The cake cutting problem is concerned with the fair allocation of a divisible good among agents whose preferences vary over it. Recently, designing strategy-proof cake cutting mechanisms has caught considerable attention from AI and MAS researchers. Previous works assumed that an agent's utility function is additive so that theoretical analysis becomes tractable. However, in practice, agents have non-additive utility over a resource. In this paper, we consider the all-or-nothing utility function as a representative example of non-additive utility because it can widely cover agents' preferences for such real-world resources as the usage of meeting rooms, time slots for computational resources, bandwidth usage, and so on. We first show the incompatibility between envy-freeness and Pareto efficiency when each agent has all-or-nothing utility. We next propose two strategy-proof mechanisms that satisfy Pareto efficiency, which are based on the serial dictatorship mechanism, at the sacrifice of envy-freeness. To address computational feasibility, we propose a heuristic-based allocation algorithm to find a near-optimal allocation in time polynomial in the number of agents, since the problem of finding a Pareto efficient allocation is NP-hard. As another approach that abandons Pareto efficiency, we develop an envy-free mechanism and show that one of our serial dictatorship based mechanisms satisfies proportionality in expectation, which is a weaker definition of proportionality. Finally, we evaluate the efficiency obtained by our proposed mechanisms by computational experiments.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics