Distributed Local Search for Minimizing Envy

The allocation of indivisible resources to multiple agents typically generate envy among the agents. An Envy Free allocation may not exist in general and one can search for a minimal envy allocation. The search problem of minimizing envy for indivisible resource allocation is presented and a negotiation based transfer algorithm for solving it is proposed. The proposed algorithm performs a distributed any time local search for minimal envy solutions. The algorithm is composed of two phases. One phase performs hill climbing by the transfer of a single good among agents. The other phase of search uses elimination of open-end envy cycles, thereby utilizing the transfer of whole bundles. An extensive experimental evaluation of the proposed algorithm demonstrates the advantage of using the combined two phase algorithm.