Reword two paragraphs in the overview.

[dunshire.git] / doc / source / overview.rst

diff --git a/doc/source/overview.rst b/doc/source/overview.rst
index f4b4220585bc176d9a976f26b8a6b8a74e783b56..d20cbe4d15bf23f71d684be97214af6b397235c5 100644 (file)
--- a/doc/source/overview.rst
+++ b/doc/source/overview.rst
@@ -1,15 +1,15 @@
 Overview
 --------
 
-Dunshire is a `CVXOPT <http://cvxopt.org/>`_-based library for solving
-linear (cone) games. The notion of a symmetric linear (cone) game was
-introduced by Gowda and Ravindran [GowdaRav]_, and extended by
-Orlitzky to asymmetric cones with two interior points.
+Dunshire is a library for solving linear (cone) games. The notion of a
+symmetric linear (cone) game was introduced by Gowda and Ravindran
+[GowdaRav]_, and extended by Orlitzky to asymmetric cones with two
+interior points.
 
 The state-of-the-art is that only symmetric games can be solved
 efficiently, and thus the linear games supported by Dunshire are a
-bastard of the two: the cones are symmetric, but the players get to
-choose two interior points.
+compromise between the two: the cones are symmetric, but the players
+get to choose two interior points.
 
 In this game, we have two players who are competing for a "payoff."
 There is a symmetric cone :math:`K`, a linear transformation :math:`L`
@@ -34,10 +34,10 @@ and player two chooses a :math:`\bar{y}` from
 
 That ends the turn, and player one is paid :math:`\left\langle
 L\left(\bar{x}\right),\bar{y}\right\rangle` out of player two's
-pocket. As is usual to assume in game theory, we suppose that player
-one wants to maximize his worst-case payoff, and that player two wants
-to minimize his worst-case *payout*. In other words, player one wants
-to solve the optimization problem,
+pocket. As is usual in game theory, we suppose that player one wants
+to maximize his worst-case payoff, and that player two wants to
+minimize his worst-case *payout*. In other words, player one wants to
+solve the optimization problem,
 
 .. math::
   \text{find }
@@ -72,13 +72,13 @@ First, we use the nonnegative orthant in :math:`\mathbb{R}^{2}`:
   >>> e2 = e1
   >>> G = SymmetricLinearGame(L,K,e1,e2)
   >>> print(G.solution())
-  Game value: 0.5000000
+  Game value: 0.500...
   Player 1 optimal:
-    [0.5000000]
-    [0.5000000]
+    [0.500...]
+    [0.500...]
   Player 2 optimal:
-    [0.5000000]
-    [0.5000000]
+    [0.500...]
+    [0.500...]
 
 Next we try the Lorentz ice-cream cone in :math:`\mathbb{R}^{2}`:
 
@@ -87,16 +87,16 @@ Next we try the Lorentz ice-cream cone in :math:`\mathbb{R}^{2}`:
   >>> from dunshire import *
   >>> K = IceCream(2)
   >>> L = [[1,0],[0,1]]
-  >>> e1 = [1,1]
+  >>> e1 = [1,0]
   >>> e2 = e1
   >>> G = SymmetricLinearGame(L,K,e1,e2)
   >>> print(G.solution())
-  Game value: 0.5000000
+  Game value: 1.000...
   Player 1 optimal:
-    [0.8347039]
-    [0.1652961]
+    [1.000...]
+    [0.000...]
   Player 2 optimal:
-    [0.5000000]
-    [0.5000000]
+    [1.000...]
+    [0.000...]
 
 Note that these solutions are not unique, although the game values are.