Centrally committed markets rely on an independent system operator to determine the commitment and dispatch of generators. This is done by solving a unit commitment model, which is an NP-hard mixed integer program that is rarely (if ever) solved to complete optimality. We demonstrate, using a case study based on the ISO New England system, that near-optimal solutions that are very close to one another in terms of overall system cost can yield very different generator surpluses and prices. We further demonstrate that peaking generators are more prone to surplus differences between near-optimal solutions and that transmission buses that are most prone to binding transmission constraints experience the greatest price fluctuations. Based on these findings, we discuss the potential benefits of a decentralized market design in providing more robust price signals.