Using agent model to find efficient envy-free allocation of a continuously divisible good between two agents
Division of a resource among multiple agents is a critical problem in multiagent systems and fair, efficient, and decentralized allocation procedures are highly valued. A division of a resource or good is envy-free when every agent believes that its share is not less than anyone else’s share by its own estimate. Envy-free procedures are not efficient, i.e., they are not Pareto optimal in general. We provide a procedure for improving the efficiency of an envy-free division of a continuously divisible good among two agents using models of agents’ utility function. We further provide an anytime recursive algorithm that increases, if possible, the efficiency of an initial envy-free allocation. Though efficient envy-free division is not possible for general utility functions, we show that our procedure produces optimal, envy-free divisions for certain classes of utility functions.
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