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It sounds like Assigner B either made a mistake or expects you to accept his assignments. It looks like you are going to have to figure out how to balance multiple assigners.
Factors that can be considered are:
Long term potential- Which assigner has the most to offer in the long term. If Assigner A has 20 schools and Assigner B has 40 schools. B likely has more potential.
Assignment patterns- Does the Assigner give everybody 5 games regardless of seniority on the staff and skill level. Or does he give more games to his top officials.
Quality of assignments- Are one assigner's games more attractive than the others. Higher quality of play, more convenient locations, better partners all can make an assignment more attractive.
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