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In their paper, Robin Pope and Reinhardt Selten argue that bets are inscribed in a temporal and not only outcome substantial reference frame and that, in their view, the models which have been offered in the past to model this feature of decision making are not satisfactory. They take in particular issues with Kreps and Porteus [3,4] contributions. One of the interesting aspects of their paper is that they offer a set of axioms on which to rely in order to properly tackle the problem. These axioms lead to the proof that taking the expectation of any kind of utility – in particular of any Von Neumann–Morgenstern utility function – cannot be, indeed a satisfactory treatment of the issue. The issue is rather tricky, because it is open to discussions by economic agents. Not knowing whether my lottery ticket will make me really rich may be part of my pleasure of gambling, this being true for many buyers of such tickets. But “subprime” credit buyers, having acquired some house, the mortgage of which has to be repaid, might fall on opportunities to buy additional credit to repay the next installments and under such circumstances, may hate not knowing whether their lottery ticket will make them rich – and therefore make useless for them to buy additional credit – or not. Von Neumann and Morgenstern, in their celebrated Theory of Games and Economic Behavior, had made clear that they had no intention to deal with such issues. Rather, their seminal work was intended to deal with the issue to value risky assets of individuals, so that, for example, individuals would know how to trade risky against non-risky assets considered in games outcomes. Only such knowledge would allow dealing with the issue of side-payments in games. Their problem had no link whatsoever with time – their model being static – neither with any kind of preference on time directly nor with preference on the pleasure of gambling or impatience to know, etc. However, as has been argued by Drèze and Modigliani [1], Mossin [5], Spence and Zeckhauser [7], to quote only the seminal contributions, these issues cannot, in many practical situations, be considered separately from the preferences on outcome. The problem is then to derive actual preferences from ‘expected utility on outcome’ considered as a counterfactual: all contributions have shown that the notion of a simple integral like expected utility can hardly be maintained, except the stream of research initiated by Kreps and Porteus [3], which is criticized here. One sees in any case only two possibilities open: either rely on an approximation or modify expected utility. Pope has consistently advocated that modelers should choose the second alternative – in a different way than Kreps and Porteus – and started to progressively define the conditions to impose then on the analysis, in a series of papers to which Pope and Selten’s present paper refer extensively. Their present paper can be considered a climax of that stream of research, in that it offers the most general and rigorous analysis of their problem, thus complementing on this specific point Von Neumann and Morgenstern’s seminal analysis [8].

From preferences on resolution time in risky bets to the modeling of complex financialized markets