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correlatedEquilibria -- compute the correlated equilibrium polytope for a game

Description

This method constructs and returns the correlated equilibrium polytope for a finite game. The input is a list of payoff tensors, one for each player. The tensor at position i gives the payoffs for player i.

i1 : X1 = zeroTensor(QQ, {2,2});
i2 : X2 = zeroTensor(QQ, {2,2});
i3 : X1#{0,0} = -99; X1#{0,1} = 1; X1#{1,0} = 0; X1#{1,1} = 0;
i7 : X2#{0,0} = -99; X2#{0,1} = 0; X2#{1,0} = 1; X2#{1,1} = 0;
i11 : CE = correlatedEquilibria {X1, X2}

o11 = CE

o11 : Polyhedron
i12 : vertices CE

o12 = | 0 0 1/199  0      1/10000    |
      | 1 0 99/199 1/101  99/10000   |
      | 0 1 99/199 1/101  99/10000   |
      | 0 0 0      99/101 9801/10000 |

               4       5
o12 : Matrix QQ  <-- QQ
i13 : facets CE

o13 = (| -1 0   0   0  |, 0)
       | 99 -1  0   0  |
       | 99 0   -1  0  |
       | 0  0   0   -1 |
       | 0  -99 0   1  |
       | 0  0   -99 1  |

o13 : Sequence
i14 : fVector CE

o14 = {5, 9, 6, 1}

o14 : List
i15 : X = randomGame {2,2,3};
i16 : CE = correlatedEquilibria X;
i17 : dim CE

o17 = 11

See also

Ways to use correlatedEquilibria:

  • correlatedEquilibria(List)

For the programmer

The object correlatedEquilibria is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/GameTheory.m2:1297:0.