Meta-Envy-Free Cake-Cutting Protocols

This paper discusses cake-cutting protocols when the cake is a heterogeneous good that is represented by an interval in the real line. We propose a new desirable property, the meta-envy-freeness of cake-cutting, which has not been formally considered before. Though envy-freeness was considered to be one of the most important desirable properties, envy-freeness does not prevent envy about role assignment in the protocols. We define meta-envy-freeness that formalizes this kind of envy. We show that current envy-free cake-cutting protocols do not satisfy meta-envy-freeness. Formerly proposed properties such as strong envy-free, exact, and equitable do not directly consider this type of envy and these properties are very difficult to realize. This paper then shows meta-envy-free cake-cutting protocols for two and three party cases.

• Type: Journal
• Year: 2010
• Where: MFCS
• Authors: Yoshifumi Manabe, Tatsuaki Okamoto
• Keywords: Cake-cutting Protocols, Envy-free Cake-cutting Protocols, Important Desirable Properties, MFCS 2010, Theoretical Computer Science