Just wondering if the simple one-person-cuts-the-cake-and-the-other-person-chooses-her-share will not solve the problem. That way, Lucy pays for a tank full of fuel and both sisters drive like maniacs and the next time Lucy’s sister pays for the full tank and both sisters drive to extract maximum benefits and then the next time … you get the idea. They would soon settle down to an equilibrium where both are satisfied and the frequent gas station trip reduces.
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