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nashEquilibriumRing(List) -- define the Nash Equilibrium ring

Description

Let $p_{i,j}$ be the probability of $i$-th player choosing the $j$-th strategy, where $j \in \{0, \cdots, d_j-1\}$. The ideal of the totally mixed Nash equilibria of the game is defined in the polynomial ring over a field $k$ with generators $\{p_{i,j} \ | \ 0\leq i\leq n-1, 0\leq j\leq d_j-1\}$. The ring generators are ordered lexicographically.

i1 : tensors = randomGame {2,4,3};
i2 : R = nashEquilibriumRing tensors;
i3 : baseRing R

o3 = QQ

o3 : Ring
i4 : gens R

o4 = {p      , p      , p      , p      , p      , p      , p      , p      ,
       {0, 0}   {0, 1}   {1, 0}   {1, 1}   {1, 2}   {1, 3}   {2, 0}   {2, 1} 
     ------------------------------------------------------------------------
     p      }
      {2, 2}

o4 : List

See also

Ways to use this method:


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/GameTheory.m2:1332:0.