  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.
