Diner's dilemma

In game theory, the unscrupulous diner's dilemma (or just diner's dilemma) is an n-player prisoner's dilemma. The situation imagined is that several individuals go out to eat, and prior to ordering, they agree to split the check equally between all of them. Each individual must now choose whether to order the expensive or inexpensive dish. It is presupposed that the expensive dish is better than the cheaper, but not by enough to warrant paying the difference when eating alone. Each individual reasons that the expense s/he adds to their bill by ordering the more expensive item is very small, and thus the improved dining experience is worth the money. However, having all reasoned thus, they all end up paying for the cost of the more expensive meal, which by assumption, is worse for everyone than having ordered and paid for the cheaper meal.

Let g represent the joy of eating the expensive meal, b the joy of eating the cheap meal, h is the cost of the expensive meal, l the cost of the cheap meal, and n the number of players. From the description above we have the following ordering ${\displaystyle h-l>g-b}$. Also, in order to make the game sufficiently similar to the Prisoner's dilemma we presume that one would prefer to order the expensive meal given others will help defray the cost, ${\displaystyle g-{\frac {1}{n}}h>b-{\frac {1}{n}}l}$

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