Softmax Equilibria
1000 random starting points per β
β = 1.0 — 1 distinct fixed point
#1 basin: 1000/1000 (100.0%)
| Strategy | Frequency | Reward |
|---|
| mirror | 0.1719 | 6.8265 |
| universalizability | 0.1719 | 6.8265 |
| hard-line | 0.1426 | 6.6397 |
| chivalry | 0.1311 | 6.5556 |
| conditional-cooperator | 0.1096 | 6.3764 |
| anti-exploiter | 0.1053 | 6.3368 |
| friend-to-all | 0.0817 | 6.0829 |
| intelligence | 0.0710 | 5.9420 |
| tiger | 0.0151 | 4.3915 |
β = 5.0 — 1 distinct fixed point
#1 basin: 1000/1000 (100.0%)
| Strategy | Frequency | Reward |
|---|
| mirror | 0.2900 | 6.8680 |
| universalizability | 0.2900 | 6.8680 |
| hard-line | 0.1990 | 6.7926 |
| conditional-cooperator | 0.1641 | 6.7541 |
| chivalry | 0.0332 | 6.4343 |
| anti-exploiter | 0.0095 | 6.1847 |
| friend-to-all | 0.0087 | 6.1657 |
| intelligence | 0.0055 | 6.0767 |
β = 20.0 — 2 distinct fixed points
#1 basin: 702/1000 (70.2%)
| Strategy | Frequency | Reward |
|---|
| mirror | 0.2501 | 6.8680 |
| universalizability | 0.2501 | 6.8680 |
| hard-line | 0.2500 | 6.8680 |
| conditional-cooperator | 0.2499 | 6.8679 |
| chivalry | 0.0000 | 6.3480 |
#2 basin: 298/1000 (29.8%)
| Strategy | Frequency | Reward |
|---|
| mirror | 0.2058 | 6.8680 |
| universalizability | 0.2058 | 6.8680 |
| chivalry | 0.1973 | 6.8659 |
| anti-exploiter | 0.1952 | 6.8653 |
| friend-to-all | 0.1952 | 6.8653 |
| hard-line | 0.0008 | 6.5883 |
| intelligence | 0.0000 | 6.3200 |