Rubinstein2005-page47

Rubinstein2005-page47 - 12:18 master Sheet number 45 Page...

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October 21, 2005 12:18 master Sheet number 45 Page number 29 Choice 29 set from which it is to be chosen would empty the rationality hy- pothesis of its meaning. Choice Functions as “Internal Equilibria” The choice function definition we have been using requires that a single element be assigned to each choice problem. If the deci- sion maker follows the rational-man procedure using a preference relation with indifferences, the previously defined induced choice function C ( A ) might be undefined because for some choice prob- lems there would be more than one optimal element. This is one of the reasons that in some cases we use the alternative following concept to model behavior. A choice function C is required to assign to every nonempty A X a nonempty subset of A , that is, C ( A ) A . According to our in- terpretation of a choice problem, a decision maker has to select a unique element from every choice set. Thus, C ( A ) cannot be inter- preted as the choice made by the decision maker when he has to
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