Research Summary This article explicitly introduces cognitive considerations into the treatment of strategic interactions, using the value‐based framework as an extended example. Through real‐world examples and prior empirical findings, it shows that many of the implicit assumptions of the framework are regularly violated in practice when actors simplify their complex realities into incomplete, inaccurate mental models. These violations lead to outcomes that are often contrary to the predictions of the classical framework. As initial steps toward developing a cognitively grounded theory of strategic interactions, the article characterizes the core components of strategic mental models that might form the foundation of such a theory and then lays out some open questions that this theory would need to address. These questions, when answered, can point to novel cognitive capabilities. Managerial Summary This article argues that a realistic analysis of interactions between strategic agents requires us to include the mental models, that is, belief systems, of those agents into the analysis. Real‐world examples and prior empirical findings are used to show that if such mental models are not accounted for, the outcomes predicted by the analysis could be quite different from those obtained in reality. The article identifies a few key aspects of these strategic mental models that deserve attention. It also identifies a few central questions that, when answered, could allow firms to develop novel cognitive capabilities that confer competitive advantage.