Fix a minor typo and add new documentation. (#230)

* Fix a minor typo.

* Add docs to index.

docs/how-to/index.rst

@@ -25,3 +25,5 @@ How to:
    obtain-a-repeated-game.rst
    use-moran-process-on-replacement-graph.rst
    use-moran-process-on-interaction-graph.rst
+   use-imitation-dynamics.rst
+   use-regret-minimization.rst

docs/how-to/solve-with-imitation-dynamics.rst → docs/how-to/use-imitation-dynamics.rst

@@ -1,7 +1,7 @@
 .. _how-to-use-imitation-dynamics:
 
-Solve with Imitation Dynamics
-==============================
+Use Imitation Dynamics
+======================
 
 One of the algorithms implemented in :code:`Nashpy` is called
 :code:`imitation_dynamics()`, this is implemented as a method on the :code:`Game`
@@ -33,4 +33,4 @@ of the imitation dynamics algorithm::
     >>> threshold=0.3
     >>> ne_imitation_dynamics = rps.imitation_dynamics(population_size=population_size,iterations=iterations,random_seed=random_seed,threshold=threshold)
     >>> list(ne_imitation_dynamics)
-    [(array([0., 1., 0.]), array([1., 0., 1.]))]
+    [(array([0., 1., 0.]), array([1., 0., 1.]))]

docs/how-to/solve-with-regret-minimization.rst → docs/how-to/use-regret-minimization.rst

@@ -1,7 +1,7 @@
 .. _how-to-use-regret-minimization:
 
-Solve with Regret Minimization
-==============================
+Use with Regret Minimization
+============================
 
 One of the algorithms implemented in :code:`Nashpy` is called
 :code:`regret_minimization()`, this is implemented as a method on the :code:`Game`

docs/text-book/best-responses.rst

@@ -94,7 +94,7 @@ response to a row players' strategy :math:`\sigma_r` if and only if:
 
 
    The row player's best response to either of the actions of the column player
-   is :math:`\sigma_r^*=(1,0)`. This can be expressed as:
+   is :math:`\sigma_r^*=(0,1)`. This can be expressed as:
 
    .. math::
 

docs/text-book/imitation-dynamics.rst

@@ -1,5 +1,5 @@
-Detailed Mathematical Model of Imitation Dynamics
-==================================================
+Imitation Dynamics
+==================
 
 Introduction
 ------------
@@ -62,4 +62,4 @@ Using Nashpy
 ------------
 
 See :ref:`how-to-use-imitation-dynamics` for guidance of how to use Nashpy to
-simulation Imitation Dynamics.
+simulation Imitation Dynamics.

docs/text-book/index.rst

@@ -19,3 +19,5 @@ Nashpy Game Theory Text book
    replicator-dynamics.rst
    asymmetric-replicator-dynamics.rst
    moran-process.rst
+   imitation-dynamics.rst
+   regret_minimization.rst

docs/text-book/regret_minimization.rst

@@ -1,5 +1,5 @@
-Regret Minimization in Game Theory
-==================================
+Regret Minimization
+===================
 
 Introduction
 ------------

docs/text-book/solutions/.ipynb_checkpoints/normal-form-games-checkpoint.ipynb

@@ -0,0 +1,221 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "7779ca3d-99a8-4014-a001-4b4c9314e39f",
+   "metadata": {},
+   "source": [
+    "> Obtain the full game representations $(A, B)$ for the zero sum games with row play payoff matrix given by:\n",
+    "\n",
+    "   1. $A =\\begin{pmatrix}1 & 3\\\\ -1 & 4\\end{pmatrix}\\qquad B =\\begin{pmatrix}-1 & -3\\\\ 1 & -4\\end{pmatrix}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "f365cfb4-38bb-4605-b5cd-e4476bd60978",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Zero sum game with payoff matrices:\n",
+       "\n",
+       "Row player:\n",
+       "[[ 1  3]\n",
+       " [-1  4]]\n",
+       "\n",
+       "Column player:\n",
+       "[[-1 -3]\n",
+       " [ 1 -4]]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import nashpy as nash\n",
+    "import numpy as np\n",
+    "\n",
+    "A = np.array(((1, 3), (-1, 4)))\n",
+    "B = np.array(((-1, -3), (1, -4)))\n",
+    "game = nash.Game(A, B)\n",
+    "game"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "206da237-a337-434b-b5f6-0b29ef992687",
+   "metadata": {},
+   "source": [
+    "   2. $A =\\begin{pmatrix}1 & -2\\\\ -1 & 2\\end{pmatrix}\\qquad B =\\begin{pmatrix}-1 & 2\\\\ 1 & -2\\end{pmatrix}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "a8698c05-a30b-40e9-864b-081fbd31da42",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Zero sum game with payoff matrices:\n",
+       "\n",
+       "Row player:\n",
+       "[[ 1 -2]\n",
+       " [-1  2]]\n",
+       "\n",
+       "Column player:\n",
+       "[[-1  2]\n",
+       " [ 1 -2]]"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "A = np.array(((1, -2), (-1, 2)))\n",
+    "B = np.array(((-1, 2), (1, -2)))\n",
+    "game = nash.Game(A, B)\n",
+    "game"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "07878c15-fb5d-4840-9c0d-e3fe95f1226a",
+   "metadata": {},
+   "source": [
+    "   3. $A =\\begin{pmatrix}1 & -2 & 4\\\\ 2 & -1 & 2\\\\ 7 & -7 & 6\\end{pmatrix}\\qquad B =\\begin{pmatrix}-1 & 2 & -4\\\\ -2 & 1 & -2\\\\ -7 & 7 & -6\\end{pmatrix}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "fc5f7b5a-91ba-4358-b9f6-0772033fcb8c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Zero sum game with payoff matrices:\n",
+       "\n",
+       "Row player:\n",
+       "[[ 1 -2  4]\n",
+       " [ 2 -1  2]\n",
+       " [ 7 -7  6]]\n",
+       "\n",
+       "Column player:\n",
+       "[[-1  2 -4]\n",
+       " [-2  1 -2]\n",
+       " [-7  7 -6]]"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "A = np.array(((1, -2, 4), (2, -1, 2), (7, -7, 6)))\n",
+    "B = np.array(((-1, 2, -4), (-2, 1, -2), (-7, 7, -6)))\n",
+    "game = nash.Game(A, B)\n",
+    "game"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7bafa50e-ac87-4ad8-a5ed-17a5b550066c",
+   "metadata": {},
+   "source": [
+    "> `3.` Consider the game described as follows:\n",
+    "\n",
+    "   > An airline loses two suitcases belonging to two different travelers. Both suitcases have the same value. An airline manager tasked to settle the claims of both travelers explains that the airline is liable for a maximum of £5 per suitcase. \n",
+    "\n",
+    "   > To determine an honest appraised value of the suitcases, the manager separates both travelers and asks them to write down the amount of their value at no less than £2 and no larger than £5 (to the single dollar):\n",
+    "   > - If both write down the same number, that number as the true dollar value of both suitcases and reimburse both travelers that amount. \n",
+    "   > - However, if one writes down a smaller number than the other, this smaller number will be taken as the true dollar value, and both travelers will receive that amount along with a bonus/malus: £2 extra will be paid to the traveler who wrote down the lower value and a £2 deduction will be taken from the person who wrote down the higher amount. \n",
+    "   \n",
+    "   > Represent this as a Normal Form Game.\n",
+    "   \n",
+    "   \n",
+    "$$\n",
+    "A = \\begin{pmatrix}\n",
+    "2 & 4 & 4 & 4\\\\\n",
+    "0 & 3 & 5 & 5\\\\\n",
+    "0 & 1 & 4 & 6\\\\\n",
+    "0 & 1 & 2 & 5\n",
+    "\\end{pmatrix}\n",
+    "\\qquad\n",
+    "B = \\begin{pmatrix}\n",
+    "2 & 0 & 0 & 0\\\\\n",
+    "4 & 3 & 1 & 1\\\\\n",
+    "4 & 5 & 4 & 2\\\\\n",
+    "4 & 5 & 6 & 5\n",
+    "\\end{pmatrix}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "f1922cd9-a1ca-40ca-b1ad-c09de6b46a9d",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Bi matrix game with payoff matrices:\n",
+       "\n",
+       "Row player:\n",
+       "[[2 4 4 4]\n",
+       " [0 3 5 5]\n",
+       " [0 1 4 6]\n",
+       " [0 1 2 5]]\n",
+       "\n",
+       "Column player:\n",
+       "[[2 0 0 0]\n",
+       " [4 3 1 1]\n",
+       " [4 5 4 2]\n",
+       " [4 5 6 5]]"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "A = np.array(((2, 4, 4, 4), (0, 3, 5, 5), (0, 1, 4, 6), (0, 1, 2,5)))\n",
+    "B = np.array(((2, 0, 0, 0), (4, 3, 1, 1), (4, 5, 4, 2), (4, 5, 6, 5)))\n",
+    "game = nash.Game(A, B)\n",
+    "game"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}