A bargaining problem is a situation in which agents have the possibility of concluding a mutually beneficial agreement while there is a conflict of interests about which agreement to conclude and no agreement may be imposed on any agent without her approval. In real life, an impasse in negotiations is not the only route that may lead to a failure of agreement; they may terminate in disagreement when one of the bargainers unilaterally abandons the negotiation table to take up an opportunity elsewhere. This could be the case of an alternative job in a wage negotiation, a judicial intervention in a divorce proceeding, an alternative buyer/seller in a trade, etc. In all these situations the agent''s decision to take up her outside option is not an accident, it is a strategic decision. This book makes several contributions to the theory of bargaining with outside options, emphasizing situations in which outside options arise by the intervention of arbitrators. The analysis should help shed some light of the impact of such options on the outcome of the bilateral negotiations, by studying how outcomes change depending on who and when may opt out.