An analysis of feasible solutions for multi-issue negotiation involving nonlinear utility functions

This paper analyzes bilateral multi-issue negotiation between selfinterested agents. Specifically, we consider the case where issues are divisible, there are time constraints in the form of deadlines and discount factors, and the agents have different preferences over the issues. Given these differing preferences, it is possible to reach Pareto-optimal agreements by negotiating all the issues together using a package deal procedure (PDP). However, finding equilibrium strategies for this procedure is not always computationally easy. In particular, if the agents’ utility functions are nonlinear, then equilibrium strategies may be hard to compute. In order to overcome this complexity, we explore two different solutions. The first is to use the PDP for linear approximations of the given nonlinear utility functions. The second solution is to use a simultaneous procedure (SP) where the issues are discussed in parallel but independently of each other. We then compare these two solutions both in terms of their computational properties (i.e., time complexity of computing an approximate equilibrium and the associated error of approximation) and their economic properties (i.e., the agents’ utilities and social welfare of the resulting outcome). By doing so, we show that an approximate equilibrium for the PDP and the SP can be found in polynomial time. In terms of the economic properties, although the PDP is known to generate Pareto optimal outcomes, we show that, in some cases, which we identify, the SP is better for one of the two agents and also increases the social welfare.