A General Model for Pareto Optimal Multi-Attribute Negotiations

The generative model presented in this chapter focuses on the above issues, which have yet been simultaneously considered in the existing literature on multi-attribute negotiations. First, it is widely assumed, in the prior work, that agents' utility functions are explicitly given (e.g. [1, 2, 9, 19]). Although this assumption avoids the diffculty of exhaustive preference elicitation, it neglects the fact that usually in reality both parties (or at least one of the parties) may have no prepared utility functions before the negotiation starts. For example, when an individual goes to a dealer to buy a car, she seldom can have an explicit utility function over the characteristics of the car and various accessorial packages, although the dealer may possibly have a prepared utility function since she normally has a big organization and is the designer of the contracts. In such situations, the existing negotiation models may not be able to be directly applied. Second, to even simplify the reasoning and computation in the negotiation, most of the existing literature assumes agents have relatively simple (linear additive) utility functions [1, 2, 10, 18] or binary valued issues [5, 16, 24], which cannot represent the general situations. For example, the utility functions that are widely used in the economics field to represent consumer utility on multiple-goods consumption and have been shown having supports from real-world situations are usually non-linear, e.g., Cobb-Douglas utility function, constant elasticity of substitution (CES) utility function and quadratic utility functions [22]. Third, a protocol that can not only assist agents to make offers efficiently in the n-dimensional space but also give agents sufficient decision flexibility is absent in the prior work. As mentioned above, agents face an n-dimensional space to search for an offer in each step and the situation may change with time as the negotiation goes on. It becomes essential of the negotiation model to have an efficient protocol that can assist agents to negotiate in a timely manner with the updating of the negotiation history. Moreover, as we are interested in the domain where agents are self-interested, which is more common in reality, a protocol should also provide agents sufficient decision flexibility, for instance, the right to select an offer to make and the right to accept a given offer. Finally, Pareto optimality is another key aspect that usually has been overlooked [1,13,18] or has not been addressed in the general negotiation situations [9, 16, 24] in the prior work.

The rest of the chapter is organized as follows. Section 2 presents the model, in which we first introduce the modeling setup, and then discuss the negotiation protocol, negotiation strategy and the mediator's problem. Section 3 provides a numerical analysis of our model with different examples as well as a discussion on the computational burden. In Sect. 4, we compare our model to previous work in this area. Section 5 concludes and outlines the future work.