A Formal Separation Between Strategic and Nonstrategic Behavior

TL;DR

This paper introduces a formal framework to distinguish strategic from nonstrategic behavior in game theory, clarifying the boundary and providing a rigorous characterization of nonstrategic decision rules.

Contribution

It proposes a new formal definition of nonstrategic behavior that encompasses existing rules and clearly separates it from strategic behavior.

Findings

The characterization captures all known nonstrategic decision rules.

Behavior satisfying the characterization is mathematically distinct from strategic behavior.

Provides a rigorous basis for classifying decision-making in bounded rationality models.

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.