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How to make the most of a shared meal: plan the last bite first

By Lionel Levine and Katherine E. Stange

Abstract

If you are sharing a meal with a companion, how 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 Chandrasekaharan 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.Comment: AMS Latex, 20 pages, 5 figures (1 colour figure); v2 adds references, v3 incorporates referees' comments. To appear in American Math. Monthl

Topics: Computer Science - Computer Science and Game Theory, Mathematics - Combinatorics, 91A10, 91A18, 91A05, 91A50
Year: 2011
DOI identifier: 10.4169/amer.math.monthly.119.07.550
OAI identifier: oai:arXiv.org:1104.0961
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