Conflicts exist in multi-agent systems. Agents have different interests and desires. Agents also hold different beliefs and may make different assumptions. To resolve conflicts, agents need to better convey information between each other and facilitate fair negotiations that yield jointly agreeable outcomes. In this paper, we present a two-agent conflict resolution scheme developed under Assumption-Based Argumentation (ABA). Agents represent their beliefs and desires in ABA. Conflicts are resolved by merging conflicting arguments. We also discuss the notion of fairness and the use of argumentation dialogue in conflict resolution.