A Formal Separation Between Strategic and Nonstrategic Behavior
James R. Wright, Kevin Leyton-Brown
TL;DR
The paper tackles the lack of a crisp boundary between strategic and nonstrategic behavior in bounded rationality by formalizing two minimal conditions—$\text{other\ responsiveness}$ and $\text{dominance\ responsiveness}$—to define strategic behavior. It then introduces elementary behavioral models, where a single potential summarizes outcomes via a $\varphi$ that is either dictatorial or non-encoding, and shows these models are strongly nonstrategic, while many classical models (e.g., Nash, QRE, level-$k$, CH) are minimally strategic. The authors further analyze convex combinations and filtering of elementary models, showing such mixtures can be weakly nonstrategic and may fail to capture certain strategic dynamics. The work provides a structural, non-empirical separation between strategic and nonstrategic models, with implications for constructing level-0 specifications and understanding the computational/strategic properties of behavioral predictions.
Abstract
It is common to make a distinction between "strategic" behavior and other forms of intentional but "nonstrategic" behavior: typically, that strategic agents model other agents while nonstrategic agents do not. However, a crisp boundary between these concepts has proven elusive. This problem is pervasive throughout the game theoretic literature on bounded rationality and particularly critical in parts of the behavioral game theory literature that make an explicit distinction between the behavior of "nonstrategic" level-0 agents and "strategic" higher-level agents (e.g., the level-k and cognitive hierarchy models). Overall, work discussing bounded rationality rarely gives clear guidance on how the rationality of nonstrategic agents must be bounded, instead typically just singling out specific decision rules (e.g., randomizing uniformly, playing toward the best case, optimizing the worst case) and informally asserting that they are nonstrategic. In this work, we propose a new, formal characterization of nonstrategic behavior. Our main contribution is to show that it satisfies two properties: (1) it is general enough to capture all purportedly "nonstrategic" decision rules of which we are aware in the behavioral game theory literature; (2) behavior that obeys our characterization is distinct from strategic behavior in a precise sense.