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Behavioral game theory models serve two purposes: yielding insights into how human decision-making works, and predicting how people would behave in novel strategic settings. A system called GameNet represents the state of the art for predicting human behavior in the setting of unrepeated simultaneous-move games, combining a simple "level-k" model of strategic reasoning with a complex neural network model of non-strategic "level-0" behavior. Although this reliance on well-established ideas from cognitive science ought to make GameNet interpretable, the flexibility of its level-0 model raises the possibility that it is able to emulate strategic reasoning. In this work, we prove that GameNet's level-0 model is indeed too general. We then introduce ElementaryNet, a novel neural network that is provably incapable of expressing strategic behavior. We show that these additional restrictions are empirically harmless, leading ElementaryNet to statistically indistinguishable predictive performance vs GameNet. We then show how it is possible to derive insights about human behavior by varying ElementaryNet's features and interpreting its parameters, finding evidence of iterative reasoning, learning about the depth of this reasoning process, and showing the value of a rich level-0 specification.
