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spohnMatrices -- compute the list of Spohn matrices of a given game

Description

It is crucial that the formats in PR and X match up. The Spohn matrix $M_i$ is the $d_i \times 2$ matrix encoding the denominators and nominators of the conditional expected payoffs of the $i$-th player. The Spohn matrices have rank one at the dependency equilibria of the game $X$.

i1 : Di = {2,2,3};
i2 : PR = probabilityRing(Di);
i3 : X = randomGame(Di);
i4 : M = spohnMatrices(PR,X)

o4 = {| p_{0, 0, 0}+p_{0, 0, 1}+p_{0, 0, 2}+p_{0, 1, 0}+p_{0, 1, 1}+p_{0, 1,
      | p_{1, 0, 0}+p_{1, 0, 1}+p_{1, 0, 2}+p_{1, 1, 0}+p_{1, 1, 1}+p_{1, 1,
                                                                            
     ------------------------------------------------------------------------
     2} 9/2p_{0, 0, 0}+9/4p_{0, 0, 1}+3/4p_{0, 0, 2}+7/4p_{0, 1, 0}+7/9p_{0, 
     2} 7/10p_{1, 0, 0}+7/3p_{1, 0, 1}+7p_{1, 0, 2}+3/7p_{1, 1, 0}+6/7p_{1, 1
                                                                             
     ------------------------------------------------------------------------
     1, 1}+7/10p_{0, 1, 2} |, | p_{0, 0, 0}+p_{0, 0, 1}+p_{0, 0, 2}+p_{1, 0,
     , 1}+6p_{1, 1, 2}     |  | p_{0, 1, 0}+p_{0, 1, 1}+p_{0, 1, 2}+p_{1, 1,
                                                                            
     ------------------------------------------------------------------------
     0}+p_{1, 0, 1}+p_{1, 0, 2} 5/4p_{0, 0,
     0}+p_{1, 1, 1}+p_{1, 1, 2} 3/7p_{0, 1,
                                           
     ------------------------------------------------------------------------
     0}+2/9p_{0, 0, 1}+3/10p_{0, 0, 2}+10p_{1, 0, 0}+3/2p_{1, 0, 1}+7/8p_{1,
     0}+5p_{0, 1, 1}+10/9p_{0, 1, 2}+5/6p_{1, 1, 0}+5p_{1, 1, 1}+2/5p_{1, 1,
                                                                            
     ------------------------------------------------------------------------
     0, 2} |, | p_{0, 0, 0}+p_{0, 1, 0}+p_{1, 0, 0}+p_{1, 1, 0} 5/3p_{0, 0,
     2}    |  | p_{0, 0, 1}+p_{0, 1, 1}+p_{1, 0, 1}+p_{1, 1, 1} 7/2p_{0, 0,
              | p_{0, 0, 2}+p_{0, 1, 2}+p_{1, 0, 2}+p_{1, 1, 2} 2/5p_{0, 0,
     ------------------------------------------------------------------------
     0}+6/5p_{0, 1, 0}+5/3p_{1, 0, 0}+3/7p_{1, 1, 0}   |}
     1}+5/7p_{0, 1, 1}+1/10p_{1, 0, 1}+9/10p_{1, 1, 1} |
     2}+5/9p_{0, 1, 2}+4/3p_{1, 0, 2}+4/7p_{1, 1, 2}   |

o4 : List

See also

Ways to use spohnMatrices:

  • spohnMatrices(Ring,List) (missing documentation)

For the programmer

The object spohnMatrices is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/GameTheory.m2:1658:0.