More than envy-free

Researchers have developed procedures for dividing up goods between self-interested agents such that the allocation is envy-free (Brams and Taylor, 1996). An allocation is envy-free when every agent believes that its share is not less than anyone else's share. These procedures are not efficient (in the sense of Pareto optimality) in general. Envy-free procedures allow agents to ignore the utility metrics of other agents if they are satisfied with a fair share of the goods being divided. From a multiagent systems research perspective, however, we are 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 fair share. For example, it may be possible to improve the allocation to the modeling agent without decreasing the utility 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 has a model of the utility function of the other agent. 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 fair share of the allocation. The procedure also has the desired property of envy-freeness.