Friday, May 6, 2011

Information with negative value

We all have regretted some decisions we have made. But different individuals respond differently to this. Some would say "oh well, I would have done differently had I known, but this is best I could do at the time." Others are more like "OMG this is horrible, you should not have told me." An individual of the second kind finds negative value in any ex-post information and thus wants to live in a world with a different information structure from the first.

Emmanuelle Gabillon formalizes this idea and studies structure where information is available before ("flexible") or only after ("non-flexible") decisions are taken. The paper also derives the characteristics a regret utility function should have (in particular, it cannot have "rejoicing"). Information can only have negative value in the non-flexible case if preferences exhibit concavity with respect to the ex post best outcome. Interestingly, information can also have negative value in the flexible case for a regretful person. Indeed, while information is useful for all people in revising the expected utility of strategies, for a regretful person it also is useful to revise expected regret. One can thus become even more conservative and this can lead to outcomes that are inferior in expectation to those where one would not have had the information.

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