We introduce the Multiagent Agreement Problem (MAP) to represent a class of multiagent scheduling problems. MAP is based on the Distributed Constraint Reasoning (DCR) paradigm and requires agents to choose values for variables to satisfy not only their own constraints, but also equality constraints with other agents. The goal is to represent problems in which agents must agree on scheduling decisions, for example, to agree on the start time of a meeting. We investigate a challenging class of MAP -- private, incremental MAP (piMAP) in which agents do incremental scheduling of activities and there exist privacy restrictions on information exchange. We investigate a range of strategies for piMAP, called bumping strategies. We empirically evaluate these strategies in the domain of calendar management where a personal assistant agent must schedule meetings on behalf of its human user. Our results show that bumping decisions based on scheduling difficulty models of other agents can significantly improve performance over simpler bumping strategies.