Truthful Cake Sharing

@inproceedings{Bei2022TruthfulCS,
  title={Truthful Cake Sharing},
  author={Xiaohui Bei and Xinhang Lu and Warut Suksompong},
  booktitle={AAAI Conference on Artificial Intelligence},
  year={2022}
}
The classic cake cutting problem concerns the fair allocation of a heterogeneous resource among interested agents. In this paper, we study a public goods variant of the problem, where instead of competing with one another for the cake, the agents all share the same subset of the cake which must be chosen subject to a length constraint. We focus on the design of truthful and fair mechanisms in the presence of strategic agents who have piecewise uniform utilities over the cake. On the one hand… 

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References

SHOWING 1-10 OF 34 REFERENCES

On Existence of Truthful Fair Cake Cutting Mechanisms

This paper proves that there does not exist a deterministic, truthful and proportional cake cutting mechanism, even in the special case where all of the followings hold: • there are only two agents; • each agent’s valuation is a piecewise-constant function;• each agent is hungry; and the impossibility result extends to the case where the mechanism is allowed to leave some part of the cake unallocated.

Truthful fair division without free disposal

This work exhibits a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations and complements this result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms.

Cake Cutting: Envy and Truth

It is shown that no deterministic truthful envy-free mechanism exists in the connected piece scenario, and the same impossibility result for the general setting with some additional mild assumptions on the allocations is shown.

Monotonicity and competitive equilibrium in cake-cutting

We study monotonicity properties of solutions to the classic problem of fair cake-cutting—dividing a heterogeneous resource among agents with different preferences. Resource- and

Deterministic, Strategyproof, and Fair Cake Cutting

This work presents some negative results when considering an approximate notion of strategyproofness, shows a connection between direct-revelation mechanisms and mechanisms in the Robertson-Webb model when agents have piecewise constant valuations, and presents a modification to the well-known Even-Paz algorithm.

Fair Division with Binary Valuations: One Rule to Rule Them All

This work establishes maximum Nash welfare as the ultimate allocation rule in the realm of binary additive preferences and proves that fractional MNW -- known to be group strategyproof, envy-free, and Pareto optimal -- can be implemented as a distribution over deterministic MNW allocations, which are envy- free up to one good.

Almost Envy-Freeness with General Valuations

This work proves an exponential lower bound on the number of value queries needed to identify an EFX allocation, even for two players with identical valuations, and suggests that there is a rich landscape of problems to explore in the fair division of indivisible goods with different classes of player valuations.

A Dictatorship Theorem for Cake Cutting

It is shown that any deterministic strategy-proof protocol for two agents in the standard Robertson-Webb query model is dictatorial, that is, there is a fixed agent to which the protocol allocates the entire cake, and randomized protocols are exhibited that are truthful in expectation and compute approximately fair allocations.

How to Cut a Cake Before the Party Ends

This work proposes an envy-free cake cutting protocol for agents with piecewise linear valuations, which requires a number of operations that is polynomial in natural parameters of the given instance.

Fair and Efficient Memory Sharing: Confronting Free Riders

It is demonstrated that mechanisms blocking agents from accessing parts of the memory can achieve improved efficiency guarantees, despite the inherent inefficiencies of blocking.