This article explores the application of oblivious equilibrium (OE) to highly concentrated markets. We define a natural extended notion of OE, called partially oblivious equilibrium (POE), that allows for there to be a set of strategically important firms (the 'dominant' firms), whose firm states are always monitored by every other firm in the market. We perform computational experiments that explore the characteristics of POE, OE, and Markov perfect equilibrium (MPE), and find that POE generally performs well in highly concentrated markets. We also derive error bounds for evaluating the performance of POE for cases where MPE cannot be computed.
