might do. In strategic situations—like negotiations, auctions, or policymaking—we make a few steps of reasoning and then stop. This may be regarded as a deviation from 'full' rationality due to, e.g., cognitive limitations, or because one believes that their co-players are limited themselves. A new study, “Reasoning about Bounded Reasoning,” by Shuige Liu and Gabriel Ziegler, shows that this limited or bounded reasoning can still be seen as rational behavior. The paper develops a simple but rigorous framework that explains how people reason about others and connects two main traditions in game theory.
Game theory studies how people make decisions that depend on others’ choices. Classic theory assumes that players reason endlessly: “I think that you think that I think…” and so on. But experiments show that real people usually stop after a few steps. Understanding this limited reasoning is essential for explaining how people actually behave in markets, coordination problems, and strategic decision-making.
The authors start from two existing ways to model reasoning. The first, used in behavioral game theory, describes reasoning as a sequence of steps. In the level-k model, for example, a “level-0” player acts without strategy, a level-1 player best responds to that, a level-2 player reacts to the level-1 player, and so on. The second, used in epistemic game theory, formalizes reasoning through belief hierarchies—what each player believes about others’ actions and beliefs, and what others believe about them, and so on. Both approaches capture strategic reasoning but describe it in very different formal languages.
Liu and Ziegler’s key contribution is to show that these two perspectives can be expressed in one unified model. They reformulate a standard game to include not just uncertainty about what others will do, but also about how deeply others reason. Each player is assigned a “type” that represents their reasoning level—directly describing what they think about the level of their co-players. For instance, a player might be a “level-1 type,” meaning they assume others are a “level-0 type” playing non-strategically according to an exogenously specified anchor. In turn, a “level-1 type” assumes that others are of “level-2”. This setup turns limits to reasoning into clear belief restrictions that describe what each type believes about others’ possible types and actions.
With this reformulation, the implications of structural behavioral models emerge as special cases within a belief-based epistemic using the appropriate belief restrictions together with sufficiently high reasoning about rationality. In particular, the paper shows how two well-known models—level-k rationalizability (each level assumes opponents think one step less), and cognitive-hierarchy rationalizability (where reasoning levels follow a probability distribution)—fit neatly within the same structure, but the structure can also capture a broad, general benchmark through a new solution concept called downward rationalizability. This structure allows and, in fact, necessitates, the separation of how much of what we observe in experiments comes from the assumed depth of reasoning and how much comes from beliefs about others’ reasoning ability.
The framework also connects bounded reasoning to ideas from mechanism design, a field studying how to design systems or institutions that work well even when participants have limited information. By interpreting bounded reasoning as rational behavior under strategic and structural uncertainty—uncertainty not only about what others will do but also about how they think—the paper gives behavioral models a formal foundation and clarifies when they align with rational decision-making.
In essence, the study shows that thinking only a few steps ahead does not make people irrational. When players expect that others have limited reasoning capacity, it is rational for them to stop early too. This insight bridges behavioral and theoretical economics, offering a unified and transparent way to model how humans actually reason in strategic situations.
About the Authors
Shuige Liu
Research fellow at the Department of Decision Sciences, Bocconi University, Milan. Her research focuses on Epistemic game theory and logic, psychological games, political economy, self-confirming equilibrium and learning, algorithmic game theory, and Kolmogorov complexity and its application in games.
Gabriel Ziegler
Postdoctoral researcher at Freie Universität Berlin. His research focuses on economic theory, with particular emphasis on game theory and information economics. His work examines decision-making under uncertainty, strategic thinking in interactive problems, the foundations of game theory, and matching and school choice. His research has been published on multiple occasions in Games and Economic Behavior.
