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| Distributed Nash equilibrium seeking with order-reduced dynamics based on consensus exact penalty |
| ShuLiang1,2,ShuyuLiu1,2,YiguangHong1,2,JieChen1,2 |
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| (1 The Department of Control Science and Engineering, Tongji University, Shanghai 201804, China
2 Shanghai Research Institute for Intelligent Autonomous Systems, Shanghai 201210, China) |
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| 摘要: |
| In this paper, we consider a networked game with coupled constraints and focus on variational Nash equilibrium seeking. For
distributed algorithm design, we eliminate the coupled constraints by employing local Lagrangian functions and construct
exact penalty terms to attain multipliers’ optimal consensus, which yields a set of equilibrium conditions without any coupled
constraint and consensus constraint. Moreover, these conditions are only based on strategy and multiplier variables, without
auxiliary variables. Then, we present a distributed order-reduced dynamics that updates the strategy and multiplier variables
with guaranteed convergence. Compared with many other distributed algorithms, our algorithm contains no auxiliary variable,
and therefore, it can save computation and communication. |
| 关键词: Game theory · Nash equilibrium seeking · Distributed algorithm · Coupled constraints · Order-reduced dynamics |
| DOI：https://doi.org/10.1007/s11768-023-00166-7 |
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| 基金项目:This work was supported in part by the National Key Research and Development Program of China under grant 2022YFA1004700, and in part by the Natural Science Foundation of China under grant 72171171, and in part by Shanghai Municipal Science and Technology Major Project under grant 2021SHZDZX0100. |
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| Distributed Nash equilibrium seeking with order-reduced dynamics based on consensus exact penalty |
| Shu Liang1,2,Shuyu Liu1,2,Yiguang Hong1,2,Jie Chen1,2 |
| (1 The Department of Control Science and Engineering, Tongji University, Shanghai 201804, China
2 Shanghai Research Institute for Intelligent Autonomous Systems, Shanghai 201210, China) |
| Abstract: |
| In this paper, we consider a networked game with coupled constraints and focus on variational Nash equilibrium seeking. For
distributed algorithm design, we eliminate the coupled constraints by employing local Lagrangian functions and construct
exact penalty terms to attain multipliers’ optimal consensus, which yields a set of equilibrium conditions without any coupled
constraint and consensus constraint. Moreover, these conditions are only based on strategy and multiplier variables, without
auxiliary variables. Then, we present a distributed order-reduced dynamics that updates the strategy and multiplier variables
with guaranteed convergence. Compared with many other distributed algorithms, our algorithm contains no auxiliary variable,
and therefore, it can save computation and communication. |
| Key words: Game theory · Nash equilibrium seeking · Distributed algorithm · Coupled constraints · Order-reduced dynamics |
