2010
DOI: 10.1007/s10589-010-9331-9
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Decomposition algorithms for generalized potential games

Abstract: We analyze some new decomposition schemes for the solution of generalized Nash equilibrium problems. We prove convergence for a particular class of generalized potential games that includes some interesting engineering problems. We show that some versions of our algorithms can deal also with problems lacking any convexity and consider separately the case of two players for which stronger results can be obtained.

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Cited by 119 publications
(132 citation statements)
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“…Since (i) the payoff function Θ p of PaaS provider depends only on his own strategies N s , (ii) the payoff function Θ s of each SaaS provider s only depends on his own strategies X s and R P s , and (iii) constraints (17) and (18) are shared among the players, we can conclude that this game is a generalized potential game [27,34] where the potential function is simply the sum of the players payoff functions. This potential function represents a social welfare for the game.…”
Section: Potential Functionmentioning
confidence: 91%
See 1 more Smart Citation
“…Since (i) the payoff function Θ p of PaaS provider depends only on his own strategies N s , (ii) the payoff function Θ s of each SaaS provider s only depends on his own strategies X s and R P s , and (iii) constraints (17) and (18) are shared among the players, we can conclude that this game is a generalized potential game [27,34] where the potential function is simply the sum of the players payoff functions. This potential function represents a social welfare for the game.…”
Section: Potential Functionmentioning
confidence: 91%
“…If we denote L i k ≥ 0, for k ∈ A and i = 1, 2, 3, the KKT multipliers associated to constraints (25) and (26), and L 4 ≥ 0, the multiplier associated to constraint (27), then the KKT system is the following:…”
Section: Thus the Hessian Matrix Of H Ismentioning
confidence: 99%
“…Since each agent has a pay-off function of the same structure, the resulting game is a potential game, Facchinei et al (2011);Voorneveld (2000).…”
Section: Electric Vehicle Charging Control Problemmentioning
confidence: 99%
“…Utility functions satisfying (6) can be found in so called "network transmission games," see, e.g., Facchinei et al (2011) and references therein, which are somewhat similar to Rosenthal's (1973) congestion games, but do not belong to the class. There is a directed graph with the set of links E; each player i ∈ N is assigned a path π i ⊆ E in the graph (between a source and a target) and sends a flow x i ∈ [0, b i ] ⊂ R along the path, getting a reward w i (x i ) depending on her flow and bearing costs e∈π i c e ( j: e∈π j x j ) depending on the total flow through each link…”
Section: Games With Structured Utilitiesmentioning
confidence: 99%