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How to Make the Most of a Shared Meal: Plan the Last Bite First

Lionel Levine and Katherine E. Stange
The American Mathematical Monthly
Vol. 119, No. 7 (August‒September 2012), pp. 550-565
DOI: 10.4169/amer.math.monthly.119.07.550
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Page Count: 16
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How to Make the Most of a Shared Meal: Plan the Last Bite First
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Abstract If you are sharing a meal with a companion, then how is it best to make sure you get your favourite mouthfuls? Ethiopian Dinner is a game in which two players take turns eating morsels from a common plate. Each morsel comes with a pair of utility values measuring its tastiness to the two players. Kohler and Chandrasekaran discovered a good strategy—a subgame perfect equilibrium, to be exact—for this game. We give a new visual proof of their result. The players arrive at the equilibrium by figuring out their last move first and working backward. We conclude that it’s never too early to start thinking about dessert.

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