A Formal Separation Between Strategic and Nonstrategic Behavior

2018-12-30

ACM Conference on Economics and Computation

AI Summary

This paper addresses the ambiguous boundary between “strategic” and “non-strategic” behavior in behavioral game theory—particularly the lack of a rigorous, formal definition of non-strategic behavior under bounded rationality. To resolve this, we introduce the first axiomatic characterization of non-strategic behavior: actions that do not model others’ beliefs or decision processes. Our definition subsumes all canonical non-strategic rules in the literature—including Nash indifference, level-0 reasoning in cognitive hierarchy models, and reactive heuristics—and is provably disjoint from any strategic behavior in a mathematically precise sense. Methodologically, we integrate tools from game theory, formal logic, and decision theory, constructing an axiom system and establishing separation via model-theoretic proofs. The resulting framework provides the first universally applicable and decidable formal foundation for modeling bounded rationality, designing multi-agent systems, and advancing cognitive hierarchy theory.

Abstract

It is common in multiagent systems 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 and informally asserting them to be nonstrategic (e.g., truthfully revealing private information; randomizing uniformly). 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.

Problem

• Define nonstrategic behavior formally
• Distinguish strategic from nonstrategic behavior
• Generalize nonstrategic decision rules

Innovation

• Formal characterization of nonstrategic behavior
• Distinct properties from strategic behavior
• Captures all known nonstrategic decision rules