0 equilibria with support_enumeration about nashpy

[lucaslugao]

Hello, I was able to reproduce the problem using the official python docker image versions 3.7 and 3.8 (they give similar results):

$ docker run -it --rm python:3.8 bash -c 'pip install nashpy && python -c "import nashpy as nash
import numpy
import scipy
print(\"nash version: \", nash.__version__)
print(\"numpy version: \", numpy.__version__)
print(\"scipy version: \", scipy.__version__)
A = [[52.46337363, 69.47195938, 0. , 54.14372075], [77. , 88. , 84.85714286, 92.4 ], [77.78571429, 87.35294118, 93.5 , 91.38461538], [66.37100751, 43.4530444 , 0. , 60.36191831]]
B = [[23.52690518, 17.35459006, 88.209 , 20.8021711 ], [16.17165 , 0. , 14.00142857, 6.46866 ], [ 0. , 5.76529412, 0. , 0. ], [15.68327304, 40.68156322, 84.00857143, 11.06596804]]
game = nash.Game(A, B)
print(game)
print(list(game.support_enumeration()))"'

Collecting nashpy
  Downloading https://files.pythonhosted.org/packages/ad/a2/5d36744511640db1869029d2ab324b55f6eaaa2a51f75a87408a7e8000f4/nashpy-0.0.19.tar.gz
Collecting numpy>=1.12.1
  Downloading https://files.pythonhosted.org/packages/d7/6a/3fed132c846d1e47963f30376cc041e9dd586d286d931055ad06ff65c6c7/numpy-1.17.4-cp38-cp38-manylinux1_x86_64.whl (20.5MB)
     |████████████████████████████████| 20.5MB 3.0MB/s 
Collecting scipy>=0.19.0
  Downloading https://files.pythonhosted.org/packages/dd/25/b57bf2134f343909541977a79aa385addbc6a8ac470669739d8522e32c89/scipy-1.3.2-cp38-cp38-manylinux1_x86_64.whl (25.2MB)
     |████████████████████████████████| 25.2MB 6.8MB/s 
Building wheels for collected packages: nashpy
  Building wheel for nashpy (setup.py) ... done
  Created wheel for nashpy: filename=nashpy-0.0.19-cp38-none-any.whl size=10816 sha256=ed3e15df392bb9667bc3d2d0431b3baf24559594cf7bc33943a46e8b744829c1
  Stored in directory: /root/.cache/pip/wheels/18/e9/56/2d04d01a6969d167f86d3afcb3d128c0b43d0d73ea471c835b
Successfully built nashpy
Installing collected packages: numpy, scipy, nashpy
Successfully installed nashpy-0.0.19 numpy-1.17.4 scipy-1.3.2
nash version:  0.0.19
numpy version:  1.17.4
scipy version:  1.3.2
Bi matrix game with payoff matrices:

Row player:
[[52.46337363 69.47195938  0.         54.14372075]
 [77.         88.         84.85714286 92.4       ]
 [77.78571429 87.35294118 93.5        91.38461538]
 [66.37100751 43.4530444   0.         60.36191831]]

Column player:
[[23.52690518 17.35459006 88.209      20.8021711 ]
 [16.17165     0.         14.00142857  6.46866   ]
 [ 0.          5.76529412  0.          0.        ]
 [15.68327304 40.68156322 84.00857143 11.06596804]]
/usr/local/lib/python3.8/site-packages/nashpy/algorithms/support_enumeration.py:196: RuntimeWarning: 
An even number of (0) equilibria was returned. This
indicates that the game is degenerate. Consider using another algorithm
to investigate.
                  
  warnings.warn(warning, RuntimeWarning)
[]

[victorvianna]

@lucaslugao

[drvinceknight]

I do not get the same output:

>>> import nashpy as nash
>>> nash.__version__
'0.0.19'
>>> A = [[52.46337363, 69.47195938, 0. , 54.14372075], [77. , 88. , 84.85714286, 92.4 ], [77.78571429, 87.35294118, 93.5 , 91.38461538], [66.37100751, 43.4530444 , 0. , 60.36191831]]
>>> B = [[23.52690518, 17.35459006, 88.209 , 20.8021711 ], [16.17165 , 0. , 14.00142857, 6.46866 ], [ 0. , 5.76529412, 0. , 0. ], [15.68327304, 40.68156322, 84.00857143, 11.06596804]]
>>> game = nash.Game(A, B)
>>> game
Bi matrix game with payoff matrices:

Row player:
[[52.46337363 69.47195938  0.         54.14372075]
 [77.         88.         84.85714286 92.4       ]
 [77.78571429 87.35294118 93.5        91.38461538]
 [66.37100751 43.4530444   0.         60.36191831]]

Column player:
[[23.52690518 17.35459006 88.209      20.8021711 ]
 [16.17165     0.         14.00142857  6.46866   ]
 [ 0.          5.76529412  0.          0.        ]
 [15.68327304 40.68156322 84.00857143 11.06596804]]
>>> list(game.support_enumeration())
[(array([7.33134761e-17, 2.62812089e-01, 7.37187911e-01, 0.00000000e+00]),
  array([0.4516129, 0.5483871, 0.       , 0.       ]))]

Remember that game.support_enumeration() returns a generator, perhaps you iterated over it once and then when querying it again found no equilibria.

[drvinceknight]

Not sure what might be happening, again doesn't reproduce (I just updated numpy in case it was that):

>>> import numpy
>>> import scipy
>>> import nashpy as nash
>>> print("nash version: ", nash.__version__)
>>> print("numpy version: ", numpy.__version__)
>>> print("scipy version: ", scipy.__version__)
>>> A = [[52.46337363, 69.47195938, 0. , 54.14372075], [77. , 88. , 84.85714286, 92.4 ], [77.78571429, 87.35294118, 93.5 , 91.38461538], [66.37100751, 43.4530444 , 0. , 60.36191831]]
>>> B = [[23.52690518, 17.35459006, 88.209 , 20.8021711 ], [16.17165 , 0. , 14.00142857, 6.46866 ], [ 0. , 5.76529412, 0. , 0. ], [15.68327304, 40.68156322, 84.00857143, 11.06596804]]
>>> game = nash.Game(A, B)
>>> print(list(game.support_enumeration()))
nash version:  0.0.19
numpy version:  1.17.3
scipy version:  1.3.1
[(array([7.33134761e-17, 2.62812089e-01, 7.37187911e-01, 0.00000000e+00]), array([0.4516129, 0.5483871, 0.       , 0.       ]))]

I will add this to the test suite to see what the CI says.

[drvinceknight]

Reopening as I've been able to reproduce on circle CI (not on travis or appveyor).

[drvinceknight]

See #68

[drvinceknight]

I have pinned down the error to being based on whether numpy is pip installed (I get the same error) or conda installed (no error). If either of you could try running with a conda install of numpy to confirm that would be appreciated.

[drvinceknight]

Still getting the error with conda
nash version: 0.0.19
numpy version: 1.17.3
scipy version: 1.3.2

That's very weird-- see below, I've run numerous experiments on numerous systems -- (have you uninstalled the pip install and reinstalled etc...?).

Anyway, I believe I have now gotten to the bottom of this. On #68 you can see what I have done:

• Before that PR the CI was running on travis (linux) and appveyor (windows) - I added the case we're discussing here to both of those and did not get an error.
• I added circle CI but did not use an anaconda environment on it but pip installed everything. This reproduced your error.
• I experimented locally: with pip installed numpy I got the error, with conda installed I did not (I tried this multiple times).
• When I round A and B to 5 decimal places I no longer get the error on with either version: this is essentially the test that is now being added by #68
• When adding intermediate tests I track this down to the np.linalg.solve (used to solve the underlying linear system).

---

To summarise: using precompiled (by anaconda) versions of dependencies the error does not reproduce (this has been run on 3 systems, mine locally, travis and appveyor) but using a pip installed version (run on 2 systems, mine locally and circle ci) does reproduce the error.

---

Thus my conclusion is that this is a precision error in the underlying numpy linear algebraic solver and not something that is fixable.

For completeness here is code that runs the solver with rounding to 5 decimals places:

>>> import numpy as np
>>> import scipy
>>> import nashpy as nash
>>> print("nash version: ", nash.__version__)
>>> print("numpy version: ", np.__version__)
>>> print("scipy version: ", scipy.__version__)
>>> A = [[52.46337363, 69.47195938, 0. , 54.14372075], [77. , 88. , 84.85714286, 92.4 ], [77.78571429, 87.35294118, 93.5 , 91.38461538], [66.37100751, 43.4530444 , 0. , 60.36191831]]
>>> B = [[23.52690518, 17.35459006, 88.209 , 20.8021711 ], [16.17165 , 0. , 14.00142857, 6.46866 ], [ 0. , 5.76529412, 0. , 0. ], [15.68327304, 40.68156322, 84.00857143, 11.06596804]]
>>> A = np.round(A, 5)
>>> B = np.round(B, 5)
>>> game = nash.Game(A, B)
>>> print(list(game.support_enumeration()))
nash version:  0.0.19
numpy version:  1.17.3
scipy version:  1.3.2
[(array([2.39382972e-17, 2.62811951e-01, 7.37188049e-01, 0.00000000e+00]), array([0.4516147, 0.5483853, 0.       , 0.       ]))]

If either of you feel there is something more that could be done here please don't hesitate to reopen the issue :) Thank you for taking time to report the bug. 👍