ABSTRACT
Again, this seems right. As we said above, the risk-averse agent wants the highest utility, but she also cares about how sure she was to obtain it. The less risk-averse agent – whose risk function is r
2 – is suffi ciently sure that h would obtain for her
at least the utility of x 2 and possibly more that she assigns higher value to getting
x 2 as a result of h than to getting it as a result of x
2 . For the more risk-averse agent
– whose risk function is r 3 – she is not suffi ciently sure. And reversed versions of
these points can be made for risk-seeking agents with risk functions r 0.5 and r
, for instance. Thus, we can see why it makes sense to demand of an agent that her utility function u∗ on ∗ encodes attitudes to risk relative to a risk function in the sense that was made precise above – see Equation 1 .
