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They are not yet statements about the preferences expressed by desires. If (4a) is true, then the attribute ‘having vanilla taste’ is a relevant attribute of ice cream in situations in which John has to choose between different instances of ice cream. How to Set Up Normal Optimal Answer Models 25 Hence, we explicate the predicate desire in (5) as a short form for a statement about preferences over attribute combinations. These preferences over attribute combinations can be represented by a multi-attribute utility function U .

Consider the signalling game with the payoff structure in Table 1. The sender (she) observes whether the state of nature is t1 or t2 . Each of these states occur with probability 12 . The receiver (he) can choose among action a1 , a2 or a3 . After having observed the state of nature, and prior to the receiver taking one of the actions, the sender can send a signal ‘s1 ’, a signal ‘s2 ’ to the receiver, or no signal at all. Sending a signal comes at no cost whatsoever to the sender. The meaning of the signals is completely conventional, but we focus on separating equilibria where each signal is sent more often in one particular state, thus justifying the labels of the signals.

We can even simplify this description as only the numbers n of attributes and m of domain objects count. Furthermore, in all those cases in which U only ranges over values in {0, 1}, we can characterise U by a formula Good(d) which only contains formulas of the form Ai (d) with d = 1, . . , m. Finally, if there is no reason to assume otherwise, α = 12 . Then, σ only depends on a quadruple n, m, Good( . ), l . A full justification of these default rules can only be given by examples. Table 2 shows the combined table for examples (8a) and (8b).

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