Solving an infinite decision problem

Abstract
Barrett and Artzenius posed a problem concerning infinite sequences of decisions. It appeared that the strategy of making the rational choice at each stage of the game was, in some circumstances, guaranteed to lead to lower returns than the strategy of making the irrational choice at each stage. This paper shows that there is only the appearance of paradox. The choices that Barrett and Artzenius were calling ‘rational’ cannot be economically justified, and so it is not surprising that someone who makes them ends up with sub-optimal returns. A solution to the more general problem they pose is also advanced.
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