Fair division protocols

Envy-graph procedure

The envy-graph procedure (also called the envy-cycles procedure) is a procedure for fair item allocation. It can be used by several people who want to divide among them several discrete items, such as heirlooms, sweets, or seats in a class. Ideally, we would like the allocation to be envy-free (EF). i.e., to give each agent a bundle that he/she prefers over the bundles of all other agents. However, the items are discrete and cannot be cut, so an envy-free assignment might be impossible (for example, consider a single item and two agents). The envy-graph procedure aims to achieve the "next-best" option -- envy-freeness up to at most a single good (EF1): it finds an allocation in which the envy of every person towards every other person is bounded by the maximum marginal utility it derives from a single item. In other words, for every two people i and j, there exists an item such that, if that item is removed, i does not envy j. The procedure was presented by Lipton and Markakis and Mossel and Saberi and it is also described in . (Wikipedia).

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Related pages

Depth-first search | Round-robin item allocation | Directed cycle | Monotonic function | Undercut procedure | Directed graph | Envy-free item allocation | Greedy number partitioning | Decreasing Demand procedure | Fair item allocation