Cohomology has appeared in game theoretic research on equilibrium refinements. Loosely speaking, John Nash's 1951 original notion of an equilibrium point does too little to limit the set of 'reasonable' outcomes. A variety of so-called 'equilibrium refinements' sprang up in the economic literature intended to address this. A common theme in many of them was robustness to perturbation (if one perturbs the underlying game played, one would wish that 'nearby fixed point problems have nearby solutions').

In 1989 JF Mertens formulated a notion of a stable equilibrium over two papers that relies on the cohomological essentiality of a projection map from the graph of the equilibrium correspondence to the space of games (the two papers may be found here and here) to arrive at a solution concept with a number of normatively reasonable properties.