Prisoners' Dilemma
1 | 2 | |
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
1 | 2 | |
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
1 | 2 | |
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
1 | 2 | |
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
1 | 2 | |
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
1 | 2 | |
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
1 | 2 | |
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
1 | 2 | |
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
1 | 2 | |
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
1 | 2 | 3 | |
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
1 | 2 | |
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
1 | 2 | 3 | |
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)
1 | 2 | 3 | |
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
1 | 2 | 3 | |
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
1 | 2 | 3 | |
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
1 | 2 | 3 | |
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
1 | 2 | 3 | |
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
1 | 2 | 3 | |
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
1 | 2 | 3 | |
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
1 | 2 | 3 | |
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