How much are you Willing to Pay to Play the Saint Petersburg Gamble?
Samih Antoine Azar
International Journal of Financial Economics, 2015, vol. 4, issue 2, 101-108
The Saint Petersburg gamble has an infinite expected payoff but few people would pay more than 32 dollars as an entrance fee to play it. In fact under reasonable conditions the maximum willingness to pay to play the game is much lower at around $ 4, and seems to always converge to a maximum price. This is what emerges from the analysis in this paper. The procedure adopted is by a simulation of 1000 tosses of an honest coin, calculating the expected utility, and solving for the entrance fee that equates this expected utility to the certainty-equivalent utility. As predictable this fee depends positively on initial wealth and negatively on risk aversion. There is evidence that this game is a poor manâ€™s game as will be shown empirically. All these results vindicate the expected utility paradigm, and show that this framework can still be valuable to depict and explain behavior towards risk, and other issues related to risk tolerance.
Keywords: Bernoulliâ€™s game; infinite payoff; expected utility; log utility; risk aversion; initial wealth; spreadsheet simulation; entrance fee; regression; wealth effect; necessity goods; poor manâ€™s game (search for similar items in EconPapers)
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