Load save functionality

INFOS/EQDIAG/degen1.fig

@@ -0,0 +1,238 @@
+#FIG 3.2  Produced by xfig version 3.2.5c
+Landscape
+Center
+Metric
+A4      
+100.00
+Single
+0
+1200 2
+5 1 0 1 0 2 50 -1 -1 0.000 0 0 0 0 -916.875 7183.125 0 7200 -225 7785 -900 8100
+5 1 0 1 0 2 50 -1 -1 0.000 0 0 0 0 -847.500 7252.500 1800 7200 1350 8730 -900 9900
+5 1 0 1 0 2 50 -1 -1 0.000 0 0 0 0 -714.375 7385.625 2700 7200 2250 9090 -900 10800
+1 3 0 3 13 2 30 -1 20 0.000 1 0.0000 -7200 8100 127 127 -7200 8100 -7110 8190
+1 3 0 3 13 2 30 -1 20 0.000 1 0.0000 -12600 8100 127 127 -12600 8100 -12510 8190
+2 1 0 2 1 7 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 2.00 120.00 240.00
+	 -7200 4500 -4050 4500
+2 1 0 2 1 7 70 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 2.00 120.00 240.00
+	 0 4500 0 450
+2 1 0 3 1 7 72 -1 -1 0.000 0 0 -1 0 0 2
+	 0 1800 2700 4500
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -4500 4500 -4500 900
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 2.00 120.00 240.00
+	 -7200 4500 -7200 450
+2 1 0 3 1 7 74 -1 -1 0.000 0 0 -1 0 0 2
+	 0 4500 2700 3150
+2 1 0 2 4 1 70 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 2.00 120.00 240.00
+	 0 4500 3150 4500
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 4500 -7425 4500
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 3825 -7425 3825
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 3150 -7425 3150
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 2475 -7425 2475
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 1800 -7425 1800
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 1125 -7425 1125
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 0 4500 -225 4500
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 0 3825 -225 3825
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 0 2475 -225 2475
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 0 1800 -225 1800
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 0 1125 -225 1125
+2 3 0 0 1 1 76 -1 30 0.000 0 0 -1 0 0 8
+	 0 900 0 1800 1800 3600 2700 3150 2700 900 2160 720
+	 1170 1080 0 900
+2 1 0 2 1 7 70 -1 -1 0.000 0 0 -1 0 0 2
+	 2700 4500 2700 900
+2 1 0 3 4 1 52 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 3825 -4500 3825
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -4500 4725 -4500 4500
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -6525 4725 -6525 4500
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 4725 -7200 4500
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 0 4725 0 4500
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 1800 4725 1800 4500
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 2700 4725 2700 4500
+2 2 0 2 1 7 50 -1 -1 0.000 0 0 -1 0 0 5
+	 -11901 1916 -11420 1916 -11420 2474 -11901 2474 -11901 1916
+2 2 0 2 1 7 50 -1 -1 0.000 0 0 -1 0 0 5
+	 -10558 3259 -10077 3259 -10077 3816 -10558 3816 -10558 3259
+2 2 0 2 4 7 50 -1 -1 0.000 0 0 -1 0 0 5
+	 -11167 3791 -10685 3791 -10685 4347 -11167 4347 -11167 3791
+2 2 0 2 4 7 50 -1 -1 0.000 0 0 -1 0 0 5
+	 -12509 2448 -12027 2448 -12027 3006 -12509 3006 -12509 2448
+2 1 0 2 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -11281 4476 -9930 4476
+2 1 0 2 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -9930 3125 -9930 4476
+2 1 0 2 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -11281 3125 -11281 4476
+2 1 0 2 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -12632 4476 -11281 4476
+2 1 0 2 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -12632 3125 -11281 3125
+2 1 0 2 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -11281 1775 -11281 3125
+2 1 0 2 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -11281 3125 -9930 3125
+2 1 0 2 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -9930 1775 -9930 3125
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 0 3150 -225 3150
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 2925 3150 2700 3150
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -4275 3825 -4500 3825
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -11281 4476 -9930 4476
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -12632 4476 -11281 4476
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -11281 3125 -11281 4476
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -9930 3125 -9930 4476
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -11281 3125 -9930 3125
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -9930 1775 -9930 3125
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -11281 1775 -11281 3125
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -12632 3125 -11281 3125
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -12632 3125 -12632 4476
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -12632 1775 -12632 3125
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -12632 1775 -11281 1775
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -11281 1775 -9930 1775
+2 1 0 3 0 0 997 0 -1 5.000 0 0 -1 0 0 2
+	 -13471 954 -12641 1784
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 6885 -7200 6615
+2 1 0 2 1 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 -4500 6885 -4500 6615
+2 1 0 3 4 1 52 -1 -1 0.000 0 0 -1 0 0 2
+	 0 6750 2700 6750
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 0 6885 0 6615
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 1800 6885 1800 6615
+2 1 0 2 4 1 50 -1 -1 0.000 0 0 -1 0 0 2
+	 2700 6885 2700 6615
+2 1 0 1 0 2 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 1.00 90.00 120.00
+	 -7200 7200 -7200 7875
+2 1 0 1 0 2 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 1.00 90.00 120.00
+	 -4500 7200 -4500 7875
+2 1 0 1 0 2 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 1.00 90.00 120.00
+	 -855 8100 -4275 8100
+2 1 0 1 0 2 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 1.00 90.00 120.00
+	 -900 9900 -4275 9900
+2 1 0 1 0 2 50 -1 -1 0.000 0 0 -1 1 0 2
+	1 1 1.00 90.00 120.00
+	 -900 10800 -4275 10800
+2 2 0 2 4 7 50 -1 -1 0.000 0 0 -1 0 0 5
+	 -11167 2459 -10685 2459 -10685 3015 -11167 3015 -11167 2459
+2 3 0 0 4 4 56 -1 30 0.000 0 0 -1 0 0 8
+	 -7200 900 -7200 3825 -4500 3825 -4500 1800 -4500 900 -5580 1080
+	 -6120 540 -7200 900
+2 1 0 3 4 1 54 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 4500 -4500 3825
+2 1 0 4 4 1 40 -1 -1 0.000 0 0 -1 0 0 3
+	 -7200 8100 -4500 8100 -4500 10800
+2 2 0 1 0 2 99 -1 -1 0.000 0 0 -1 0 0 5
+	 -7200 8100 -4500 8100 -4500 10800 -7200 10800 -7200 8100
+2 2 0 3 13 2 100 -1 20 0.000 0 0 -1 0 0 5
+	 -4590 9855 -4410 9855 -4410 10890 -4590 10890 -4590 9855
+2 1 0 4 1 1 38 -1 -1 0.000 0 0 -1 0 0 4
+	 -7200 8100 -7200 9945 -4500 9945 -4500 10800
+2 1 1 4 4 1 38 -1 -1 10.000 0 0 -1 0 0 2
+	 -4500 9945 -4500 10845
+2 1 0 3 1 1 52 -1 -1 0.000 0 0 -1 0 0 2
+	 -7200 6750 -4500 6750
+2 2 0 3 13 2 32 -1 20 0.000 0 0 -1 0 0 5
+	 -12645 9990 -12465 9990 -12465 10845 -12645 10845 -12645 9990
+4 0 1 50 -1 3 30 0.0000 4 450 1485 -3960 4680 prob(r)\001
+4 0 4 70 -1 3 30 0.0000 4 450 1620 3240 4680 prob(B)\001
+4 0 4 50 -1 0 30 0.0000 4 435 2985 -7470 180 payoff player I\001
+4 0 1 70 -1 0 30 0.0000 4 435 3150 -180 180 payoff player II\001
+4 0 1 74 -1 3 30 0.0000 4 225 195 2340 3645 r\001
+4 0 1 72 -1 3 30 0.0000 4 345 135 675 3060 l\001
+4 0 4 52 -1 3 30 0.0000 4 330 300 -7155 4230 T\001
+4 1 4 70 -1 16 25 0.0000 4 285 240 0 5220 0\001
+4 1 1 50 -1 16 25 0.0000 4 285 240 -4500 5220 1\001
+4 1 1 50 -1 16 25 0.0000 4 285 240 -7200 5220 0\001
+4 0 1 994 0 16 35 0.0000 4 405 330 -11798 3745 0\001
+4 0 4 993 0 16 35 0.0000 4 405 330 -11087 2932 1\001
+4 0 1 992 0 16 35 0.0000 4 405 330 -10447 3745 2\001
+4 0 1 991 0 16 35 0.0000 4 405 330 -11798 2394 4\001
+4 0 4 990 0 16 35 0.0000 4 405 330 -12438 2932 1\001
+4 0 4 988 0 16 35 0.0000 4 405 330 -12438 4283 0\001
+4 0 1 986 0 16 35 0.0000 4 405 330 -10447 2394 0\001
+4 0 4 984 0 16 35 0.0000 4 405 330 -11087 4283 1\001
+4 0 1 996 0 0 34 0.0000 4 375 390 -13063 1133 II\001
+4 0 4 989 0 0 34 0.0000 4 375 195 -13522 1714 I\001
+4 0 4 983 0 3 35 0.0000 4 390 360 -13145 2663 T\001
+4 0 4 995 0 3 35 0.0000 4 390 390 -13209 4014 B\001
+4 0 1 987 0 3 35 0.0000 4 420 165 -12038 1617 l\001
+4 0 1 985 0 3 35 0.0000 4 270 225 -10718 1617 r\001
+4 1 1 50 -1 0 25 0.0000 4 285 540 -6525 5220 1/4\001
+4 1 4 70 -1 0 25 0.0000 4 285 540 1800 5220 2/3\001
+4 1 4 70 -1 0 25 0.0000 4 285 210 2700 5220 1\001
+4 1 4 70 -1 16 25 0.0000 4 285 240 -7650 2610 3\001
+4 1 4 70 -1 16 25 0.0000 4 285 240 -7650 1260 5\001
+4 1 4 70 -1 16 25 0.0000 4 285 240 -7650 3960 1\001
+4 1 4 70 -1 16 25 0.0000 4 285 240 -7650 3285 2\001
+4 1 4 70 -1 16 25 0.0000 4 285 240 -7650 1935 4\001
+4 1 4 70 -1 16 25 0.0000 4 285 240 -7650 4635 0\001
+4 1 1 70 -1 16 25 0.0000 4 285 240 -450 2610 3\001
+4 1 1 70 -1 16 25 0.0000 4 285 240 -450 1260 5\001
+4 1 1 70 -1 16 25 0.0000 4 285 240 -450 3960 1\001
+4 1 1 70 -1 16 25 0.0000 4 285 240 -450 3285 2\001
+4 1 1 70 -1 16 25 0.0000 4 285 240 -450 1935 4\001
+4 1 1 70 -1 16 25 0.0000 4 285 240 -450 4635 0\001
+4 1 1 70 -1 16 25 0.0000 4 285 240 3150 3285 2\001
+4 1 4 70 -1 16 25 0.0000 4 285 240 -4050 3960 1\001
+4 0 1 81 -1 3 30 0.0000 4 345 675 -4230 6885 l=0\001
+4 0 4 80 -1 3 30 0.0000 4 330 870 -1170 6885 B=0\001
+4 0 1 81 -1 3 30 0.0000 4 330 735 -8190 6885 r=0\001
+4 0 4 80 -1 3 30 0.0000 4 330 840 2970 6885 T=0\001
+4 0 4 54 -1 3 30 0.0000 4 330 330 -7875 10980 B\001
+4 0 1 74 -1 3 30 0.0000 4 225 195 -4545 11475 r\001
+4 0 1 72 -1 3 30 0.0000 4 345 135 -7245 11475 l\001
+4 0 4 52 -1 3 30 0.0000 4 330 300 -7875 8280 T\001
+4 0 1 72 -1 3 30 0.0000 4 345 135 720 6615 l\001
+4 0 1 74 -1 3 30 0.0000 4 225 195 2205 6615 r\001
+4 1 1 54 -1 0 20 0.0000 4 300 3150 1350 6075 best responses player II\001
+4 1 4 54 -1 0 20 0.0000 4 300 3045 -5850 6075 best responses player I\001
+4 0 4 52 -1 3 30 0.0000 4 330 300 -12060 8280 T\001
+4 0 1 72 -1 3 30 0.0000 4 345 135 -11520 8280 l\001
+4 0 13 52 -1 3 30 0.0000 4 450 3480 -12645 7245 Nash equilibria :\001
+4 0 4 54 -1 3 30 0.0000 4 330 330 -5040 4365 B\001
+4 0 4 54 -1 3 25 0.0000 4 390 3045 -12240 10710 prob(B) in [2/3,1]\001
+4 0 1 74 -1 3 30 0.0000 4 225 195 -8910 10710 r\001
+4 0 4 54 -1 3 30 0.0000 4 330 330 -4635 6525 B\001
+4 0 4 52 -1 3 30 0.0000 4 330 300 -6525 6525 T\001

INFOS/eqdiagrams.md

@@ -231,3 +231,64 @@ and not the other possibilities which are seen on the left.
 At a later stage, the fineness of the grid should be
 adjustable, e.g. to multiples of 0.5 or 0.1.
 
+## Degenerate games
+
+The following picture shows a _degenerate_ game.
+
+![](./EQDIAG/degen1.png)
+
+In two-player games, a game is degenerate if some player has
+a mixed strategy which assigns positive probability to exactly _k_
+pure strategies, against which the other player has _more
+than k_ pure best responses.
+
+Hence, a 2x2 game is degenerate if and only if there is a
+pure strategy that has 2 best responses, like strategy _l_
+in the above game. (This holds because the only case where
+the definition of degeneracy can apply is when _k_=1).
+
+A degenerate game can have an infinite number of Nash
+equilibria. However, these will always be part of sets of
+``interchangeable'' equilibria where it suffices to specify
+the extreme points. In the above example, the two
+best-response curves intersect in an interval where player II
+play r for sure, and the two best responses T and B of
+player I can now be mixed so that r stays a best response,
+i.e. whenever prob(B) >= 2/3.
+
+This is a whole _interval_ of NE.
+In the diagram this is indicated by a green rectangle.
+It is displayed so that the two intersecting best response
+curves are drawn with first (at lowest visual depth) the
+green equilibrium rectangle, then (second-lowest depth) the
+blue best response curve, then (highest, most visible depth)
+for the interval where the two curves intersect the red
+best-reponse curve as a DOTTED LINE.
+(This is fine-tuning, but the green rectangle should be
+shown for sure.)
+
+The intersection of the two best-response curves can result
+in a single interval, and the two curves can even intersect
+_completely_ in which case we get the union of two NE line
+segments.
+
+### "Very" degenerate game: all strategies are best responses
+
+As an even further complication, two strategies can
+_simultaneously_ be best responses, where they define the
+same line segment in the goalpost diagram. In that case
+the best response "curve" (normally the Z-like line with a
+connecting orthogonal cross segment) is in fact the WHOLE
+SQUARE (because that player can always play everything),
+and the intersection is simply the other person's best
+response curve. Which in turn may also be the whole square.
+In other words, this case arises if the two strategies have
+identical payoffs for the player, and then the two strategies may be arbitrarily
+substituted for each other, or played in an arbitrary mixture.
+(On the other hand, the two strategies may still have different effects 
+on the other player, and therefore one cannot just ignore one of them.)
+This is the case, for example, when all payoffs are zero.
+It may be confusing to display the equilibria for this came
+and therefore be advisable not use this as the default game,
+but rather, for example, one of the standard games such as
+Battle of the Sexes.

INFOS/largergames.md

@@ -0,0 +1,9 @@
+## Larger games
+
+The following is an upper envelope diagram of a 4x2 game:
+
+![](./EQDIAG/42upper.png)
+
+which is the following game:
+
+