I study split-pie bargaining problems between two agents. In chapter two, the types of both agents determine the value of outside options -- I refer to these as interdependent outside options. Since a direct mechanism stipulates outcomes as functions of agents' types, a player can update beliefs about another player’s type upon receiving a recommended outcome. I term this phenomenon as information leakage. I discuss binding arbitration, where players must stay with a recommended outcome, and non-binding arbitration, where players are not obliged to stay with an allocation. The total pie is reduced if the outcome is an outside option. With respect to efficiency, I derive a necessary and sufficient condition for first best mechanisms. These are mechanisms that assign zero probability to outside options for every report received. The condition describes balanced forces in conflict (outside options) and is the same in the cases of binding and non-binding arbitration. I also show a strong link between conflict and information: when conflict exists, information leakage occurs. Hence, non-binding arbitration may seem more restrictive than binding arbitration. To analyze why this is the case, I solve for second best mechanisms with binding arbitration and find a condition under which they can be implemented under non-binding arbitration. Thus, I show that non-binding arbitration can be as effective as binding arbitration in terms of efficiency. I also examine whether the equivalence between binding and non-binding arbitration can cease to hold, and provide analysis of why this happens. In chapter three, the bargaining problem entails no uncertainty but rather envy. Players can feel envy about the allocation of the other player. The Nash Bargaining solution is obtained in this context and some comparative statics are shown. The introduction of envy makes the more envious party a tougher negotiator.