background and objectives: the quality of cakes made of wheat flour depends on the quantity and quality of its gluten proteins however, these proteins may have side effects for some people, including the patients with celiac, and the only way to cure this disease is to take a lifelong gluten-free diet. materials and methods: this research aims to produce gluten- free cake by using rice flour an...

This paper discusses cake-cutting protocols when the cake is a heterogeneous good, represented by an interval on the real line. We propose a new desirable property, the meta-envy-freeness of cake-cutting, which has not been formally considered before. Meta-envy-free means there is no envy on role assignments, that is, no party wants to exchange his/her role in the protocol with the one of any o...

Background and Objectives: The quality of cakes made of wheat flour depends on the quantity and quality of its gluten proteins however, these proteins may have side effects for some people, including the patients with celiac, and the only way to cure this disease is to take a lifelong gluten-free diet. Materials and Methods: This research aims to produce gluten- free cake by using rice flour a...

This paper discusses cake-cutting protocols when the cake is a heterogeneous good that is represented by an interval in the real line. We propose a new desirable property, the meta-envy-freeness of cake-cutting, which has not been formally considered before. Though envy-freeness was considered to be one of the most important desirable properties, envy-freeness does not prevent envy about role a...

Cake cutting is a fundamental model in fair division; it represents the problem of fairly allocating a heterogeneous divisible good among agents with different preferences. The central criteria of fairness are proportionality and envy-freeness, and many of the existing protocols are designed to guarantee proportional or envy-free allocations, when the participating agents follow the protocol. H...

Fair cake-cutting is the division of a cake or resource among N users so that each user is content. Users may value a given piece of cake differently, and information about how a user values different parts of the cake can only be obtained by requesting users to “cut” pieces of the cake into specified ratios. One of the most interesting open questions is to determine the minimum number of cuts ...

For decades researchers have struggled with the problem of envy-free cake cutting: how to divide a divisible good between multiple agents so that each agent likes his own allocation best. Although an envy-free cake cutting protocol was ultimately devised, it is unbounded, in the sense that the number of operations can be arbitrarily large, depending on the preferences of the agents. We ask whet...

Cloutier, Nyman, and Su (Mathematical Social Sciences 59 (2005), 26–37) initiated the study of envy-free cake-cutting problems involving several cakes. The classical result in this area is that when there are q players and one cake, an envy-free cake-division requiring only q − 1 cuts exists under weak and natural assumptions. Among other results, Cloutier, Nyman, and Su showed that when there ...

Fair cake-cutting is the division of a cake or resource among N users so that each user is content. Users may value a given piece of cake differently, and information about how a user values different parts of the cake can only be obtained by requesting users to “cut” pieces of the cake into specified ratios. Many distributed computing problems which involve resource sharing can be expressed as...

We consider the problem of fairly dividing a heterogeneous divisible good among agents with different preferences. Previous work has shown that envy-free allocations, i.e., where each agent prefers its own allocation to any other, may not be efficient, in the sense of maximizing the total value of the agents. Our goal is to pinpoint the most efficient allocations among all envy-free allocations...