TY - JOUR
T1 - A Generalized Two-Agent Location Problem
T2 - Asymmetric Dynamics and Coordination
AU - Golany, Boaz
AU - Kogan, Konstantin
AU - Rothblum, Uriel G.
N1 - Funding Information:
Acknowledgements The research of the first two authors was partially supported by the Gordon Center for Systems Engineering and the Center for Science & Technology of Security, both at the Technion, Israel Institute of Technology, and by a grant for Promotion of Research at the Technion.
PY - 2011/2
Y1 - 2011/2
N2 - 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.
AB - 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.
KW - Coordination
KW - Dynamic control
KW - Homeland security
KW - Nash equilibrium
UR - http://www.scopus.com/inward/record.url?scp=79952242561&partnerID=8YFLogxK
U2 - 10.1007/s10957-010-9750-x
DO - 10.1007/s10957-010-9750-x
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:79952242561
SN - 0022-3239
VL - 148
SP - 336
EP - 363
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 2
ER -