Approximating Constraint-Based Utility Spaces Using Generalized Gaussian Mixture Models
Complex negotiations are characterized by a particular type of utility spaces that is usually non-linear and non-monotonic. An example of such utility spaces are constraint-based utility spaces. The multitude of constraints’ shapes that could potentially be used by the negotiating agents makes any opponent modeling attempt more challenging. The same problem persists even when the agent is exploring her own utility space as to find her optimal contracts. Seeking a unified form for constraint-based utility representation might shed some light on how to tackle these problems.
In this paper, we propose to find an approximation for constraint-based preferences, used mainly in complex negotiation with non-linear utility spaces. The proposed approximation yields a compact form that unifies a whole family of constraints (Cubic, Bell, Conic, etc.). Results show that the new canonical form can in fact be an alternative representation for all known constraint-based utility functions. Additionally, it leads us to a potential parametric model that could be used for opponent modeling in complex non-linear negotiations.
KeywordsUtility Function Multiagent System Optimal Contract Constant Relative Risk Aversion Utility Space
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