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Whether volunteering is actually undertaken or not depends on the comparison between the expected utility from volunteering and the opportunity cost for volunteering.
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First, the expected utility of a lottery is equal to the expectation of the expected utilities of its prizes.
The Bayesian OED is based on maximizing the expected utility function taken as the Kullback-Leibler divergence between the prior and posterior distribution of the model parameters.
The expected utility in the second period is the difference between the intrinsic value and the second-period price, multiplied by the probability of non-stockout, 1−ε.
Note the expected utility model underlying Gore's approach.
We thus conclude that a user who maximizes the expected utility of wealth and who has a power utility function will select a distribution for which there is a linear relationship between ln(pi) and ln(wi), with the slope of the line equal to the negative of the exponent g in the underlying utility function.
This model is able to encompass rational decision behaviors that the Expected Utility model cannot accommodate.
Using conditional probabilities, the expected utility of acting cooperatively exceeds the expected utility of acting uncooperatively.
The crucial trade-off the player faces at each trial is between exploitation of the action that has the highest expected utility and exploration of new actions to get more information about the expected utility performance of the other actions.
Why think the expected utility representation is the right one?
The expected utility criterion has been criticized along several lines.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com