SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Game	Maximize Player 1's utility	Maximize Player 2's utility	Maximize Player 3's utility
LP	Ours (DCFFR)	Ours (PCFR+)	LP	Ours (DCFFR)	Ours (PCFR+)	LP	Ours (DCFFR)	Ours (PCFR+)
D32	12.00s	0.76s	[1.0]	0.40s	[1.0]	11.00s	0.35s	[1.0]	0.85s	[1.0]	10.00s	0.66s
D33	timeout	timeout	[—]	timeout	[—]	timeout	timeout	[—]	timeout	[—]	timeout	[—]
GL3	0.00s	0.01s	[1.0]	0.02s	[1.0]	0.00s	0.01s	[1.0]	0.02s	[0.1]	0.00s	0.01s
K35	57.00s	0.55s	[1.0]	1.08s	[0.1]	55.00s	1.03s	[1.0]	1.47s	[0.1]	60.00s	1.26s
L3132	8m 18s	6.10s	[0.1]	7.85s	[0.1]	8m 57s	7.65s	[0.1]	12.08s	[0.1]	7m 35s	6.78s
L3133	21m 25s	6.84s	[0.1]	12.97s	[0.1]	21m 43s	10.76s	[0.1]	18.44s	[0.1]	19m 58s	10.28s
L3151	timeout	timeout	[—]	timeout	[—]	timeout	timeout	[—]	timeout	[—]	timeout	[—]
L3223	2m 2s	5.52s	[0.1]	8.74s	[0.1]	1m 50s	6.46s	[0.1]	10.70s	[0.1]	2m 0s	5.94s
L3523	timeout	timeout	[—]	timeout	[—]	timeout	timeout	[—]	timeout	[—]	timeout	[—]
TP3	timeout	13.46s	[10.0]	20.25s	[1.0]	timeout	14.25s	[1.0]	22.19s	[10.0]	timeout	14.48s
G.4.4 Results for COMM solution concept
Game	Maximize Player 1's utility	Maximize Player 2's utility	Maximize Player 3's utility
LP	Ours (DCFR)	Ours (PCFR+)	LP	Ours (DCFR)	Ours (PCFR+)	LP	Ours (DCFR)	Ours (PCFR+)
D32	0.00s	0.06s	[1.0]	0.12s	[1.0]	1.00s	0.06s	[1.0]	0.18s	[0.1]	1.00s	0.18s
D33	timeout	4m 37s	[1.0]	9m 46s	[1.0]	timeout	1m 31s	[1.0]	3m 5s	[1.0]	timeout	2m 38s
GL3	timeout	7.72s	[0.1]	11.24s	[0.1]	timeout	7.50s	[1.0]	11.02s	[1.0]	timeout	11.42s
K35	1.00s	0.03s	[1.0]	0.03s	[0.1]	1.00s	0.02s	[1.0]	0.03s	[0.1]	1.00s	0.03s
L3132	8.00s	3.46s	[0.1]	5.65s	[0.1]	8.00s	3.37s	[0.1]	5.89s	[0.1]	7.00s	4.02s
L3133	12.00s	3.40s	[0.1]	7.98s	[0.1]	12.00s	3.54s	[0.1]	7.89s	[0.1]	11.00s	3.52s
L3151	timeout	16.73s	[0.1]	18.42s	[0.1]	timeout	15.80s	[0.1]	29.51s	[0.1]	timeout	18.00s
L3223	19.00s	18.19s	[0.1]	29.24s	[0.01]	18.00s	15.30s	[0.1]	27.38s	[0.1]	21.00s	18.77s
L3523	timeout	timeout	[—]	timeout	[—]	timeout	timeout	[—]	timeout	[—]	timeout	[—]
TP3	timeout	timeout	[—]	timeout	[—]	timeout	timeout	[—]	timeout	[—]	timeout	[—]
G.4.5 Results for NFCCERT solution concept
Game	Maximize Player 1's utility	Maximize Player 2's utility	Maximize Player 3's utility
LP	Ours (DCFFR)	Ours (PCFR+)	LP	Ours (DCFFR)	Ours (PCFR+)	LP	Ours (DCFFR)	Ours (PCFR+)
D32	0.00s	0.00s	[10.0]	0.00s	[1.0]	0.00s	0.00s	[1.0]	0.00s	0.00s	[1.0]	0.00s
D33	0.00s	0.04s	[1.0]	0.05s	[1.0]	0.00s	0.06s	[1.0]	0.06s	0.00s	[1.0]	0.05s
GL3	0.00s	0.00s	[1.0]	0.00s	[1.0]	0.00s	0.00s	[1.0]	0.00s	0.00s	[10.0]	0.00s
K35	0.00s	0.00s	[1.0]	0.00s	[1.0]	0.00s	0.00s	[1.0]	0.00s	0.00s	[1.0]	0.00s
L3132	0.00s	0.02s	[0.1]	0.02s	[1.0]	0.00s	0.02s	[0.1]	0.02s	0.00s	[0.1]	0.02s
L3133	0.00s	0.02s	[0.1]	0.02s	[0.1]	0.00s	0.02s	[1.0]	0.02s	0.00s	[0.1]	0.03s
L3151	0.00s	0.03s	[0.1]	0.08s	[0.1]	0.00s	0.04s	[0.1]	0.04s	0.00s	[0.1]	0.04s
L3223	0.00s	0.03s	[0.1]	0.04s	[0.1]	0.00s	0.05s	[0.1]	0.04s	0.00s	[0.1]	0.05s
L3523	13.00s	7.41s	[0.1]	14.31s	[0.1]	15.00s	8.17s	[0.1]	9.36s	[0.1]	17.00s	10.60s
TP3	47.00s	4.56s	[1.0]	10.06s	[10.0]	48.00s	4.97s	[10.0]	8.55s	[1.0]	45.00s	7.38s
G.4.6 Results for CCERT solution concept
Game	Maximize Player 1's utility	Maximize Player 2's utility	Maximize Player 3's utility
LP	Ours (DCFR)	Ours (PCFR+)	LP	Ours (DCFR)	Ours (PCFR+)	LP	Ours (DCFR)	Ours (PCFR+)
D32	0.00s	0.00s	[1.0]	0.00s	[1.0]	0.00s	0.00s	[1.0]	0.00s	[1.0]	0.00s	[1.0]
D33	1.00s	0.20s	[1.0]	0.29s	[1.0]	1.00s	0.13s	[1.0]	0.30s	[1.0]	1.00s	[0.1]
GL3	0.00s	0.01s	[0.1]	0.01s	[1.0]	0.00s	0.02s	[1.0]	0.01s	[1.0]	0.00s	[0.1]
K35	0.00s	0.00s	[1.0]	0.00s	[1.0]	0.00s	0.00s	[0.1]	0.00s	[1.0]	0.00s	[1.0]
L3132	0.00s	0.06s	[0.1]	0.05s	[0.1]	0.00s	0.05s	[0.1]	0.07s	[0.1]	0.00s	[0.1]
L3133	0.00s	0.04s	[0.1]	0.05s	[0.1]	0.00s	0.08s	[0.1]	0.11s	[0.1]	0.00s	[0.1]
L3151	1.00s	0.12s	[0.1]	0.27s	[0.1]	1.00s	0.16s	[0.1]	0.35s	[0.1]	1.00s	[0.1]
L3223	1.00s	0.23s	[0.1]	0.52s	[0.1]	1.00s	0.26s	[0.1]	0.43s	[0.1]	1.00s	[0.1]
L3523	timeout	1m 17s	[0.01]	2m 47s	[0.01]	timeout	1m 16s	[0.01]	3m 6s	[0.01]	timeout	1m 13s
TP3	timeout	10.23s	[10.0]	18.00s	[1.0]	timeout	10.38s	[10.0]	19.88s	[10.0]	timeout	11.95s
G.4.7 Results for CERT solution concept
Game	Maximize Player 1's utility	Maximize Player 2's utility	Maximize Player 3's utility
LP	Ours (DCFR)	Ours (PCFR+)	LP	Ours (DCFR)	Ours (PCFR+)	LP	Ours (DCFR)	Ours (PCFR+)
D32	0.00s	0.01s	[1.0]	0.01s	[1.0]	0.00s	0.01s	[1.0]	0.01s	[1.0]	0.00s	0.01s	[1.0]	0.02s	[1.0]
D33	4.00s	3.14s	[1.0]	6.08s	[1.0]	4.00s	2.02s	[1.0]	3.18s	[0.1]	4.00s	2.10s	[1.0]	3.89s	[0.1]
GL3	0.00s	0.02s	[1.0]	0.03s	[0.1]	0.00s	0.02s	[1.0]	0.03s	[1.0]	0.00s	0.03s	[0.1]	0.03s	[0.1]
K35	0.00s	0.01s	[1.0]	0.01s	[1.0]	0.00s	0.00s	[1.0]	0.01s	[0.1]	0.00s	0.00s	[1.0]	0.01s	[0.1]
L3132	1.00s	0.15s	[0.1]	0.10s	[0.1]	1.00s	0.18s	[0.1]	0.22s	[0.1]	0.00s	0.18s	[0.1]	0.35s	[0.1]
L3133	1.00s	0.22s	[0.1]	0.42s	[1.0]	1.00s	0.19s	[0.1]	0.33s	[0.1]	1.00s	0.25s	[0.1]	0.38s	[0.1]
L3151	2.00s	0.21s	[0.1]	0.42s	[0.1]	2.00s	0.22s	[0.1]	0.44s	[0.1]	2.00s	0.29s	[0.1]	0.53s	[0.1]
L3223	1.00s	0.61s	[0.1]	1.43s	[0.01]	1.00s	0.61s	[0.1]	1.13s	[0.01]	1.00s	0.68s	[0.1]	0.98s	[0.01]
L3523	timeout	2m 58s	[0.01]	timeout	[—]	timeout	4m 33s	[0.01]	timeout	[—]	timeout	3m 55s	[0.01]	timeout	[—]
TP3	timeout	26.70s	[1.0]	40.73s	[1.0]	timeout	25.08s	[1.0]	35.99s	[10.0]	timeout	36.36s	[10.0]	Im 0s	[1.0]
H Experimental results for binary search-based Lagrangian
In this section, we compare the performance of our "direct" Lagrangian approach against our binary search-based Lagrangian approach for computing several equilibrium concepts at the approximation level defined as  $1\%$  of the payoff range of the game.
For each solution concept, we identify the same three objectives as Appendix G (maximizing each player's individual utility, and maximizing the social welfare in our two-player general-sum games). For each objective, each of the following tables compares three runtimes:
- The time required by the linear program (column 'LP');
- The time required by the "direct" (non-binary search-based) Lagrangian approach, taking the fastest between the implementations using DCFR and  $\mathrm{PCFR}^+$  as the underlying no-regret algorithms (column 'Lagrangian').
- The time required by the binary search-based Lagrangian approach, taking the fastest between the implementations using DCFR and  $\mathrm{PCFR}^{+}$  as the underlying no-regret algorithms (column 'BinSearch').
We observe that our two approaches behave similarly in small games. In larger games, especially with three players, the direct Lagrangian tends to be 2-4 times faster.
H.1 Detailed Breakdown by Equilibrium and Objective Function (Two-Player Games)
H.1.1 Results for NFCCE solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize social welfare
LP Lagrangian	BinSearch	LP Lagrangian	BinSearch	LP Lagrangian	BinSearch	LP Lagrangian	BinSearch
B2222	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
B2322	0.00s	0.03s	0.04s	0.00s	0.04s	0.03s	0.00s	0.01s	0.01s
B2323	7.00s	1.05s	1.67s	6.00s	1.01s	1.23s	6.00s	0.33s	0.17s
B2324	50.00s	15.57s	18.23s	37.00s	12.80s	11.11s	38.00s	2.73s	1.41s
S2122	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
S2123	0.00s	0.01s	0.01s	0.00s	0.01s	0.01s	0.00s	0.01s	0.01s
S2133	1.00s	0.02s	0.03s	1.00s	0.02s	0.02s	1.00s	0.02s	0.02s
S2254	2m 1s	6.96s	6.03s	1m 14s	10.43s	7.12s	1m 58s	7.43s	3.64s
S2264	3m 36s	13.96s	7.64s	2m 24s	18.46s	14.57s	3m 43s	11.74s	7.69s
RS212	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
RS213	timeout	34.52s	28.65s	timeout	20.29s	26.25s	timeout	14.68s	7.44s
RS222	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
RS223	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
H.1.2 Results for EFCCE solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize social welfare
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
B2222	0.00s	0.01s	0.01s	0.00s	0.01s	0.01s	0.00s	0.01s	0.01s
B2322	3.00s	0.41s	0.54s	3.00s	0.69s	0.60s	3.00s	0.69s	0.41s
B2323	1m 35s	9.11s	16.32s	1m 30s	12.39s	8.62s	1m 21s	14.23s	6.89s
B2324	timeout	1m 53s	2m 5s	timeout	2m 44s	3m 14s	timeout	3m 1s	1m 27s
S2122	0.00s	0.01s	0.00s	0.00s	0.00s	0.00s	0.00s	0.01s	0.00s
S2123	1.00s	0.03s	0.04s	1.00s	0.05s	0.04s	1.00s	0.06s	0.03s
S2133	3.00s	0.12s	0.11s	2.00s	0.20s	0.32s	3.00s	0.11s	0.22s
S2254	timeout	27.31s	30.66s	timeout	37.43s	1m 17s	timeout	22.01s	36.62s
S2264	timeout	46.07s	1m 9s	timeout	2m 18s	1m 26s	timeout	39.23s	1m 4s
RS212	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
RS213	timeout	28.80s	36.02s	timeout	31.02s	29.54s	timeout	15.54s	9.84s
RS222	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
RS223	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
H.1.3 Results for EFCE solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize social welfare
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
B2222	0.00s	0.01s	0.02s	0.00s	0.05s	0.01s	0.00s	0.02s	0.02s
B2322	9.00s	1.23s	4.49s	9.00s	4.63s	2.04s	9.00s	1.60s	1.57s
B2323	3m 54s	48.40s	1m 44s	4m 9s	1m 27s	40.91s	3m 40s	44.87s	1m 19s
B2324	timeout	9m 3s	16m 45s	timeout	10m 21s	13m 15s	timeout	10m 48s	8m 12s
S2122	0.00s	0.01s	0.01s	0.00s	0.02s	0.01s	0.00s	0.02s	0.01s
S2123	1.00s	0.09s	0.06s	1.00s	0.34s	0.10s	1.00s	0.15s	0.08s
S2133	4.00s	0.52s	0.32s	3.00s	1.31s	0.77s	3.00s	0.49s	0.43s
S2254	timeout	2m 10s	2m 19s	timeout	timeout	4m 1s	timeout	3m 34s	2m 10s
S2264	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
RS212	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
RS213	timeout	35.37s	34.00s	timeout	32.49s	36.52s	timeout	23.37s	22.16s
RS222	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
RS223	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
H.1.4 Results for COMM solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize social welfare
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
B2222	2.00s	0.88s	3.39s	2.00s	0.89s	2.70s	2.00s	1.49s	2.80s
B2322	timeout	5m 47s	7m 28s	timeout	3m 45s	10m 31s	timeout	4m 41s	7m 20s
B2323	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
B2324	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
S2122	2.00s	0.21s	0.42s	2.00s	0.48s	0.28s	2.00s	0.35s	0.40s
S2123	1m 30s	38.95s	1m 36s	1m 36s	1m 10s	1m 7s	1m 33s	59.63s	51.54s
S2133	timeout	4m 26s	10m 23s	timeout	7m 27s	6m 17s	timeout	12m 11s	5m 57s
S2254	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
S2264	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
RS212	2.00s	0.01s	0.01s	2.00s	0.01s	0.01s	2.00s	0.01s	0.00s
RS213	6m 51s	10.24s	18.82s	6m 27s	12.83s	24.61s	6m 25s	8.74s	8.18s
RS222	3.00s	0.01s	0.01s	3.00s	0.02s	0.02s	3.00s	0.01s	0.01s
RS223	8m 41s	5.79s	9.71s	8m 24s	8.45s	12.94s	8m 54s	4.00s	4.54s
H.1.5 Results for NFCCERT solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize social welfare
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
B2222	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
B2322	0.00s	0.02s	0.03s	0.00s	0.02s	0.02s	0.00s	0.01s	0.00s
B2323	2.00s	0.62s	0.64s	1.00s	0.48s	0.51s	2.00s	0.14s	0.08s
B2324	11.00s	4.88s	9.86s	11.00s	5.24s	6.26s	10.00s	1.82s	0.70s
S2122	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
S2123	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
S2133	0.00s	0.01s	0.00s	0.00s	0.01s	0.01s	0.00s	0.01s	0.00s
S2254	25.00s	1.23s	0.84s	24.00s	3.02s	2.41s	28.00s	1.32s	0.70s
S2264	56.00s	2.71s	1.72s	42.00s	5.43s	3.81s	50.00s	2.73s	1.24s
U212	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
U213	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
U222	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
U223	0.00s	0.00s	0.01s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
H.1.6 Results for CCERT solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize social welfare
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
B2222	0.00s	0.00s	0.01s	0.00s	0.01s	0.00s	0.00s	0.01s	0.00s
B2322	0.00s	0.07s	0.11s	0.00s	0.15s	0.09s	0.00s	0.22s	0.09s
B2323	7.00s	3.75s	3.55s	6.00s	4.69s	3.54s	8.00s	5.39s	2.64s
B2324	timeout	54.92s	49.66s	timeout	59.02s	59.88s	timeout	1m 31s	37.51s
S2122	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
S2123	0.00s	0.01s	0.02s	0.00s	0.02s	0.02s	0.00s	0.01s	0.02s
S2133	1.00s	0.04s	0.04s	1.00s	0.08s	0.06s	1.00s	0.05s	0.03s
S2254	1m 41s	8.61s	11.29s	1m 47s	23.28s	16.40s	2m 3s	8.22s	16.31s
S2264	timeout	20.11s	21.42s	timeout	1m 5s	38.76s	timeout	16.50s	20.62s
RS212	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
RS213	0.00s	0.01s	0.00s	0.00s	0.01s	0.01s	0.00s	0.01s	0.00s
RS222	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
RS223	0.00s	0.01s	0.01s	0.00s	0.01s	0.01s	0.00s	0.01s	0.00s
H.1.7 Results for CERT solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize social welfare
LP Lagrangian	BinSearch	LP Lagrangian	BinSearch	LP Lagrangian	BinSearch
B2222	0.00s	0.01s	0.01s	0.00s	0.02s	0.01s	0.00s	0.02s	0.02s
B2322	2.00s	1.05s	0.95s	2.00s	1.16s	0.66s	2.00s	1.24s	1.20s
B2323	40.00s	47.11s	21.54s	33.00s	58.20s	22.16s	37.00s	40.45s	59.67s
B2324	timeout	8m 29s	4m 38s	timeout	timeout	3m 40s	timeout	6m 14s	4m 1s
S2122	0.00s	0.02s	0.01s	0.00s	0.02s	0.01s	0.00s	0.02s	0.01s
S2123	1.00s	0.19s	0.09s	1.00s	0.28s	0.20s	1.00s	0.15s	0.12s
S2133	3.00s	0.96s	0.43s	2.00s	1.10s	0.81s	2.00s	0.92s	0.41s
S2254	timeout	3m 26s	2m 54s	timeout	6m 15s	4m 14s	timeout	2m 42s	2m 53s
S2264	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
RS212	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
RS213	0.00s	0.02s	0.03s	0.00s	0.02s	0.04s	0.00s	0.02s	0.01s
RS222	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
RS223	1.00s	0.01s	0.02s	1.00s	0.02s	0.02s	1.00s	0.01s	0.01s
H.2 Detailed Breakdown by Equilibrium and Objective Function (Three-Player Games)
H.2.1 Results for NFCCE solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize Pl. 3's utility
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
D32	0.00s	0.01s	0.02s	0.00s	0.01s	0.02s	0.00s	0.01s	0.02s
D33	2m 17s	12.93s	21.46s	2m 8s	16.40s	28.63s	2m 23s	17.57s	19.74s
GL3	0.00s	0.01s	0.02s	0.00s	0.01s	0.02s	0.00s	0.02s	0.02s
K35	49.00s	0.76s	1.52s	55.00s	0.56s	1.39s	55.00s	0.64s	1.67s
L3132	26.00s	0.59s	1.72s	24.00s	0.79s	1.63s	24.00s	0.77s	1.91s
L3133	38.00s	0.94s	1.79s	38.00s	0.89s	1.83s	37.00s	1.11s	1.90s
L3151	timeout	15.12s	30.01s	timeout	12.74s	35.58s	timeout	18.03s	30.87s
L3223	4.00s	0.44s	0.91s	4.00s	0.45s	1.84s	4.00s	0.52s	1.58s
L3523	timeout	1m 7s	4m 21s	timeout	1m 2s	4m 27s	timeout	1m 9s	4m 35s
TP3	1m 38s	7.44s	8.43s	1m 40s	7.63s	9.41s	1m 44s	11.45s	11.85s
H.2.2 Results for EFCCE solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize Pl. 3's utility
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
D32	0.00s	0.02s	0.03s	0.00s	0.01s	0.03s	0.00s	0.02s	0.03s
D33	timeout	1m 46s	2m 32s	timeout	1m 16s	2m 28s	timeout	1m 44s	3m 7s
GL3	1.00s	0.02s	0.04s	1.00s	0.03s	0.05s	1.00s	0.03s	0.05s
K35	46.00s	0.67s	2.09s	55.00s	0.75s	1.90s	51.00s	0.68s	1.85s
L3132	8m 43s	5.13s	18.75s	9m 17s	6.27s	13.48s	9m 44s	7.76s	18.47s
L3133	20m 26s	8.88s	19.52s	timeout	8.19s	23.17s	23m 15s	10.86s	27.48s
L3151	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
L3223	1m 10s	2.94s	14.79s	1m 10s	3.22s	12.23s	1m 2s	3.24s	13.68s
L3523	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
TP3	timeout	13.76s	15.36s	timeout	15.03s	13.64s	timeout	15.27s	15.10s
H.2.3 Results for EFCE solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize Pl. 3's utility
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
D32	12.00s	0.40s	1.11s	11.00s	0.35s	1.32s	10.00s	0.66s	1.23s
D33	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
GL3	0.00s	0.01s	0.03s	0.00s	0.01s	0.03s	0.00s	0.01s	0.06s
K35	57.00s	0.55s	1.50s	55.00s	1.03s	2.37s	60.00s	1.26s	2.22s
L3132	8m 18s	6.10s	14.02s	8m 57s	7.65s	16.25s	7m 35s	6.78s	19.11s
L3133	21m 25s	6.84s	25.83s	21m 43s	10.76s	26.37s	19m 58s	10.28s	20.65s
L3151	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
L3223	2m 2s	5.52s	28.79s	1m 50s	6.46s	29.37s	2m 0s	5.94s	17.13s
L3523	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
TP3	timeout	13.46s	13.78s	timeout	14.25s	13.71s	timeout	14.48s	11.48s
H.2.4 Results for COMM solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize Pl. 3's utility
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
D32	0.00s	0.06s	0.24s	1.00s	0.06s	0.21s	1.00s	0.17s	0.32s
D33	timeout	4m 37s	5m 35s	timeout	1m 31s	4m 27s	timeout	2m 38s	5m 21s
GL3	timeout	7.72s	26.48s	timeout	7.50s	21.91s	timeout	11.42s	25.44s
K35	1.00s	0.03s	0.07s	1.00s	0.02s	0.07s	1.00s	0.03s	0.05s
L3132	8.00s	3.46s	10.64s	8.00s	3.37s	8.44s	7.00s	4.02s	9.57s
L3133	12.00s	3.40s	12.82s	12.00s	3.54s	10.70s	11.00s	3.52s	12.35s
L3151	timeout	16.73s	55.51s	timeout	15.80s	57.66s	timeout	18.00s	56.83s
L3223	19.00s	18.19s	1m 0s	18.00s	15.30s	1m 17s	21.00s	18.77s	57.11s
L3523	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
TP3	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout	timeout
H.2.5 Results for NFCCERT solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize Pl. 3's utility
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
D32	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
D33	0.00s	0.04s	0.05s	0.00s	0.06s	0.05s	0.00s	0.04s	0.03s
GL3	0.00s	0.00s	0.01s	0.00s	0.00s	0.01s	0.00s	0.00s	0.01s
K35	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
L3132	0.00s	0.02s	0.03s	0.00s	0.02s	0.02s	0.00s	0.02s	0.03s
L3133	0.00s	0.02s	0.03s	0.00s	0.02s	0.04s	0.00s	0.02s	0.04s
L3151	0.00s	0.03s	0.04s	0.00s	0.04s	0.07s	0.00s	0.03s	0.07s
L3223	0.00s	0.03s	0.06s	0.00s	0.04s	0.05s	0.00s	0.05s	0.08s
L3523	13.00s	7.41s	13.51s	15.00s	8.17s	16.32s	17.00s	10.60s	22.93s
TP3	47.00s	4.56s	4.98s	48.00s	4.97s	8.12s	45.00s	7.38s	7.50s
H.2.6 Results for CCERT solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize Pl. 3's utility
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
D32	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
D33	1.00s	0.20s	0.27s	1.00s	0.13s	0.32s	1.00s	0.19s	0.25s
GL3	0.00s	0.01s	0.02s	0.00s	0.01s	0.02s	0.00s	0.01s	0.01s
K35	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s	0.00s
L3132	0.00s	0.05s	0.08s	0.00s	0.05s	0.09s	0.00s	0.05s	0.07s
L3133	0.00s	0.04s	0.13s	0.00s	0.08s	0.20s	0.00s	0.12s	0.09s
L3151	1.00s	0.12s	0.36s	1.00s	0.16s	0.32s	1.00s	0.16s	0.31s
L3223	1.00s	0.23s	0.72s	1.00s	0.26s	0.58s	1.00s	0.24s	0.67s
L3523	timeout	1m 17s	13m 19s	timeout	1m 16s	16m 19s	timeout	1m 13s	6m 41s
TP3	timeout	10.23s	16.79s	timeout	10.38s	12.96s	timeout	11.95s	11.91s
H.2.7 Results for CERT solution concept
Game	Maximize Pl. 1's utility	Maximize Pl. 2's utility	Maximize Pl. 3's utility
LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch	LP	Lagrangian	BinSearch
D32	0.00s	0.01s	0.01s	0.00s	0.01s	0.01s	0.00s	0.01s	0.02s
D33	4.00s	3.14s	7.11s	4.00s	2.02s	2.26s	4.00s	2.10s	9.88s
GL3	0.00s	0.02s	0.04s	0.00s	0.02s	0.05s	0.00s	0.03s	0.05s
K35	0.00s	0.01s	0.01s	0.00s	0.00s	0.01s	0.00s	0.00s	0.01s
L3132	1.00s	0.10s	0.28s	1.00s	0.18s	0.37s	0.00s	0.18s	0.35s
L3133	1.00s	0.22s	0.41s	1.00s	0.19s	0.44s	1.00s	0.25s	0.30s
L3151	2.00s	0.21s	0.86s	2.00s	0.22s	0.75s	2.00s	0.29s	0.72s
L3223	1.00s	0.61s	1.48s	1.00s	0.61s	1.65s	1.00s	0.68s	1.95s
L3523	timeout	2m 58s	timeout	timeout	4m 33s	timeout	timeout	3m 55s	timeout
TP3	timeout	26.70s	34.23s	timeout	25.08s	28.22s	timeout	36.36s	27.68s