Fuzzy Preferences for Multi-Criteria Negotiation

We are interested in how cooperation can arise in types of environments, such as open systems, where little or nothing is known about the other agents. We view the negotiation problem as a strategic and communication rich process between different local preference/decision models. This contrasts with the classical cooperative game theoretic (axiomatic) view of negotiation process as a centralized and linear optimization problem. Although unconcerned with the processes of negotiation, such axiomatic models of negotiation (in particular those of mechanism design tradition) has assumed optimality can be achieved through design of normative roles of interactions that incents agents to act rationally (Neumann & Morgemstern 194.4),(Rosenschein & Zlotkin 1994),(Binmore 1990),(Shehory & Kraus 1995),(Sandholm 1999). Likewise, in eration research the focus is the design of optimal solution algorithms based on mathematical programming techniques (Kraus 1997),(Ehtamo, Ketteunen, & Hamalainen 2001),(Heiskanen 1999),(Teich et al. 1996). In both cases optimality is achieved because: a) the geometry of the solution set is assumed to be described by a closed and convex set (therefore there is a bounded number of solution points), b) the objective functions of the individuals (the utility function) are concave and differentiable and c) some global information (such as the actual utility of the agents or the utility gradient increase vector (Ehtamo, Ketteunen, & Hamalainen 2001)) is stored by a (hypothetical) centralized mediator that (incents) acts to direct problem solvers towards pareto-optimality. However, although analytically elegant, such optimality can not be guaranteed in decentralized autonomous agent systems operating in open environments where information is sparse. Indeed, lack of information or knowledge oftenteads to inefficiencies and suboptimality in the negotiated outcome. A classic solution for handling such uncertainties is to assume agents have means to compute conditional probabilities and formulate subjective expected utilities. However this approach is problematic. Firstly, assigning prior probabilities is practically impossible. Even if assigning prior probabilities was practically achievable for interactions that are repeated (hence permitting the use of probability update mechanisms such as Bayes rule (Raiffa 1968)), the same is not true for encounters in open systems. In such environments the prior probabilities may simply be wrong, a fact that is exacerbated by the one-off nature of encounters which prevents the update of prior distributions. Secondly, the formulation of decisions based on subjective expected utility introduces the silent out-guessing problem (Young 1975)--the agent designer’s choice of probabilities is based on guesses about the probable choices of others, whose choice in turn is dependent on the guesses about the probable choices of the first, and so on. One solution to this problem is the design of mechanisms that model degrees of beliefs an agent can hold. We have previously motivated and shown how a fuzzy model is well suited for this class of problems (Faratin, Sierra, & Jennings 2000). Below we describe a new fuzzy model of choice applied to the context of buyer seller negotiation that is normatively specified by a Request For Quote (RFQ) protocol. claim that in the absence of precise information/preferences such models can be usefully executed by agents to make choices.