Statistical physics approach to graphical games: local and global interactions

Details Statistical physics approach to graphical games: local and global interactions Statistical physics approach to graphical games: local and global interactions

2011-04-11

arxiv.org/abs/1104.1929v1

Eur. Phys. J. B 81, 327 (2011)

Physics

Condensed Matter

Statistical Mechanics

32 pages, 11 figures, to be published in Eur. Phys. J. B

Scientific paper

10.1140/epjb/e2011-10963-x

In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium (solution). We consider a representation of games that extends over graphical games to deal conveniently with both local a global interactions and use the cavity method of statistical physics to study the geometrical structure of the equilibria space. The method also provides a distributive and local algorithm to find an equilibrium. For simplicity we consider only pure Nash equilibria but the methods can as well be extended to deal with (approximated) mixed Nash equilirbia.

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