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| Distributed projection subgradient algorithm for two-network zero-sum game with random sleep scheme |
| HongyunXiong,JiangxiongHan,XiaohongNian,ShilingLi |
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| (School of Automation, Central South University, Changsha 410075, China) |
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| DOI：https://doi.org/10.1007/s11768-021-00055-x |
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| Distributed projection subgradient algorithm for two-network zero-sum game with random sleep scheme |
| Hongyun Xiong,Jiangxiong Han,Xiaohong Nian,Shiling Li |
| (School of Automation, Central South University, Changsha 410075, China) |
| Abstract: |
| In this paper, a zero-sum game Nash equilibrium computation problem with a common constraint set is investigated under
two time-varying multi-agent subnetworks, where the two subnetworks have opposite payoff function. A novel distributed
projection subgradient algorithm with random sleep scheme is developed to reduce the calculation amount of agents in the
process of computing Nash equilibrium. In our algorithm, each agent is determined by an independent identically distributed
Bernoulli decision to compute the subgradient and perform the projection operation or to keep the previous consensus
estimate, it effectively reduces the amount of computation and calculation time. Moreover, the traditional assumption of
stepsize adopted in the existing methods is removed, and the stepsizes in our algorithm are randomized diminishing. Besides,
we prove that all agents converge to Nash equilibrium with probability 1 by our algorithm. Finally, a simulation example
verifies the validity of our algorithm. |
| Key words: Zero-sum game · Nash equilibrium · Time-varying multi-agent network · Projection subgradient algorithm · Random sleep scheme |
