Prisoners' Dilemma

12
1( +3.00, +3.00 )( -1.00, +5.00 )
2( +5.00, -1.00 )( +1.00, +1.00 )
Nash equilibria:
  1: ([0.0, 1.0], [0.0, 1.0])

Networks' output (x, y):
  x = [0. 1.]
  y = [0. 1.]

Expected payoffs:
  Row player:    1.000
  Column player: 1.000

Regret:
  Row player:    0.000
  Column player: 0.000

Stag Hunt

12
1( +10.00, +10.00 )( +1.00, +8.00 )
2( +8.00, +1.00 )( +5.00, +5.00 )
Nash equilibria:
  1: ([1.0, 0.0], [1.0, 0.0])
  2: ([0.0, 1.0], [0.0, 1.0])
  3: ([0.667, 0.333], [0.667, 0.333])

Networks' output (x, y):
  x = [0. 1.]
  y = [0. 1.]

Expected payoffs:
  Row player:    5.000
  Column player: 5.000

Regret:
  Row player:    0.000
  Column player: 0.000

Asymmetric Stag Hunt

12
1( +10.00, +9.00 )( +1.00, +7.00 )
2( +8.00, +2.00 )( +5.00, +4.00 )
Nash equilibria:
  1: ([1.0, 0.0], [1.0, 0.0])
  2: ([0.0, 1.0], [0.0, 1.0])
  3: ([0.5, 0.5], [0.667, 0.333])

Networks' output (x, y):
  x = [0. 1.]
  y = [0. 1.]

Expected payoffs:
  Row player:    5.000
  Column player: 4.000

Regret:
  Row player:    0.000
  Column player: 0.000

Battle of the Sexes

12
1( +2.00, +1.00 )( +0.00, +0.00 )
2( +0.00, +0.00 )( +1.00, +2.00 )
Nash equilibria:
  1: ([1.0, 0.0], [1.0, 0.0])
  2: ([0.0, 1.0], [0.0, 1.0])
  3: ([0.667, 0.333], [0.333, 0.667])

Networks' output (x, y):
  x = [0. 1.]
  y = [0. 1.]

Expected payoffs:
  Row player:    1.000
  Column player: 2.000

Regret:
  Row player:    0.000
  Column player: 0.000

Asymmetric Battle of the Sexes

12
1( +4.00, +2.00 )( +0.00, +0.00 )
2( +0.00, +0.00 )( +1.00, +5.00 )
Nash equilibria:
  1: ([1.0, 0.0], [1.0, 0.0])
  2: ([0.0, 1.0], [0.0, 1.0])
  3: ([0.714, 0.286], [0.2, 0.8])

Networks' output (x, y):
  x = [1. 0.]
  y = [1. 0.]

Expected payoffs:
  Row player:    4.000
  Column player: 2.000

Regret:
  Row player:    0.000
  Column player: 0.000

Chicken Game

12
1( +0.00, +0.00 )( +7.00, +2.00 )
2( +2.00, +7.00 )( +5.00, +5.00 )
Nash equilibria:
  1: ([1.0, 0.0], [0.0, 1.0])
  2: ([0.0, 1.0], [1.0, 0.0])
  3: ([0.5, 0.5], [0.5, 0.5])

Networks' output (x, y):
  x = [0. 1.]
  y = [0. 1.]

Expected payoffs:
  Row player:    5.000
  Column player: 5.000

Regret:
  Row player:    2.000
  Column player: 2.000

Asymmetric Chicken Game

12
1( +0.00, +0.00 )( +8.00, +1.00 )
2( +2.00, +7.00 )( +5.00, +4.00 )
Nash equilibria:
  1: ([1.0, 0.0], [0.0, 1.0])
  2: ([0.0, 1.0], [1.0, 0.0])
  3: ([0.75, 0.25], [0.6, 0.4])

Networks' output (x, y):
  x = [0. 1.]
  y = [1. 0.]

Expected payoffs:
  Row player:    2.000
  Column player: 7.000

Regret:
  Row player:    0.000
  Column player: 0.000

Matching Pennies

12
1( +1.00, -1.00 )( -1.00, +1.00 )
2( -1.00, +1.00 )( +1.00, -1.00 )
Nash equilibria:
  1: ([0.5, 0.5], [0.5, 0.5])

Networks' output (x, y):
  x = [0.512 0.488]
  y = [0.492 0.508]

Expected payoffs:
  Row player:    -0.000
  Column player: 0.000

Regret:
  Row player:    0.016
  Column player: 0.024

Deadlock

12
1( +1.00, +1.00 )( -1.00, +5.00 )
2( +5.00, -1.00 )( +3.00, +3.00 )
Nash equilibria:
  1: ([0.0, 1.0], [0.0, 1.0])

Networks' output (x, y):
  x = [0. 1.]
  y = [0. 1.]

Expected payoffs:
  Row player:    3.000
  Column player: 3.000

Regret:
  Row player:    0.000
  Column player: 0.000

Coordination Game

123
1( +3.00, +3.00 )( +0.00, +0.00 )( +0.00, +0.00 )
2( +0.00, +0.00 )( +2.00, +2.00 )( +0.00, +0.00 )
3( +0.00, +0.00 )( +0.00, +0.00 )( +1.00, +1.00 )
Nash equilibria:
  1: ([1.0, 0.0, 0.0], [1.0, 0.0, 0.0])
  2: ([0.0, 1.0, 0.0], [0.0, 1.0, 0.0])
  3: ([0.0, 0.0, 1.0], [0.0, 0.0, 1.0])
  4: ([0.4, 0.6, 0.0], [0.4, 0.6, 0.0])
  5: ([0.25, 0.0, 0.75], [0.25, 0.0, 0.75])
  6: ([0.0, 0.333, 0.667], [0.0, 0.333, 0.667])
  7: ([0.182, 0.273, 0.545], [0.182, 0.273, 0.545])

Networks' output (x, y):
  x = [1. 0. 0.]
  y = [1. 0. 0.]

Expected payoffs:
  Row player:    3.000
  Column player: 3.000

Regret:
  Row player:    0.000
  Column player: 0.000

Asymmetric coordination Game

12
1( +1.00, +2.00 )( +0.00, +0.00 )
2( +0.00, +0.00 )( +2.00, +3.00 )
Nash equilibria:
  1: ([1.0, 0.0], [1.0, 0.0])
  2: ([0.0, 1.0], [0.0, 1.0])
  3: ([0.6, 0.4], [0.667, 0.333])

Networks' output (x, y):
  x = [0. 1.]
  y = [0. 1.]

Expected payoffs:
  Row player:    2.000
  Column player: 3.000

Regret:
  Row player:    0.000
  Column player: 0.000

Rock Paper Scissor

123
1( +0.00, +0.00 )( -1.00, +1.00 )( +1.00, -1.00 )
2( +1.00, -1.00 )( +0.00, +0.00 )( -1.00, +1.00 )
3( -1.00, +1.00 )( +1.00, -1.00 )( +0.00, +0.00 )
Nash equilibria:
  1: ([0.333, 0.333, 0.333], [0.333, 0.333, 0.333])

Networks' output (x, y):
  x = [0.508 0.16  0.333]
  y = [0.403 0.18  0.417]

Expected payoffs:
  Row player:    0.044
  Column player: -0.044

Regret:
  Row player:    0.193
  Column player: 0.219

Rock Paper Scissor (Shapley's variation)

123
1( +0.00, +0.00 )( +0.00, +1.00 )( +1.00, +0.00 )
2( +1.00, +0.00 )( +0.00, +0.00 )( +0.00, +1.00 )
3( +0.00, +1.00 )( +1.00, +0.00 )( +0.00, +0.00 )
Nash equilibria:
  1: ([0.333, 0.333, 0.333], [0.333, 0.333, 0.333])

Networks' output (x, y):
  x = [0.552 0.229 0.218]
  y = [0.162 0.16  0.677]

Expected payoffs:
  Row player:    0.446
  Column player: 0.279

Regret:
  Row player:    0.231
  Column player: 0.273

Predator-Prey Game

123
1( +1.00, +1.00 )( -1.00, +2.00 )( +0.00, +0.00 )
2( +2.00, -1.00 )( +0.00, +0.00 )( -2.00, +1.00 )
3( +0.00, +0.00 )( +1.00, -2.00 )( -1.00, -1.00 )
Nash equilibria:
  1: ([0.333, 0.333, 0.333], [0.333, 0.333, 0.333])

Networks' output (x, y):
  x = [0.51  0.161 0.329]
  y = [0.402 0.178 0.42 ]

Expected payoffs:
  Row player:    0.029
  Column player: 0.135

Regret:
  Row player:    0.195
  Column player: 0.229

Public Goods Game

123
1( +8.00, +8.00 )( +6.00, +9.00 )( +4.00, +10.00 )
2( +9.00, +6.00 )( +7.00, +7.00 )( +5.00, +8.00 )
3( +10.00, +4.00 )( +8.00, +5.00 )( +6.00, +6.00 )
Nash equilibria:
  1: ([0.0, 0.0, 1.0], [0.0, 0.0, 1.0])

Networks' output (x, y):
  x = [0. 0. 1.]
  y = [0. 0. 1.]

Expected payoffs:
  Row player:    6.000
  Column player: 6.000

Regret:
  Row player:    0.000
  Column player: 0.000

Iesds Solvable Game

123
1( +8.00, +4.00 )( -2.00, +6.00 )( -2.00, +3.00 )
2( +6.00, -2.00 )( +2.00, +2.00 )( -1.00, +3.00 )
3( +3.00, -2.00 )( +3.00, -1.00 )( +1.00, +1.00 )
Nash equilibria:
  1: ([0.0, 0.0, 1.0], [0.0, 0.0, 1.0])

Networks' output (x, y):
  x = [0. 0. 1.]
  y = [0. 0. 1.]

Expected payoffs:
  Row player:    1.000
  Column player: 1.000

Regret:
  Row player:    0.000
  Column player: 0.000

Asymmetric Game

123
1( +8.00, +2.00 )( +5.00, +6.00 )( -6.00, +2.00 )
2( +0.00, +8.00 )( +1.00, +2.00 )( -1.00, +2.00 )
3( +2.00, +6.00 )( +8.00, -9.00 )( +4.00, +4.00 )
Nash equilibria:
  1: ([0.789, 0.0, 0.211], [0.333, 0.667, 0.0])

Networks' output (x, y):
  x = [0.918 0.    0.082]
  y = [0.86  0.032 0.108]

Expected payoffs:
  Row player:    6.060
  Column player: 2.389

Regret:
  Row player:    0.326
  Column player: 2.381

Optional Prisoners' Dilemma

123
1( +3.00, +3.00 )( +0.00, +5.00 )( +2.00, +2.00 )
2( +5.00, +0.00 )( +1.00, +1.00 )( +2.00, +2.00 )
3( +2.00, +2.00 )( +2.00, +2.00 )( +2.00, +2.00 )
Nash equilibria:
  1: ([0.0, 1.0, 0.0], [0.0, 0.0, 1.0])
  2: ([0.0, 0.0, 1.0], [0.0, 1.0, 0.0])
  3: ([0.0, 0.0, 1.0], [0.0, 0.0, 1.0])

Networks' output (x, y):
  x = [0.    0.005 0.995]
  y = [0.001 0.013 0.986]

Expected payoffs:
  Row player:    2.000
  Column player: 2.000

Regret:
  Row player:    0.000
  Column player: 0.000

Degenerate Game 1

123
1( +0.00, +0.00 )( -1.00, +1.00 )( +1.00, -1.00 )
2( -1.00, +1.00 )( +0.00, +0.00 )( +1.00, -1.00 )
3( -1.00, +1.00 )( +0.00, +0.00 )( +1.00, -1.00 )
Nash equilibria:
  1: ([0.5, 0.5, 0.0], [0.5, 0.5, 0.0])
  2: ([0.5, 0.0, 0.5], [0.5, 0.5, 0.0])

Networks' output (x, y):
  x = [0.57  0.425 0.005]
  y = [0.488 0.512 0.   ]

Expected payoffs:
  Row player:    -0.502
  Column player: 0.502

Regret:
  Row player:    0.014
  Column player: 0.068

Degenerate Game 2

123
1( -1.00, +1.00 )( +1.00, -1.00 )( +1.00, -1.00 )
2( -1.00, +1.00 )( -1.00, +1.00 )( +1.00, -1.00 )
3( -1.00, +1.00 )( -1.00, +1.00 )( -1.00, +1.00 )
Nash equilibria:
  1: ([1.0, 0.0, 0.0], [1.0, 0.0, 0.0])
  2: ([0.0, 1.0, 0.0], [1.0, 0.0, 0.0])
  3: ([0.0, 0.0, 1.0], [1.0, 0.0, 0.0])

Networks' output (x, y):
  x = [0.087 0.912 0.001]
  y = [0.999 0.001 0.   ]

Expected payoffs:
  Row player:    -1.000
  Column player: 1.000

Regret:
  Row player:    0.003
  Column player: 0.000