Abstract
This paper presents a potential game-theoretic interpretation and analysis of a decentralized task allocation algorithm, consensus-based bundled algorithm, which was developed by the authors’ prior work. It is, in particular, proved that the consensus-based bundle algorithm converges to a pure strategy Nash equilibrium of some distributed welfare game, and the price of anarchy and the price of stability of this equilibrium are 1/2 and 1, respectively.
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Notes
- 1.
This inequality/equality relation may not always hold; for the case of time-windowed, adjustment of the arrival time of the first-visiting task may be needed to make both tasks.
- 2.
The action set can be defined over \(2^\mathcal {R}\) as long as the separability condition in (1) is satisfied.
- 3.
Notice the notational difference in the meaning of \(s_{rn}(A)\) and \(s_{rn}[B]\). The formal indicates the marginal reward of n with the total assignment of A including n, while the second indicates the marginal reward of n when committed on B, which excludes n.
References
Arslan, G., Marden, J.R., Shamma, J.S.: Autonomous vehicle-target assignment: a game theoretical formulation. ASME J. Dyn. Syst. Measur. Control 129(5), 584–596 (2007)
Choi, H.L., Brunet, L., How, J.P.: Consensus-based decentralized auctions for robust task allocation. IEEE Trans. Robot. 25(4), 912–926 (2009). doi:10.1109/TRO.2009.2022423
Johnson, L., Choi, H.L., How, J.P.: Using non-submodular score functions in decentralized task allocation. IEEE Trans. Robot. (submitted)
Johnson, L.B., Choi, H.L., How., J.P.: Convergence analysis of the hybrid information and plan consensus algorithm. In: American Control Conference (ACC) (2014)
Johnson, L.B., Choi, H.L., Ponda, S.S., How., J.P.: Allowing non-submodular score functions in distributed task allocation. In: IEEE Conference on Decision and Control (CDC) (2012)
Marden, J.R.: State based potential games. Automatica 48(12), 3075–3088 (2012)
Marden, J.R., Arslan, G., Shamma, J.: Cooperative control and potential games. IEEE Trans. Syst. Man Cybern. Part B Cybern. 39(6), 1393–1407 (2009)
Marden, J.R., Arslan, G., Shamma, J.: Joint strategy fictitious play with inertia for potential games. IEEE Trans. Autom. Control 54(2), 208–220 (2013)
Marden, J.R., Wierman, A.: Distributed welfare games. Oper. Res. 61(1), 155–168 (2013)
Marden, J.R., Wierman, A.: Overcoming the limitations of utility design for multiagent systems. IEEE Trans. Autom. Control 58(6), 1402–1415 (2013)
Monderer, D., Shapley, L.S.: Potential games. Games Econ. Behav. 14, 124–143 (1996)
Rosenthal, R.: The network equilibrium problem in integers. Networks 3(1), 53–59 (1973)
Acknowledgments
This work was supported in part by the Agency for Defense Development (Contract # UE123026JD) and in part by the KI project through KAIST Institute of Design of Complex Systems.
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Choi, HL., Kim, KS., Johnson, L.B., How, J.P. (2016). Potential Game-Theoretic Analysis of a Market-Based Decentralized Task Allocation Algorithm. In: Chong, NY., Cho, YJ. (eds) Distributed Autonomous Robotic Systems. Springer Tracts in Advanced Robotics, vol 112 . Springer, Tokyo. https://doi.org/10.1007/978-4-431-55879-8_15
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DOI: https://doi.org/10.1007/978-4-431-55879-8_15
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