Single attribute utility functions

To develop the multiattribute utility function, the single-attribute utility functions ( ) and the importance weights (fc ) are determined by assessing preferences between alternatives. Methods of doing so are discussed in Section 3.4. 

Multiattribute tility theory (Keeney and Raiffa 1976) extends SEU to the case where the decision maker has multiple objectives. The approach is equally applicable for describing utility and vtdue functions. Following this approach, the utility (or value) of an alternative A, with multiple attributes X, is described with the multiattribute utihty (or value) function m(Xj. . . x ), where u(x. . . x ) is some function f(x. . . xjof the attributes x. In the simplest case, multiattribute utihty theory (MAUT) describes the utility of an alternative as an additive function of the single attribute utihty functions M (x ). That is. 

Indifference methods are illustrated by the variable probability and certeiinty equivalent methods of eliciting utility functions presented in the previous section. There, indifference points were obtained by varying either probabilities or values of outcomes. Similar approaches have been appUed to develop multiattribute utility or value functions. This approach involves four steps (1) develop the single attribute utility or value functions, (2) assume a functional form for the multiattribute function, (3) assess the indifference point between various multiattribute altematives, and (4) calculate the substitution rate or relative importance of one attribute compared to the other. The single-attribute functions might be developed by indifference methods (i.e., the variable probabihty or certainty equivalent methods) or direct-assessment methods, as discussed later. Indifference points between multiattribute outcomes are obtained through an interactive process in which the values of attributes are systematically increased or decreased. Substitution rates are then obtained from the indifference points. 

Resources The first step is to identify the set of resources over which the negotiation is to be conducted. The resource could be a single item or multiple items, with a single or multiple units of each item. An additional consideration common in real settings is the type of the item, i.e. is this a standard commodity or multiattribute commodity. In the case of multiattribute items, the agents might need to specify the non-price attributes and some utility/scoring function to tradeoff across these attributes. 

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