A compositional game to fairly divide homogeneous cake
Abel Jansma

TL;DR
This paper introduces a new game-theoretic model for fairly dividing a homogeneous cake among multiple players, achieving a Nash equilibrium with contiguous pieces and linear complexity, addressing fairness issues in traditional cake-cutting mechanisms.
Contribution
The paper proposes a novel compositional game for homogeneous cake division that guarantees fairness, contiguous pieces, and linear complexity, improving upon naive methods.
Findings
Nash equilibrium with equal division and contiguous pieces.
Naive composition leads to exponential unfairness and high Price of Anarchy.
The Biggest Player rule achieves decentralized fairness with linear complexity.
Abstract
The central question in the game theory of cake-cutting is how to fairly distribute a finite resource among multiple players. Most research has focused on how to do this for a heterogeneous cake in a situation where the players do not have access to each other's valuation function, but I argue that even sharing homogeneous cake can have interesting mechanism design. Here, I introduce a new game, based on the compositional structure of iterated cake-cutting, that in the case of a homogeneous cake has a Nash equilibrium where each of players gets of the cake. Furthermore, the equilibrium distribution is the result of just cuts, so each player gets a contiguous piece of cake. Naive composition of the `I cut you choose' rule leads to an exponentially unfair cake distribution with a Gini-coefficient that approaches 1, and suffers from a high Price of Anarchy. This cost is…
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Taxonomy
TopicsEconomic theories and models · Game Theory and Applications · Experimental Behavioral Economics Studies
