Abstract
Nover and Hájek (2004) suggested a variant of the St Petersburg game which they dubbed the Pasadena game. They hold that their game ‘is more paradoxical than the St Petersburg game in several aspects’. The purpose of this article is to demonstrate theoretically and to validate by simulation, that their game does not lead to a paradox at all, let alone in the St Petersburg game sense. Their game does not produce inconsistencies in decision theory.
Highlights
The paradox of the St Petersburg paradoxThe St Petersburg game and the associated paradox are important in the field of decision theory involving situations of risk and uncertainty (Vivian, 2003)
Nover and Hájek (2004) suggested a variant of the St Petersburg game which they dubbed the Pasadena game
Lies the paradox or as Todhunter (1865: 220) put it, The paradox is that the mathematical theory is apparently directly opposed to the dictates of common sense. In order that the Pasadena game constitute a paradox, in the St Petersburg game sense, it is necessary to show that empirical evidence about amounts wagered is grossly out of line with that suggested by decision theory, in particular, the expected value decision criterion
Summary
The St Petersburg game and the associated paradox are important in the field of decision theory involving situations of risk and uncertainty (Vivian, 2003). It can be shown that the Pasadena game does not produce a problem for decision theory since the series is (a) infinite in length only if an infinite number of games is played (which is impossible), (b) the order in which if the terms arise, arise naturally and once the vast number of negative terms, omitted by the authors in series (3) or positive terms omitted in series (4) is accounted for, the expected value is finite and still converges on ln 2. That single game can be any of the N games (i.e. it need not be the last game in the series of N games) but the probability decreases by 1⁄2, (since an additional flip of the coin is required), for each term beyond Tk, that this surviving game is expected to end It should be noted even if an enormous number of games is played, the series will be relatively short; certainly short enough to be summated manually, if necessary. A similar analysis can be carried out on series (4) which will produce a similar outcome
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