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With increasing game size, a problem of computational complexity arises. Thisis especially true in real world problems such as in social systems, wherethere is a significant population of players involved in the game, and thecomplexity problem is critical. Previous studies in algorithmic game theorypropose succinct games that enable small descriptions of payoff matrices andreduction of complexities. However, some of the suggested compromises losegenerality with strict assumptions such as symmetries in utility functions andcannot be applied to the full range of real world problems that may bepresented. Graphical games are relatively promising, with a good balancebetween complexity and generality. However, they assume a given graph structureof players' interactions and cannot be applied to games without such knowngraphs. This study proposes a method to identify an interaction graph betweenplayers and subsequently decompose games into smaller components by cutting outweak interactions for the purpose of reducing complexity. At the beginning,players' mutual dependencies on their utilities are quantified asvariance-covariance matrices among players. Then, the interaction graphs amongplayers are identified by solving eigenvalue problems. Players' interactionsare further decomposed into linear combinations of games. This helps to find aconsistent equilibrium, which is a Nash equilibrium specified by thedecomposition, with reduced computational complexity. Finally, experiments onsimple example games are shown to verify the proposed method.

Linear Game Theory : Reduction of complexity by decomposing large games into partial games