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Combined Learning
Published in Hamidou Tembine, Distributed Strategic Learning for Wireless Engineers, 2018
Definition 4.4.3.3 (State-dependent potential games). We say that the gameG(w)is a potential game if there exists a function ϕ (w, a) and functionsB˜j(w,a−j)such that the payoff function of player j can be written asR˜j(w,a)=ϕ(w,a)+B˜j(w,a−j).
Application of Game Theory for Big Data Analytics
Published in Mohiuddin Ahmed, Al-Sakib Khan Pathan, Data Analytics, 2018
Mohammad Muhtady Muhaisin, Taseef Rahman
A potential game is one where the incentives of all the players to change their strategies can be expressed using one global function called potential function. Two types of potential games are the ordinal and cardinal potential games. In cardinal games, the difference in individual payoffs for each player obtained by individually changing one’s strategy only must have the same value as the difference in values for the potential function. In ordinal games, only the signs of the differences have to be the same.
Game theory and hybrid genetic algorithm for energy management and real-time pricing in smart grid: the Tunisian case
Published in International Journal of Green Energy, 2020
Mohamed Maddouri, Habib Elkhorchani, Khaled Grayaa
As it was already proven in cited works (Belgana, Rimal, and Maier 2014; Maddouri et al. 2018; Saad et al. 2012) that the potential game Γ with potential function has distinct computational advantages in that any maximizer of the potential function yields a pure-strategy Nash equilibrium. Consequently, the computation of the equilibrium became equivalent to the solution of an optimization problem: this means there is no need for computational fixed-point theory. Thus, the set of maximizers provide a natural equilibrium and all equilibria are local maximizers of the potential.
A finite convergence algorithm for solving linear-quadratic network games with strategic complements and bounded strategies
Published in Optimization Methods and Software, 2023
A game in strategic form is called a potential game if it exists a function such that, for each , for all and for all :