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When dividing a valuable resource amongst a group of players, it is desirable to have each player believe that their allocation is at least as valuable as everyone else's allocation. This condition, where nobody is envious of anybody else's share in a division, is called envy-freeness. Fair division problems over continuous pools of resources are affectionately known as cake-cutting problems, as they resemble attempts to slice and distribute cake amongst guests as fairly as possible. Previous work in multi-cake fair division problems have attempted to prove that certain conditions do not allow for guaranteed envy-free divisions. In this paper, we examine and attempt to generalize a series of proofs by Cloutier, Nyman, and Su regarding the existence of envy-free divisions of multiple cakes amongst two players.
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Shin, Justin J., "Envy-Free Fair Division With Two Players and Multiple Cakes" (2016). Senior Projects Fall 2016. 37.