Bargaining over multiple issues in finite horizon alternating-offers protocol

In this paper we study multi issue alternating-offers bargaining in a perfect information finite horizon setting, we determine the pertinent subgame perfect equilibrium, and we provide an algorithm to compute it. The equilibrium is determined by making a novel use of backward induction together with convex programming techniques in multi issue settings. We show that the agents reach an agreement immediately and that such an agreement is Pareto efficient. Furthermore, we prove that, when the multi issue utility functions are linear, the problem of computing the equilibrium is tractable and the related complexity is polynomial with the number of issues and linear with the deadline of bargaining.