This thesis is devoted to the study of bargaining using the methods of non-cooperative game theory. In Part I (chapters 1 and 2) we examine the role of commitment in bilateral bargaining. Two different notions of commitment in bargaining are explored in two different non-cooperative infinite-time horizon sequential games with complete and perfect information. In Part II (chapters 3 and 4) we examine the role of outside options in bilateral bargaining. Two models are presented, each model is a non cooperative infinite-time horizon sequential game with complete information. The two models differ in their approach to modelling the interlacing of the search and bargaining processes. In the final part of this thesis, Part III (chapter 5)z we present a a of decentralised market, based on the idea that the agents of the market search for partners with whom to trade and when a buyer and a seller meet they initiate a sequential bargaining process over the terms of trade.