# drvinceknight/Nashpy

Release v0.0.17

 @@ -8,11 +8,12 @@ one described in [Nisan2007]_. The algorithm is as follows: For a nondegenerate 2 player game :math:(A, B)\in{\mathbb{R}^{m\times n}}^2 For a degenerate 2 player game :math:(A, B)\in{\mathbb{R}^{m\times n}}^2 the following algorithm returns all nash equilibria: 1. For all :math:1\leq k\leq \min(m, n); 2. For all pairs of support :math:(I, J) with :math:|I|=|J|=k 1. For all :math:1\leq k_1\leq m and :math:1\leq k_2\leq n; 2. For all pairs of support :math:(I, J) with :math:|I|=k_1 and :math:|J|=k_2. 3. Solve the following equations (this ensures we have best responses): .. math:: @@ -37,8 +38,9 @@ Discussion 1. Step 1 is a complete enumeration of all possible strategies that the equilibria could be. 2. Step 2 is based on the definition of a non degenerate game which ensures that equilibria will be on supports of the same size. 2. Step 2 can be modified to only consider degenerate games ensuring that only supports of equal size are considered :math:|I|=|J|. This is described further in :ref:degenerate-games. 3. Step 3 are the linear equations that are to be solved, for a given pair of supports these ensure that neither player has an incentive to move to another strategy on that support.