Yes, the agent should—given the defined utility function and that the agent is rational. If, however, the agent is irrational and prone to risk aversion, it will consistently prefer the sure deal to the bet, and therefore be willing to pay a finite cost for replacing the bet with the sure deal, hence losing utility.
Yes, the agent should—given the defined utility function and that the agent is rational. If, however, the agent is irrational and prone to risk aversion, it will consistently prefer the sure deal to the bet, and therefore be willing to pay a finite cost for replacing the bet with the sure deal, hence losing utility.