Alternating-offers bargaining in one-to-many and many-to-many settings

Automating negotiations in markets where multiple buyers and sellers operate is a scientific challenge of extraordinary importance. One-to-one negotiations are classically studied as bilateral bargaining problems, while one-to-many and many-to-many negotiations are studied as auctioning problems. This paper aims at bridging together these two approaches, analyzing agents’ strategic behavior in one-to-many and many-to-many negotiations when agents follow the alternating-offers bargaining protocol (Rubinstein Econometrica 50(1), 97–109, 33). First, we extend this protocol, proposing a novel mechanism that captures the peculiarities of these settings. Then, we analyze agents’ equilibrium strategies in complete information bargaining and we find that for a large subset of the space of the parameters, the equilibrium outcome depends on the values of a narrow number of parameters. Finally, we study incomplete information bargaining with one-sided uncertainty regarding agents’ reserve prices and we provide an algorithm based on the combination of game theoretic analysis and search techniques which finds agents’ equilibrium in pure strategies when they exist.