Network design for fast convergence to the nash equilibrium in a class of repeated games

This work studies the problem of designing a Network such that a set of dynamic rules, in a class of repeated games, converges quickly to the Nash equilibrium. Particularly a very simple class of repeated games with mean field interactions is considered and we assume that the actions of the particip...

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Bibliographic Details
Published in2016 24th Mediterranean Conference on Control and Automation (MED) pp. 1026 - 1032
Main Authors Kordonis, I., Papavassilopoulos, G. P.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2016
Subjects
Convergence
Eigenvalues and eigenfunctions
Games
Heuristic algorithms
Laplace equations
Nash equilibrium
Vehicle dynamics
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Summary:This work studies the problem of designing a Network such that a set of dynamic rules, in a class of repeated games, converges quickly to the Nash equilibrium. Particularly a very simple class of repeated games with mean field interactions is considered and we assume that the actions of the participants are determined using some simple myopic gradient based dynamic rules. The information about the actions of the other players is transmitted through a Network, using a consensus type dynamics. The speed of the convergence to equilibrium is characterized, using the Lyapunov equation involving a Laplacian like matrix. A topology optimization problem for the communication graph is then stated and an algorithm, based on the effects of new edges to the speed of convergence, is proposed. Numerical results are also given.
DOI:10.1109/MED.2016.7535941