The Bounded Strength of Weak Expectations

The rational price of the Pasadena and Altadena games, introduced by Nover and Hajek (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.