Task assignment with controlled and autonomous agents |
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| Affiliation: | 1. International School of Economics at Tbilisi State University, Georgia;2. Electronics and Computer Science, University of Southampton, UK;3. Schools of Mathematics & Management, University of Southampton, UK;1. European University at St. Petersburg. 3 Gagarinskaya st., St. Petersburg, 191187, Russia;2. St. Petersburg Institute for Economics and Mathematics RAS. 1 Chaikovskogo st., St. Petersburg, 191187, Russia;3. St. Petersburg State University. 62 Chaikovskogo st., St. Petersburg, 191123, Russia;1. Department of Economics and Management, Tuscia University, Via del Paradiso 47, Viterbo, Italy;2. Sogei S.p.A., IT Economia - Modelli di Previsione ed Analisi Statistiche, Via Isonzo 19/E, Rome, Italy;3. Department of Methods and Models for Economics, Territory and Finance, Sapienza University, via Castro Laurenziano 9, Rome, Italy |
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| Abstract: | We analyse assignment problems in which not every agent is controlled by the central planner. The autonomous agents search for vacant tasks guided by their own preference orders over available tasks. The goal of the central planner is to maximise the total value of the assignment, taking into account the behaviour of the uncontrolled agents. Such optimisation problems arise in numerous real-world situations, ranging from organisational economics to “crowdsourcing” and disaster response. We show that the problem faced by the central planner can be transformed into a mixed integer bilevel optimisation problem. Then we demonstrate how this program can be reduced to a disjoint bilinear program, which is much more manageable computationally. |
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