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

TL;DR

This paper explores strategic decision-making in shared meals, specifically in Ethiopian Dinner, demonstrating how players can optimize their outcomes by planning their last move first using a visual proof of the subgame perfect equilibrium.

Contribution

It provides a new visual proof of the equilibrium strategy in Ethiopian Dinner, emphasizing backward reasoning for optimal decision-making in shared resource scenarios.

Findings

Players can determine optimal moves by planning backwards from the last bite.

The visual proof simplifies understanding of the subgame perfect equilibrium.

Strategic planning in shared meals can be formalized using game theory principles.

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.