相关论文: Throw One's Cake --- and Have It Too

In this article we propose a probabilistic framework in order to study the fair division of a divisible good, e.g., a cake, between n players. Our framework follows the same idea than the ''Full independence model'' used in the study of…

Given a set of $p$ players we consider problems concerning envy-free allocation of collections of $k$ pieces from a given set of goods or chores. We show that if $p\le n$ and each player can choose $k$ pieces out of $n$ pieces of a cake,…

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…

We analyze lower bounds for the number of envy-free divisions, in the classical Woodall-Stormquist setting and in a non-classical case, when envy-freeness is combined with the equipartition of a measure. 1. In the first scenario, there are…

Predictive algorithms are now used to help distribute a large share of our society's resources and sanctions, such as healthcare, loans, criminal detentions, and tax audits. Under the right circumstances, these algorithms can improve the…

Inheritances, divorces or liquidations of companies require common assets to be divided among the entitled parties. Legal methods usually consider the market value of goods, while fair division theory takes into account the parties'…

The paper considers fair allocation of indivisible nondisposable items that generate disutility (chores). We assume that these items are placed in the vertices of a graph and each agent's share has to form a connected subgraph of this…

Fairness and privacy are two important concerns in social decision-making processes such as resource allocation. We study privacy in the fair allocation of indivisible resources using the well-established framework of differential privacy.…

A collection of objects, some of which are good and some are bad, is to be divided fairly among agents with different tastes, modeled by additive utility functions. If the objects cannot be shared, so that each of them must be entirely…

We study the fundamental problem of allocating indivisible goods to agents with additive preferences. We consider eliciting from each agent only a ranking of her $k$ most preferred goods instead of her full cardinal valuations. We…

In many developing countries, the total electricity demand is larger than the limited generation capacity of power stations. Many countries adopt the common practice of routine load shedding - disconnecting entire regions from the power…

Does a high dispersal rate provide a competitive advantage when risking competitive exclusion? To this day, the theoretical literature cannot answer this question in full generality. The present paper focuses on the simplest mathematical…

The problem of dividing resources fairly occurs in many practical situations and is therefore an important topic of study in economics. In this paper, we investigate envy-free divisions in the setting where there are multiple players in…

We examine the history of cake cutting mechanisms and discuss the efficiency of their allocations. In the case of piecewise uniform preferences, we define a game that in the presence of strategic agents has equilibria that are not dominated…

In this article, the issue of choice cuts made to a rectangular region are considered and explored. Results show that this problem is not trivial. Outcomes for teaching and learning are considered.

We study classic cake-cutting problems, but in discrete models rather than using infinite-precision real values, specifically, focusing on their communication complexity. Using general discrete simulations of classical infinite-precision…

Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion. These Notes provide a succinct introduction to the field. We cover three main topics. First, we…

We prove an $\Omega(n^2)$ lower bound on the query complexity of local proportionality in the Robertson-Webb cake-cutting model. Local proportionality requires that each agent prefer their allocation to the average of their neighbors'…

The classic cake-cutting problem provides a model for addressing the fair and efficient allocation of a divisible, heterogeneous resource among agents with distinct preferences. Focusing on a standard formulation of cake cutting, in which…

In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n=2 it implies a dictatorial allocation, whereas for n > 2 it requires that one agent receives no cake. We show that a weaker version of this…