A distributed proximal-point algorithm for nash equilibrium seeking in generalized potential games with linearly coupled cost functions

Giuseppe Belgioioso, Sergio Grammatico

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)

Abstract

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.

LanguageEnglish
Title of host publication2019 18th European Control Conference, ECC 2019
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages3390-3395
Number of pages6
ISBN (Electronic)978-3-907144-00-8
DOIs
StatePublished - 1 Jun 2019
Event18th European Control Conference, ECC 2019 - Naples, Italy
Duration: 25 Jun 201928 Jun 2019

Conference

Conference18th European Control Conference, ECC 2019
CountryItaly
CityNaples
Period25/06/1928/06/19

Fingerprint

Potential Games
Generalized Game
Proximal Point Algorithm
games
Nash Equilibrium
Cost functions
Cost Function
Linearly
costs
Parallel algorithms
Telecommunication networks
communication networks
Gradient Algorithm
Subdifferential
Equilibrium Problem
Distributed Algorithms
Communication Networks
Monotonicity
Computer simulation
Game

Cite this

Belgioioso, G., & Grammatico, S. (2019). A distributed proximal-point algorithm for nash equilibrium seeking in generalized potential games with linearly coupled cost functions. In 2019 18th European Control Conference, ECC 2019 (pp. 3390-3395). [8795852] Piscataway: Institute of Electrical and Electronics Engineers. DOI: 10.23919/ECC.2019.8795852
Belgioioso, Giuseppe ; Grammatico, Sergio. / A distributed proximal-point algorithm for nash equilibrium seeking in generalized potential games with linearly coupled cost functions. 2019 18th European Control Conference, ECC 2019. Piscataway : Institute of Electrical and Electronics Engineers, 2019. pp. 3390-3395
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Belgioioso, G & Grammatico, S 2019, A distributed proximal-point algorithm for nash equilibrium seeking in generalized potential games with linearly coupled cost functions. in 2019 18th European Control Conference, ECC 2019., 8795852, Institute of Electrical and Electronics Engineers, Piscataway, pp. 3390-3395, 18th European Control Conference, ECC 2019, Naples, Italy, 25/06/19. DOI: 10.23919/ECC.2019.8795852

A distributed proximal-point algorithm for nash equilibrium seeking in generalized potential games with linearly coupled cost functions. / Belgioioso, Giuseppe; Grammatico, Sergio.

2019 18th European Control Conference, ECC 2019. Piscataway : Institute of Electrical and Electronics Engineers, 2019. p. 3390-3395 8795852.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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N2 - 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.

AB - 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.

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Belgioioso G, Grammatico S. A distributed proximal-point algorithm for nash equilibrium seeking in generalized potential games with linearly coupled cost functions. In 2019 18th European Control Conference, ECC 2019. Piscataway: Institute of Electrical and Electronics Engineers. 2019. p. 3390-3395. 8795852. Available from, DOI: 10.23919/ECC.2019.8795852