We argue that behavioral science models of online content-sharing overlook the role of strategic interactions between users. Borrowing from accuracy-nudges studies decision-theoretic models, we propose a basic game model and explore special cases with idealized parameter settings to identify refinements necessary to capture real-world online social network behavior. Anticipating those refinements, we sketch a strategic analysis of content amplification and draw a connection between Keynes's beauty contest analogy and recent social-epistemological work on echo chambers. We conclude on the model's prospects from analytical and empirical perspectives.