Add exercises to text book and clean up pdf output.

.gitignore

@@ -11,3 +11,10 @@ build/
 env/
 .tox/
 *.DS_Store
+*.aux
+*.log
+*.fdb_latexmk
+*.fls
+*.xdv
+env*
+

benchmarks/test_support_enumeration.py

@@ -1,6 +1,7 @@
 """
 Benchmarks for support enumeration
 """
+
 import unittest
 
 import numpy as np
@@ -13,12 +14,21 @@ def test_support_enumeration_on_two_by_two_game(benchmark):
     eqs = support_enumeration(A, -A)
     benchmark(tuple, eqs)
 
+
 def test_support_enumeration_on_three_by_three_game(benchmark):
     A = np.array(((0, 1, -1), (-1, 0, 1), (1, -1, 0)))
     eqs = support_enumeration(A, -A)
     benchmark(tuple, eqs)
 
+
 def test_support_enumeration_on_four_by_four_game(benchmark):
-    A = np.array(((0, 1, -1, 1/4), (-1, 0, 1, 1/4), (1, -1, 0, 1/4), (1/4, 1/4, 1/4, 1/4)))
+    A = np.array(
+        (
+            (0, 1, -1, 1 / 4),
+            (-1, 0, 1, 1 / 4),
+            (1, -1, 0, 1 / 4),
+            (1 / 4, 1 / 4, 1 / 4, 1 / 4),
+        )
+    )
     eqs = support_enumeration(A, -A)
     benchmark(tuple, eqs)

docs/Makefile

@@ -17,4 +17,4 @@ help:
 # Catch-all target: route all unknown targets to Sphinx using the new
 # "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
 %: Makefile
-	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)

docs/_static/discussion/extensive-form-game-example-with-perfect-information_one_step_backwards_induction/README.md

@@ -0,0 +1,8 @@
+Source files for an image used in the description of extensive form games.
+
+Compilation instructions:
+
+```
+$ latexmk --xelatex main.tex
+$ convert -density 300 main.pdf -quality 90 main.png
+```

docs/_static/discussion/extensive-form-game-example-with-perfect-information_one_step_backwards_induction/main.tex

@@ -0,0 +1,29 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usetikzlibrary{calc}
+
+\begin{document}
+
+\begin{tikzpicture}
+    \node [draw, color=red] (A1) at (0, 0) {\(A_1\)};
+        \node [draw, color=blue] (B1) at ($(A1) + (-2.5, -2)$) {\(B_1\)};
+            \node [draw] (O1) at ($(B1) + (-1, -2)$) {\tiny{\(O_1\)}};
+            \node (SS) at ($(O1) + (0, -.5)$) {\((4, 1)\)};
+            \node [draw] (O2) at ($(B1) + (1, -2)$) {\tiny{\(O_2\)}};
+            \node (SC) at ($(O2) + (0, -.5)$) {\((3, 5)\)};
+        \node [draw, color=blue] (B2) at ($(A1) + (2.5, -2)$) {\(B_2\)};
+                \node [draw] (O3) at ($(B2) + (-1, -2)$) {\tiny{\(O_3\)}};
+                \node (CS) at ($(O3) + (0, -.5)$) {\((4, 2)\)};
+            \node [draw] (O5) at ($(B2) + (1, -2)$) {\tiny{\(O_5\)}};
+            \node (CC) at ($(O5) + (0, -.5)$) {\((2, 0)\)};
+
+    \draw (A1) -- node[left=3mm] {X} (B1);
+    \draw (A1) -- node[right=3mm] {W} (B2);
+        \draw (B1)  -- node[left=3mm] {a} (O1);
+        \draw (B1) -- node[right=3mm] {b} (O2);
+        \draw (B2) -- node[left=3mm] {c} (O3);
+        \draw (B2) -- node[right=3mm] {d} (O5);
+\end{tikzpicture}
+
+\end{document}

docs/_static/discussion/extensive-form-game-example-with-perfect-information_three_steps_backwards_induction/README.md

@@ -0,0 +1,8 @@
+Source files for an image used in the description of extensive form games.
+
+Compilation instructions:
+
+```
+$ latexmk --xelatex main.tex
+$ convert -density 300 main.pdf -quality 90 main.png
+```

docs/_static/discussion/extensive-form-game-example-with-perfect-information_three_steps_backwards_induction/main.tex

@@ -0,0 +1,19 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usetikzlibrary{calc}
+
+\begin{document}
+
+\begin{tikzpicture}
+    \node [draw, color=red] (A1) at (0, 0) {\(A_1\)};
+            \node [draw] (O2) at ($(A1) + (-2.5, -2)$) {\tiny{\(O_2\)}};
+            \node (SC) at ($(O2) + (0, -.5)$) {\((3, 5)\)};
+                \node [draw] (O3) at ($(A1) + (2.5, -2)$) {\tiny{\(O_3\)}};
+                \node (CS) at ($(O3) + (0, -.5)$) {\((4, 2)\)};
+
+    \draw (A1) -- node[left=3mm] {X} (O2);
+    \draw (A1) -- node[right=3mm] {W} (O3);
+\end{tikzpicture}
+
+\end{document}

docs/_static/discussion/extensive-form-game-example-with-perfect-information_two_steps_backwards_induction/README.md

@@ -0,0 +1,8 @@
+Source files for an image used in the description of extensive form games.
+
+Compilation instructions:
+
+```
+$ latexmk --xelatex main.tex
+$ convert -density 300 main.pdf -quality 90 main.png
+```

docs/_static/discussion/extensive-form-game-example-with-perfect-information_two_steps_backwards_induction/main.tex

@@ -0,0 +1,24 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usetikzlibrary{calc}
+
+\begin{document}
+
+\begin{tikzpicture}
+    \node [draw, color=red] (A1) at (0, 0) {\(A_1\)};
+        \node [draw, color=blue] (B1) at ($(A1) + (-2.5, -2)$) {\(B_1\)};
+            \node [draw] (O1) at ($(B1) + (-1, -2)$) {\tiny{\(O_1\)}};
+            \node (SS) at ($(O1) + (0, -.5)$) {\((4, 1)\)};
+            \node [draw] (O2) at ($(B1) + (1, -2)$) {\tiny{\(O_2\)}};
+            \node (SC) at ($(O2) + (0, -.5)$) {\((3, 5)\)};
+                \node [draw] (O3) at ($(A1) + (2.5, -2)$) {\tiny{\(O_3\)}};
+                \node (CS) at ($(O3) + (0, -.5)$) {\((4, 2)\)};
+
+    \draw (A1) -- node[left=3mm] {X} (B1);
+    \draw (A1) -- node[right=3mm] {W} (O3);
+        \draw (B1)  -- node[left=3mm] {a} (O1);
+        \draw (B1) -- node[right=3mm] {b} (O2);
+\end{tikzpicture}
+
+\end{document}

docs/_static/discussion/extensive-form-game-exercise-four/main.tex

@@ -0,0 +1,19 @@
+\documentclass[tikz]{standalone}
+\usepackage{tikz,amsmath}
+\begin{document}
+\tikzstyle{level 1}=[level distance=3.5cm, sibling distance=3.5cm]
+\tikzstyle{level 2}=[level distance=3.5cm, sibling distance=2cm]
+\tikzstyle{player} = [text width=5em, draw, text centered, rectangle, fill=blue!20, inner sep=1pt]
+\tikzstyle{nature} = [minimum width=3pt,circle,  draw, fill=red!20, inner sep=1pt]
+\tikzstyle{end} = [circle, minimum width=3pt, fill, inner sep=0pt, right]
+\begin{tikzpicture}[grow=right, sloped]
+    \node[player]{a: 1}
+        child  {node (C2)  [player] {b: 1}
+                child {node[end] {} node[right] {$(3,2)$} edge from parent node[below] {A}}
+                child {node[end] {} node[right] {$(1,1)$} edge from parent node[below] {B}} edge from parent node[below] {A}}
+        child {node (1stC) (C1) [player] {c: 2}
+                child {node[end] {} node[right] {$(0,0)$} edge from parent node[below] {A}}
+                child {node[end] {} node[right] {$(4,0)$} edge from parent node[below] {B}}
+                child {node[end] {} node[right] {$(2,3)$} edge from parent node[below] {C}} edge from parent node[below] {B}};
+\end{tikzpicture}
+\end{document}

docs/_static/discussion/extensive-form-game-exercise-one/main.tex

@@ -0,0 +1,29 @@
+\documentclass[tikz]{standalone}
+\usepackage{tikz,amsmath}
+\begin{document}
+\tikzstyle{level 1}=[level distance=3.5cm, sibling distance=3.5cm]
+\tikzstyle{level 2}=[level distance=3.5cm, sibling distance=2cm]
+\tikzstyle{player} = [text width=5em, draw, text centered, rectangle, fill=blue!20, inner sep=1pt]
+\tikzstyle{nature} = [minimum width=3pt,circle,  draw, fill=red!20, inner sep=1pt]
+\tikzstyle{end} = [circle, minimum width=3pt, fill, inner sep=0pt, right]
+\begin{tikzpicture}[grow=right, sloped]
+    \node[player]{a: 1}
+        child {node[player] {b: 2}
+            child {node[player] {c: 1}
+                child {node[player] {d: 2}
+                    child {node[player] {e: 1}
+                        child {node[end] {} node [right] {$(2,17)$} edge from parent node[below] {W}}
+                        child {node[end] {} node [right] {$(6,4)$} edge from parent node[below] {Y}}
+                    edge from parent node[below] {J}
+                    }
+                    child {node[end] {} node [right] {$(7,30)$} edge from parent node[below] {X}}
+                    edge from parent node[below] {F}}
+                child {node[end] {} node [right] {$(70,3)$} edge from parent node[below] {Z}}
+                edge from parent node[below] {D}
+            edge from parent node[below] {D}}
+            child {node[end] {} node [right] {$(1,6)$}
+            edge from parent node[below] {C}}
+        edge from parent node[below] {B}}
+        child {node[end] {} node [right] {$(3,2)$} edge from parent node[below] {A}};
+\end{tikzpicture}
+\end{document}

docs/_static/discussion/extensive-form-game-exercise-three/main.tex

@@ -0,0 +1,34 @@
+\documentclass[tikz]{standalone}
+\usepackage{tikz,amsmath}
+\begin{document}
+\tikzstyle{level 1}=[level distance=3.5cm, sibling distance=3.5cm]
+\tikzstyle{level 2}=[level distance=3.5cm, sibling distance=1cm]
+\tikzstyle{player} = [text width=5em, draw, text centered, rectangle, fill=blue!20, inner sep=1pt]
+\tikzstyle{nature} = [minimum width=3pt,circle,  draw, fill=red!20, inner sep=1pt]
+\tikzstyle{end} = [circle, minimum width=3pt, fill, inner sep=0pt, right]
+\begin{tikzpicture}[grow=right, sloped]
+    \node[player]{a: 1}
+        child  {node (C2)  [player] {b: 2}
+                child {node[end] {} node[right] {$(3,2,1)$} edge from parent node[below] {B}}
+                child {node (C3)[player] {e: 3}
+                    child {node [end] {} node[right] {$(60,1,53)$}
+                edge from parent node[below] {B}}
+                    child {node [end] {} node[right] {$(6,0,2)$}
+                edge from parent node[below] {A}}
+                edge from parent node[below] {A}
+        }
+        edge from parent node[below] {B}}
+        child {node (1stC) (C1) [player] {c: 2}
+                child {node (C4) [player] {d: 3}
+                    child {node [end] {} node[right] {$(20,50,80)$}
+                edge from parent node[below] {B}}
+                    child {node [end] {} node[right] {$(30,40,50)$}
+                edge from parent node[below] {A}}
+            edge from parent node[below] {B}
+                }
+                child {node[end] {} node[right] {$(4,0,3)$} edge from parent node[below] {A}}
+                 edge from parent node[below] {A}};
+        \draw [dashed] (C2) -- (C1);
+        \draw [dashed] (C3) -- (C4);
+\end{tikzpicture}
+\end{document}

docs/_static/discussion/extensive-form-game-exercise-two/main.tex

@@ -0,0 +1,31 @@
+\documentclass[tikz]{standalone}
+\usepackage{tikz,amsmath}
+\begin{document}
+\tikzstyle{level 1}=[level distance=3.5cm, sibling distance=3.5cm]
+\tikzstyle{level 2}=[level distance=3.5cm, sibling distance=2cm]
+\tikzstyle{level 3}=[level distance=3.5cm, sibling distance=1cm]
+\tikzstyle{player} = [text width=5em, draw, text centered, rectangle, fill=blue!20, inner sep=1pt]
+\tikzstyle{nature} = [minimum width=3pt,circle,  draw, fill=red!20, inner sep=1pt]
+\tikzstyle{end} = [circle, minimum width=3pt, fill, inner sep=0pt, right]
+\begin{tikzpicture}[grow=right, sloped]
+    \node[player]{a: 1}
+        child {node[player] {c: 2}
+                child {node[player] {g: 1}
+                    child{node[end] {} node[right]{$(3,2)$} edge from parent node[below]{K}}
+                    child{node [end] {} node[right]{$(6,7)$} edge from parent node[below]{L}}edge from parent node[below] {B}}
+                child {node[player] {f: 1}
+                    child{node[end] {} node[right]{$(1,3)$} edge from parent node[below]{K}}
+                    child{node [end] {} node[right]{$(5,10)$} edge from parent node[below]{L}}edge from parent node[below] {A}}
+                edge from parent node[below] {W}}
+        child {node[player] {b: 2}
+                child {node[player] {e: 1}
+                    child {node[end] {} node [right] {$(2,3)$} edge from parent node[below] {Y}}
+                    child {node[end] {} node [right] {$(1,2)$} edge from parent node[below] {Z}}
+                        edge from parent node[below] {C}}
+                child {node [player] {d: 1}
+                    child{node[end] {} node [right] {$(10,1)$} edge from parent node[below] {M}}
+                    child{node[end] {} node [right] {$(5,2)$} edge from parent node[below] {N}}
+                edge from parent node[below] {D}}
+edge from parent node[below] {Y}};
+\end{tikzpicture}
+\end{document}

docs/_static/learning/asymmetric_evolutionary_dynamics/non_convergence_example/main.py

@@ -5,6 +5,7 @@
 
 The code should match the reference code in the documentation.
 """
+
 import matplotlib.pyplot as plt
 import numpy as np
 

docs/_static/learning/asymmetric_evolutionary_dynamics/steady_state_example/main.py

@@ -5,6 +5,7 @@
 
 The code should match the reference code in the documentation.
 """
+
 import matplotlib.pyplot as plt
 import numpy as np
 

docs/_static/learning/fictitious_play/convergent_example/main.py

@@ -5,6 +5,7 @@
 
 The code should match the reference code in the documentation.
 """
+
 import matplotlib.pyplot as plt
 import numpy as np
 

docs/_static/learning/fictitious_play/divergent_example/main.py

@@ -5,6 +5,7 @@
 
 The code should match the reference code in the documentation.
 """
+
 import matplotlib.pyplot as plt
 import numpy as np
 

docs/_static/learning/stochastic_fictitious_play/convergent_example/main.py

@@ -24,9 +24,11 @@
 )
 plt.figure()
 probabilities = [
-    row_play_counts / np.sum(row_play_counts)
-    if np.sum(row_play_counts) != 0
-    else row_play_counts + 1 / len(row_play_counts)
+    (
+        row_play_counts / np.sum(row_play_counts)
+        if np.sum(row_play_counts) != 0
+        else row_play_counts + 1 / len(row_play_counts)
+    )
     for (row_play_counts, col_play_counts), _ in play_counts_and_distribuions
 ]
 for number, strategy in enumerate(zip(*probabilities)):

docs/_static/learning/stochastic_fictitious_play/divergent_example/main.py

@@ -21,9 +21,11 @@
 
 plt.figure()
 probabilities = [
-    row_play_counts / np.sum(row_play_counts)
-    if np.sum(row_play_counts) != 0
-    else row_play_counts + 1 / len(row_play_counts)
+    (
+        row_play_counts / np.sum(row_play_counts)
+        if np.sum(row_play_counts) != 0
+        else row_play_counts + 1 / len(row_play_counts)
+    )
     for (row_play_counts, col_play_counts), _ in play_counts_and_distribuions
 ]
 for number, strategy in enumerate(zip(*probabilities)):

docs/conf.py

@@ -74,7 +74,7 @@
 #
 # This is also used if you do content translation via gettext catalogs.
 # Usually you set "language" from the command line for these cases.
-language = 'en'
+language = "en"
 
 # List of patterns, relative to source directory, that match files and
 # directories to ignore when looking for source files.

docs/text-book/degenerate-games.rst → docs/how-to/handle-degenerate-games.rst

@@ -1,23 +1,7 @@
 .. _degenerate-games-discussion:
 
-Degenerate games
-================
-
-A two player game is called nondegenerate if no mixed strategy of support size
-:math:`k` has more than :math:`k` pure best responses.
-
-For example, the zero sum game defined by the following matrix is degenerate:
-
-.. math::
-
-   A =
-   \begin{pmatrix}
-        0 & -1 &  1\\
-       -1 &  0 &  1\\
-       -1 &  1 &  0
-   \end{pmatrix}
-
-The third column has two pure best responses.
+Handle Degenerate games
+=======================
 
 When dealing with *degenerate* games unexpected results can occur::
 

docs/how-to/index.rst

@@ -10,6 +10,7 @@ How to:
    create-a-game.rst
    calculate-utilities.rst
    check-best-responses.rst
+   handle-degenerate-games.rst
    use-minimax.rst
    solve-with-support-enumeration.rst
    solve-with-vertex-enumeration.rst