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OOTP by default uses local times for game starts. However, depending on the start times and the geographical distribution, you might run into issues because of the international date line. For example, 8 pm in Los Angeles on April 6th is 12 noon in Tokyo on April 7th. This gets worse if you have teams in Australia and Hawaii.
I suspect OOTP works on the basis of discrete days, meaning all games set for a given date will be resolved regardless if the actual time difference between the cities would result in one of them being on the next date. But I don't know that for sure.
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