| . | Game 15 . | Game 25 . | Game 30 . | ||||||
|---|---|---|---|---|---|---|---|---|---|
| . | eff.(%) . | B (C) . | A (D) . | eff.(%) . | B (C) . | A (D) . | eff.(%) . | B (C) . | A (D) . |
| Cooperative | |||||||||
| SPB | 100 | 8.3 | 11.7 | 100 | 5 | 15 | 100 | 3.3 | 16.7 |
| Core | 100 | [0, 20] | [0, 20] | 100 | [0, 15] | [5, 20] | 100 | [0, 10] | [10, 20] |
| Core Midpoint | 100 | 10 | 10 | 100 | 7.5 | 12.5 | 100 | 5 | 15 |
| Noncooperative | |||||||||
| MPE | 100 | 10 | 10 | 72 | 6.45 | 11.45 | 50 | 4.17 | 13.33 |
| Markov Reversion | 100 | 10 | 10 | 100 | 8.75 | 11.25 | – | – | – |
| Carrot and Stick | 100 | 10 | 10 | 100 | |$(7\frac{7}{9},9\frac{4}{9})$| | |$(10\frac{5}{9},12\frac{2}{9})$| | 100 | |$(6\frac{1}{9},9\frac{4}{9})$| | |$(10\frac{5}{9},13\frac{8}{9})$| |
| . | Game 15 . | Game 25 . | Game 30 . | ||||||
|---|---|---|---|---|---|---|---|---|---|
| . | eff.(%) . | B (C) . | A (D) . | eff.(%) . | B (C) . | A (D) . | eff.(%) . | B (C) . | A (D) . |
| Cooperative | |||||||||
| SPB | 100 | 8.3 | 11.7 | 100 | 5 | 15 | 100 | 3.3 | 16.7 |
| Core | 100 | [0, 20] | [0, 20] | 100 | [0, 15] | [5, 20] | 100 | [0, 10] | [10, 20] |
| Core Midpoint | 100 | 10 | 10 | 100 | 7.5 | 12.5 | 100 | 5 | 15 |
| Noncooperative | |||||||||
| MPE | 100 | 10 | 10 | 72 | 6.45 | 11.45 | 50 | 4.17 | 13.33 |
| Markov Reversion | 100 | 10 | 10 | 100 | 8.75 | 11.25 | – | – | – |
| Carrot and Stick | 100 | 10 | 10 | 100 | |$(7\frac{7}{9},9\frac{4}{9})$| | |$(10\frac{5}{9},12\frac{2}{9})$| | 100 | |$(6\frac{1}{9},9\frac{4}{9})$| | |$(10\frac{5}{9},13\frac{8}{9})$| |
Notes: For the noncooperative theories, we list the limiting expected payoffs of players as δ → 1. For EPE, we consider two specifications: In (i) there is MPE reversion following a deviation, whereas in (ii) there are two off-path punishment states: one to punish A and B whereas rewarding C and D and another to punish C and D whereas rewarding A and B.
| . | Game 15 . | Game 25 . | Game 30 . | ||||||
|---|---|---|---|---|---|---|---|---|---|
| . | eff.(%) . | B (C) . | A (D) . | eff.(%) . | B (C) . | A (D) . | eff.(%) . | B (C) . | A (D) . |
| Cooperative | |||||||||
| SPB | 100 | 8.3 | 11.7 | 100 | 5 | 15 | 100 | 3.3 | 16.7 |
| Core | 100 | [0, 20] | [0, 20] | 100 | [0, 15] | [5, 20] | 100 | [0, 10] | [10, 20] |
| Core Midpoint | 100 | 10 | 10 | 100 | 7.5 | 12.5 | 100 | 5 | 15 |
| Noncooperative | |||||||||
| MPE | 100 | 10 | 10 | 72 | 6.45 | 11.45 | 50 | 4.17 | 13.33 |
| Markov Reversion | 100 | 10 | 10 | 100 | 8.75 | 11.25 | – | – | – |
| Carrot and Stick | 100 | 10 | 10 | 100 | |$(7\frac{7}{9},9\frac{4}{9})$| | |$(10\frac{5}{9},12\frac{2}{9})$| | 100 | |$(6\frac{1}{9},9\frac{4}{9})$| | |$(10\frac{5}{9},13\frac{8}{9})$| |
| . | Game 15 . | Game 25 . | Game 30 . | ||||||
|---|---|---|---|---|---|---|---|---|---|
| . | eff.(%) . | B (C) . | A (D) . | eff.(%) . | B (C) . | A (D) . | eff.(%) . | B (C) . | A (D) . |
| Cooperative | |||||||||
| SPB | 100 | 8.3 | 11.7 | 100 | 5 | 15 | 100 | 3.3 | 16.7 |
| Core | 100 | [0, 20] | [0, 20] | 100 | [0, 15] | [5, 20] | 100 | [0, 10] | [10, 20] |
| Core Midpoint | 100 | 10 | 10 | 100 | 7.5 | 12.5 | 100 | 5 | 15 |
| Noncooperative | |||||||||
| MPE | 100 | 10 | 10 | 72 | 6.45 | 11.45 | 50 | 4.17 | 13.33 |
| Markov Reversion | 100 | 10 | 10 | 100 | 8.75 | 11.25 | – | – | – |
| Carrot and Stick | 100 | 10 | 10 | 100 | |$(7\frac{7}{9},9\frac{4}{9})$| | |$(10\frac{5}{9},12\frac{2}{9})$| | 100 | |$(6\frac{1}{9},9\frac{4}{9})$| | |$(10\frac{5}{9},13\frac{8}{9})$| |
Notes: For the noncooperative theories, we list the limiting expected payoffs of players as δ → 1. For EPE, we consider two specifications: In (i) there is MPE reversion following a deviation, whereas in (ii) there are two off-path punishment states: one to punish A and B whereas rewarding C and D and another to punish C and D whereas rewarding A and B.
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