  With increasing game size, a problem of computational complexity arises. This
is especially true in real world problems such as in social systems, where
there is a significant population of players involved in the game, and the
complexity problem is critical. Previous studies in algorithmic game theory
propose succinct games that enable small descriptions of payoff matrices and
reduction of complexities. However, some of the suggested compromises lose
generality with strict assumptions such as symmetries in utility functions and
cannot be applied to the full range of real world problems that may be
presented. Graphical games are relatively promising, with a good balance
between complexity and generality. However, they assume a given graph structure
of players' interactions and cannot be applied to games without such known
graphs. This study proposes a method to identify an interaction graph between
players and subsequently decompose games into smaller components by cutting out
weak interactions for the purpose of reducing complexity. At the beginning,
players' mutual dependencies on their utilities are quantified as
variance-covariance matrices among players. Then, the interaction graphs among
players are identified by solving eigenvalue problems. Players' interactions
are further decomposed into linear combinations of games. This helps to find a
consistent equilibrium, which is a Nash equilibrium specified by the
decomposition, with reduced computational complexity. Finally, experiments on
simple example games are shown to verify the proposed method.
