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arXiv 1104.0961cs.GTmath.CO
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如何充分利用共享的一餐:先计划最后一口

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

Lionel Levine, Katherine E. Stange

摘要:

如果你和一个同伴一起吃饭,如何最好地确保你得到你最喜欢的一口?埃塞俄比亚晚餐是一种游戏,其中两名玩家轮流从一个共同的盘子里吃东西。每一口食物都有一对效用值来衡量它对两个玩家的美味程度。Kohler和Anglasekaharan为这个博弈发现了一个很好的策略--准确地说,是一个子博弈完美均衡。我们给出了一个新的直观证明。参与者通过先弄清楚他们的最后一步,然后向后工作来达到均衡。我们的结论是,开始考虑甜点永远不会太早。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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