2-Player games in general provide a popular platform for research in Artificial Intelligence (AI). One of the main challenges coming from this platform is approximating a Nash Equilibrium (NE) over zero-sum matrix games. While the problem of computing such a Nash Equilibrium is solvable in polynomial time using Linear Programming (LP), it rapidly becomes infeasible to solve as the size of the matrix grows; a situation commonly encountered in games. This paper focuses on improving the approximation of a NE for matrix games such that it outperforms the state-of-the-art algorithms given a finite (and rather small) number T of oracle requests to rewards. To reach this objective, we propose to share information between the different relevant pure strategies. We show both theoretically by improving the bound and empirically by experiments on artificial matrices and on a real-world game that information sharing leads to an improvement of the approximation of the NE.
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