Fair division methods offer guarantees to agents of the proportional size or quality of their share in a division of a resource (cake). These guarantees come with a price. Standard fair division methods (or "cake cutting" algorithms) do not find efficient allocations (not Pareto optimal). The lack of efficiency of these methods makes them less attractive for solving multi-agent resource and task allocation. Previous attempts to increase the efficiency of cake cutting algorithms for two agents resulted in asymmetric methods that were limited in their ability to find allocations in which both agents receive more than their proportional share. Trust can be the foundation on which agents exchange information and enable the exploration of allocations that are beneficial for both sides. On the other hand, the willingness of agents to put themselves in a vulnerable position due to their trust in others, results in loss of the fairness guarantees that motivate the design of fair division methods. In this work we extend the study on fair and efficient cake cutting algorithms by proposing a new notion of trust-based efficiency, which formulates a relation between the level of trust between agents and the efficiency of the allocation. Furthermore, we propose a method for finding trust-based efficiency. The proposed method offers a balance between the guarantees that fair division methods offer to agents and the efficiency that can be achieved by exposing themselves to the actions of other agents. When the level of trust is the highest, the allocation produced by the method is globally optimal (social welfare).
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