This paper explores the application of oblivious equilibrium to concentrated industries. We define an extended notion of oblivious equilibrium that we call partially oblivious equilibrium (POE) that allows for there to be a set of “dominant firms”, whose firm states are always monitored by every other firm in the market. We perform computational experiments that show that POE are often close to MPE in concentrated industries with characteristics similar to real world industries even when OE are not. We derive error bounds for evaluating the performance of POE when MPE cannot be computed. Finally, we demonstrate an important trade-off facing empirical researchers between implementing an equilibrium concept that is computationally light in a richer economic model, and implementing MPE in a simpler one.