Formalizing the Boundary Between Strategic and Nonstrategic Reasoning
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Research in multiagent systems often does not draw a clear distinction between strategic behavior and other forms of intentional (e.g., boundedly rational) action, which are broadly lumped under the term "nonstrategic". If we are already confident that all agents in a system are perfectly rational, as often envisioned by game theory, this issue may not be important. But in reality---particularly when modeling human behavior---it would be helpful to base these concepts on a firmer foundation. Notably, some of the most prominent models of human behavior in multiagent systems (level-k and cognitive hierarchy models) rely crucially on an explicit distinction between the behavior of nonstrategic level-0 agents and strategic higher-level agents. However, even work that uses these models typically fails to formally characterize what is meant by nonstrategic behavior; instead, authors single out specific decision rules that they informally assert to be nonstrategic (e.g., truthfully revealing private information, uniformly randomizing over actions, etc.). In this work, we give an explicit definition of the distinction between strategic and nonstrategic behavior. Our main contribution is a formal mathematical criterion, dubbed an elementary agent model, that is general enough to capture all of the nonstrategic decision rules of which we are aware in the literature. We prove that rules that satisfy this criterion are distinct from strategic behavior in a precise sense. Remarkably, several special cases of Nash equilibrium which are known to be computationally easy also turn out to satisfy this criterion.
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