17.1 exploitability of the average strategies equals the sum of the players' average regrets (zero-sum game)
  exploitability 0.021861   (max regret_x + max regret_y)/T = 0.021861

17.2 Hedge with a fixed step moves away from an interior equilibrium: KL(x*||x_t) + KL(y*||y_t)
  t=    0  distance 0.1137
  t=   10  distance 0.1202
  t=  100  distance 0.1723
  t=  500  distance 0.6136
  t= 1000  distance 1.4135
  t= 2000  distance 3.9136

17.3 ultimatum game: every threshold pair (offer x*, responder accepts iff x >= x*) is a Nash equilibrium
  Nash for x* = 0..10: [True, True, True, True, True, True, True, True, True, True, True]

17.4 debate: if each debater may reveal as many facts as its side has, the judge is always right
  accuracy 1.000

17.5 cooperative game: directional derivatives of J at pure profiles
  profile (0,0) value   12: gain for the row agent by switching to each action [  0. -37. -17.], for the column agent [  0. -37. -17.]
  profile (1,1) value    6: gain for the row agent by switching to each action [-31.   0.  -4.], for the column agent [-31.   0.  -2.]
  profile (2,2) value    3: gain for the row agent by switching to each action [-8.  1.  0.], for the column agent [-8. -1.  0.]
