Fair and Efficient Division of a Discrete Cake with Switching Utility Loss

Cake cutting is a widely studied model for allocating resources with temporal or spatial structures among agents. Recently, a new line of research has emerged that focuses on the discrete variant, where the resources are indivisible and connected by a path. In some real-world applications, the resources are interdependent, and dividing the cake may reduce their effectiveness. In this paper, we introduce a model that captures the effect of division as switching utility loss and investigate the tradeoff between fairness and efficiency for various settings. Specifically, we measure fairness and efficiency using the popular notions of envy-freeness up to one item (EF1) and social welfare, respectively. The goal of our study is to understand how much social welfare must be sacrificed to ensure EF1 allocations and design polynomial-time algorithms that can compute EF1 allocations with the best possible social welfare guarantee.