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.
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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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