More than Envy-Free

Sandip Sen and Anish Biswas

There have been several interesting results in the literature on dividing up goods between self-interested parties such that the allocation is envy-free (Brams Taylor 1996). An allocation is deemed envy-free when every party (agent) believes that its share is not less than anyone else’s share. These procedures, however, are not efficient (in the sense of pareto optimality) general. Envy-free procedures allow agents to ignore the utility metrics of other agents if they are satisfied with what can be called a fare share of the goods being divided. From the multiagent systems research perspective, however, we may be interested in studying augmentations of these procedures in which agents use models of the decision strategies or utility metrics of other agents to try to obtain more than their fare share. For example, it may be possible to improve the allocation to the modeling agent without decreasing the valuation of another agent if they trade things that one considers useless but is of value to the other agent. In particular, we are investigating the problem of dividing up a continuously divisible good among two agents. We assume that one agent have a model of the utility function of the other agent. This model need not be accurate. We have adapted an envy-free division scheme for the two-agent problem to obtain a procedure by which the modeling agent can get more than its fare share of the allocation. The procedure also has the desired property of envy-freeness. So, even if the model being used is inaccurate, or both the agents have the same utility metrics, the allocation will still give the modeling agent at least its fare share of the good.

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