We consider the problem of envy-free cake cutting, which is the distribution of a continuous heterogeneous resource among self interested players such that nobody prefers what somebody else receives to what they get. Existing work has focused on two distinct classes of solutions to this problem allocations which give each player a continuous piece of cake and allocations which give each player ...

We study the envy-free cake-cutting problem for d+1 players with d cuts, for both the oracle function model and the polynomial time function model. For the former, we derive a θ(( ǫ )) time matching bound for the query complexity of d + 1 player cake cutting with Lipschitz utilities for any d > 1. When the utility functions are given by a polynomial time algorithm, we prove the problem to be PP...

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Mathematical Association of America is collaborating with ...

Filter cake trials with sugarcane in pot and field experiments have shown large yield responses to treatment with filter cake. The first invaders of filter cake were found to be yeasts and bacteria (non-spore formers) which use the free sugars still available in the filter cake. The second invaders were several fungi which were able to attack the available fibrous matter in the filter cake. In ...

We study the problem of finding an envy-free allocation of a cake to d+1 players using d cuts. Two models are considered, namely, the oracle-function model and the polynomial-time function model. In the oracle-function model, we are interested in the number of times an algorithm has to query the players about their preferences to find an allocation with the envy less than …. We derive a matchin...

Fair allocation of goods or resources among various agents is a central task in multiagent systems and other fields. The specific setting where just one divisible resource is to be divided fairly is commonly referred to as cake cutting, and agents are called players in this setting. Cake-cutting protocols aim at dividing a cake and assigning the resulting portions to several players in a way th...

Chore division, introduced by Gardner in 1970s [10], is the problem of fairly dividing a chore among n different agents. In particular, in an envy-free chore division, we would like to divide a negatively valued heterogeneous object among a number of agents who have different valuations for different parts of the object, such that no agent envies another agent. It is the dual variant of the cel...

In this study, some anti-nutritional factors present in oil-free seeds of egusi (Citrullus colocynthis L.) seed cake were determined. Oil was extracted from the oil-free egusi seed by the Soxhlet extraction method. The anti-nutritional factors were determined using the standard methods. The result of anti-nutritional factors analysis revealed that the seed contains phytate (3.09 ± 0.65mg/100g),...

We consider the classic cake-divison problem when the cake is a heterogeneous good represented by an interval in the real line. We provide a mechanism to implement, in an anonymous way, an envy-free and e¢cient allocation when agents have private information on their preferences. The mechanism is a multistep sequential game form in which each agent at each step receives a morsel of the cake tha...