The Bounded Strength of Weak Expectations

Mind 120 (479):819-832 (2011)
Abstract
The rational price of the Pasadena and Altadena games, introduced by Nover and Hájek (2004 ), has been the subject of considerable discussion. Easwaran (2008 ) has suggested that weak expectations — the value to which the average payoffs converge in probability — can give the rational price of such games. We argue against the normative force of weak expectations in the standard framework. Furthermore, we propose to replace this framework by a bounded utility perspective: this shift renders the problem more realistic and accounts for the role of weak expectations. In particular, we demonstrate that in a bounded utility framework, all agents, even if they have different value functions and disagree on the price of an individual game, will finally agree on the rational price of a repeated, averaged game. Thus, we explain the intuitive appeal of weak expectations, while avoiding both trivialization of the original paradox and the drawbacks of previous approaches
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