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A dynamic game model of collective choice in multi-agent systems

Rabih Salhab, Roland P. Malhamé and Jérôme Le Ny

Article (2018)

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Abstract

Inspired by successful biological collective decision mechanisms such as honey bees searching for a new colony or the collective navigation of fish schools, we consider a scenario where a large number of agents engaged in a dynamic game have to make a choice among a finite set of different potential target destinations. Each individual both influences and is influenced by the group's decision, as represented by the mean trajectory of all agents. Agents are assumed linear and coupled through a modified form of quadratic cost, whereby the terminal cost captures the discrete choice component of the problem. Following the mean field games methodology, we identify sufficient conditions under which allocations of destination choices over agents lead to self replication of the overall mean trajectory under the best response by the agents. Importantly, we establish that when the number of agents increases sufficiently, (i) the best response strategies to the self replicating mean trajectories qualify as epsilon-Nash equilibria of the population game; (ii) these epsilon-Nash strategies can be computed solely based on the knowledge of the joint probability distribution of the initial conditions, dynamics parameters and destination preferences, now viewed as random variables. Our results are illustrated through numerical simulations.

Uncontrolled Keywords

Collective choice, discrete choice models, mean field games (MFG), multiagent systems, optimal control

Subjects: 2500 Electrical and electronic engineering > 2500 Electrical and electronic engineering
Department: Department of Electrical Engineering
Research Center: GERAD - Research Group in Decision Analysis
Funders: CRSNG/NSERC
Grant number: 6820-2011, 435905-13
PolyPublie URL: https://publications.polymtl.ca/2865/
Journal Title: IEEE Transactions on Automatic Control (vol. 63, no. 3)
Publisher: IEEE
DOI: 10.1109/tac.2017.2723956
Official URL: https://doi.org/10.1109/tac.2017.2723956
Date Deposited: 26 Mar 2018 12:02
Last Modified: 09 Jun 2023 09:25
Cite in APA 7: Salhab, R., Malhamé, R. P., & Le Ny, J. (2018). A dynamic game model of collective choice in multi-agent systems. IEEE Transactions on Automatic Control, 63(3), 768-782. https://doi.org/10.1109/tac.2017.2723956

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