A distributed proximal-point algorithm for Nash equilibrium seeking in generalized potential games with linearly coupled cost functions
A distributed proximal-point algorithm for Nash equilibrium seeking in generalized potential games with linearly coupled cost functions
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DOI：
10.23919/ecc.2019.8795852
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发表时间：
2019-06
期刊：
影响因子：
--
通讯作者：
Giuseppe Belgioioso;Sergio Grammatico
中科院分区：
文献类型：
--
作者：
Giuseppe Belgioioso;Sergio Grammatico
We address the generalized Nash equilibrium seeking problem for a population of noncooperative agents playing potential games with linear coupling constraints over a communication network. We consider a class of generalized potential games where the coupling in the cost functions of the agents is linear, i.e., $J_{i}(x_{i}, x_{-i}): =f_{i}(x_{i})+\ell_{i}(x_{-i})^{\top}x_{i}$ where $\ell_{i}$ is linear. By exploiting this special structure, we design a distributed algorithm with convergence guarantee under mild assumptions, i.e., (non-strict) monotonicity of the pseudo-subdifferential mapping. The potential of the proposed algorithm is shown via numerical simulations on a networked Nash Cournot game, where we observe faster convergence with respect to standard projected pseudo-gradient algorithms.
We address the generalized Nash equilibrium seeking problem for a population of noncooperative agents playing potential games with linear coupling constraints over a communication network. We consider a class of generalized potential games where the coupling in the cost functions of the agents is linear, i.e., $J_{i}(x_{i}, x_{-i}): =f_{i}(x_{i})+\ell_{i}(x_{-i})^{\top}x_{i}$ where $\ell_{i}$ is linear. By exploiting this special structure, we design a distributed algorithm with convergence guarantee under mild assumptions, i.e., (non-strict) monotonicity of the pseudo-subdifferential mapping. The potential of the proposed algorithm is shown via numerical simulations on a networked Nash Cournot game, where we observe faster convergence with respect to standard projected pseudo-gradient algorithms.