Cake Cutting Mechanisms | Egor Ianovski

Computable Component-wise Reducibility | Egor Ianovski

We consider equivalence relations and preorders complete for various levels of the arithmetical hierarchy under computable, component-wise reducibility. We show that implication in first order logic is a complete preorder for Σ1, the ≤m relation on EXPTIME sets for Σ2 and the embeddability of computable subgroups of (Q,+) for Σ3. In all cases, the symmetric fragment of the preorder is complete ...

Fairness and False-Name Manipulations in Randomized Cake Cutting

Cake cutting has been recognized as a fundamental model in fair division, and several envy-free cake cutting algorithms have been proposed. Recent works from the computer science field proposed novelmechanisms for cake cutting, whose approaches are based on the theory of mechanism design; these mechanisms are strategy-proof, i.e., no agent has any incentive to misrepresent her utility function,...

Truthful Cake Cutting Mechanisms with Externalities: Do Not Make Them Care for Others Too Much!

We study truthful mechanisms in the context of cake cutting when agents not only value their own pieces of cake but also care for the pieces assigned to other agents. In particular, agents derive benefits or costs from the pieces of cake assigned to other agents. This phenomenon is often referred to as positive or negative externalities. We propose and study the following model: given an alloca...

Two statements of the Duggan-Schwartz theorem

The Duggan-Schwartz theorem [Duggan and Schwartz, 1992] is a famous result concerning strategy-proof social choice correspondences, often stated as “A social choice correspondence that can be manipulated by neither an optimist nor a pessimist has a weak dictator”. However, this formulation is actually due to Taylor [2002], and the original theorem, at face value, looks rather different. In this...

Cake-Cutting is Not a Pie e of Cake