+ This is another Gowda/Ravindran example that is supposed to have
+ a negative game value::
+
+ >>> from dunshire import *
+ >>> from dunshire.options import ABS_TOL
+ >>> L = [[1, -2], [-2, 1]]
+ >>> K = NonnegativeOrthant(2)
+ >>> e1 = [1, 1]
+ >>> e2 = e1
+ >>> SLG = SymmetricLinearGame(L, K, e1, e2)
+ >>> SLG.solution().game_value() < -ABS_TOL
+ True
+
+ The following two games are problematic numerically, but we
+ should be able to solve them::
+
+ >>> from dunshire import *
+ >>> L = [[-0.95237953890954685221, 1.83474556206462535712],
+ ... [ 1.30481749924621448500, 1.65278664543326403447]]
+ >>> K = NonnegativeOrthant(2)
+ >>> e1 = [0.95477167524644313001, 0.63270781756540095397]
+ >>> e2 = [0.39633793037154141370, 0.10239281495640320530]
+ >>> SLG = SymmetricLinearGame(L, K, e1, e2)
+ >>> print(SLG.solution())
+ Game value: 18.767...
+ Player 1 optimal:
+ [0.000...]
+ [9.766...]
+ Player 2 optimal:
+ [1.047...]
+ [0.000...]
+
+ ::
+
+ >>> from dunshire import *
+ >>> L = [[1.54159395026049472754, 2.21344728574316684799],
+ ... [1.33147433507846657541, 1.17913616272988108769]]
+ >>> K = NonnegativeOrthant(2)
+ >>> e1 = [0.39903040089404784307, 0.12377403622479113410]
+ >>> e2 = [0.15695181142215544612, 0.85527381344651265405]
+ >>> SLG = SymmetricLinearGame(L, K, e1, e2)
+ >>> print(SLG.solution())
+ Game value: 24.614...
+ Player 1 optimal:
+ [6.371...]
+ [0.000...]
+ Player 2 optimal:
+ [2.506...]
+ [0.000...]
+
+ This is another one that was difficult numerically, and caused
+ trouble even after we fixed the first two::
+
+ >>> from dunshire import *
+ >>> L = [[57.22233908627052301199, 41.70631373437460354126],
+ ... [83.04512571985074487202, 57.82581810406928468637]]
+ >>> K = NonnegativeOrthant(2)
+ >>> e1 = [7.31887017043399268346, 0.89744171905822367474]
+ >>> e2 = [0.11099824781179848388, 6.12564670639315345113]
+ >>> SLG = SymmetricLinearGame(L,K,e1,e2)
+ >>> print(SLG.solution())
+ Game value: 70.437...
+ Player 1 optimal:
+ [9.009...]
+ [0.000...]
+ Player 2 optimal:
+ [0.136...]
+ [0.000...]
+
+ And finally, here's one that returns an "optimal" solution, but
+ whose primal/dual objective function values are far apart::
+
+ >>> from dunshire import *
+ >>> L = [[ 6.49260076597376212248, -0.60528030227678542019],
+ ... [ 2.59896077096751731972, -0.97685530240286766457]]
+ >>> K = IceCream(2)
+ >>> e1 = [1, 0.43749513972645248661]
+ >>> e2 = [1, 0.46008379832200291260]
+ >>> SLG = SymmetricLinearGame(L, K, e1, e2)
+ >>> print(SLG.solution())
+ Game value: 11.596...
+ Player 1 optimal:
+ [ 1.852...]
+ [-1.852...]
+ Player 2 optimal:
+ [ 1.777...]
+ [-1.777...]
+