Equilibrium in a two-agent Assignment Problem
by Giovanni Felici, Mariagrazia Mecoli, Pitu B. Mirchandani, Andrea Pacifici
International Journal of Operational Research (IJOR), Vol. 6, No. 1, 2009

Abstract: In this paper we address a particular generalisation of the Assignment Problem (AP) in a Multi-Agent setting, where distributed agents share common resources. We consider the problem of determining Pareto-optimal solutions that satisfy a fairness criterion (equilibrium). We show that the solution obtained is equivalent to a Kalai–Smorodinsky solution of a suitably defined bargaining problem and characterise the computational complexity of finding such an equilibrium. Additionally, we propose an exact solution algorithm based on a branch-and-bound scheme that exploits bounds obtained by suitably rounding the solutions of the corresponding linear relaxation, and give the results of extensive computational experiments.

Online publication date: Sat, 30-May-2009

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