A Generalized Two-Agent Location Problem: Asymmetric Dynamics and Coordination |
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Authors: | Boaz Golany Konstantin Kogan Uriel G Rothblum |
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Institution: | (1) Department of Mathematics, Chongqing Normal University, Chongqing, People’ Republic of China;(2) Department of Applied Mathematics, University of New South Wales, Sydney, Australia;(3) School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria, Australia; |
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Abstract: | We generalize a static two-agent location problem into dynamic, asymmetric settings. The dynamics is due to the ability of
the agents to move at limited speeds. Since each agent has its own objective (demand) function and these functions are interdependent,
decisions made by each agent may affect the performance of the other agent and thus affect the overall performance of the
system. We show that, under a broad range of system’s parameters, centralized (system-wide optimal) and non-cooperative (Nash)
behavior of the agents are characterized by a similar structure. The timing of these trajectories and the intermediate speeds
are however different. Moreover, non-cooperative agents travel more and may never rest and thus the system performance deteriorates
under decentralized decision-making. We show that a static linear reward approach, recently developed in Golany and Rothblum
(Nav. Res. Logist. 53(1):1–15, 2006), can be generalized to provide coordination of the moving agents and suggest its dynamic modification. When the reward scheme
is applied, the agents are induced to choose the system-wide optimal solution, even though they operate in a decentralized
decision-making mode. |
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