Nash Equilibrium Methods Comparison¶
For each method available for Nash equilibrium finding, this lists various information about the performance across different game types and starting locations. “Fraction of Eqa” is the mean fraction of all equilibria found via that method or starting location. “Weigted Fraction (of Eqa)” is the same, except each equilibrium is down weighted by the number of methods that found it, thus a larger weighted fraction indicates that this method found more unique equilibria. “Time” is the average time in seconds it took to run this method for every starting location. “Normalized Time” sets the minimum time for each game type and sets it to one, thus somewhat mitigating the fact that certain games may be more difficult than others. It also provides an easy comparison metric to for baseline timing.
Comparisons Between Methods¶
Method |
Fraction of Eqa |
Weighted Fraction |
Time (sec) |
Normalized Time |
|---|---|---|---|---|
Regret Minimization |
0.568731 |
0.173796 |
0.321582 |
9.26718 |
Multiplicative Weights Bandit |
0.528874 |
0.153923 |
29.4978 |
4398.16 |
Multiplicative Weights Dist |
0.521398 |
0.0959819 |
17.8935 |
768.361 |
Multiplicative Weights Stoch |
0.508405 |
0.0873798 |
62.5403 |
7982.75 |
Fictitious Play |
0.472796 |
0.0594228 |
7.73066 |
576.771 |
Fictitious Play Long |
0.466721 |
0.0552945 |
179.604 |
22325.4 |
Replicator Dynamics |
0.438658 |
0.0567802 |
1.56668 |
64.2687 |
Scarf 30 |
0.432357 |
0.071016 |
16.7026 |
309.018 |
Scarf 5 |
0.431933 |
0.0708725 |
5.81228 |
144.357 |
Scarf 1 |
0.43032 |
0.070612 |
2.01623 |
61.1935 |
Regret Matching |
0.370006 |
0.104922 |
57.9059 |
5180.56 |
Scarf 30¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Uniform |
0.994774 |
0.994774 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Scarf 1 |
1 |
5.04985 |
Scarf 5 |
1 |
2.14065 |
Replicator Dynamics |
0.892422 |
4.80821 |
Multiplicative Weights Bandit |
0.889781 |
0.0702606 |
Multiplicative Weights Stoch |
0.885552 |
0.0387107 |
Regret Minimization |
0.879359 |
33.3454 |
Fictitious Play |
0.878377 |
0.535772 |
Fictitious Play Long |
0.877982 |
0.0138415 |
Multiplicative Weights Dist |
0.875912 |
0.402178 |
Regret Matching |
0.498422 |
0.0596495 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.0555556 |
Time (sec) |
0.000148058 |
Normalized Time |
1 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.331322 |
Weighted Fraction of Eqa |
0.074747 |
Time (sec) |
10.8339 |
Normalized Time |
661.379 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5375 |
Weighted Fraction of Eqa |
0.0772222 |
Time (sec) |
0.00523914 |
Normalized Time |
1 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.312472 |
Weighted Fraction of Eqa |
0.0581924 |
Time (sec) |
1.61499 |
Normalized Time |
120.84 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.8 |
Weighted Fraction of Eqa |
0.0954167 |
Time (sec) |
0.00686474 |
Normalized Time |
1.24652 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.05 |
Time (sec) |
1.53651 |
Normalized Time |
67.9854 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.469426 |
Weighted Fraction of Eqa |
0.0632558 |
Time (sec) |
40.3947 |
Normalized Time |
634.09 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0178571 |
Weighted Fraction of Eqa |
0.00595238 |
Time (sec) |
0.0364892 |
Normalized Time |
1.00035 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.576389 |
Weighted Fraction of Eqa |
0.106637 |
Time (sec) |
0.189833 |
Normalized Time |
6.63798 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.453237 |
Weighted Fraction of Eqa |
0.0686254 |
Time (sec) |
1.63167 |
Normalized Time |
84.8835 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.155377 |
Weighted Fraction of Eqa |
0.0352583 |
Time (sec) |
87.0647 |
Normalized Time |
2682.6 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.333333 |
Weighted Fraction of Eqa |
0.0333333 |
Time (sec) |
0.000152111 |
Normalized Time |
1 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.525 |
Weighted Fraction of Eqa |
0.148674 |
Time (sec) |
0.00902817 |
Normalized Time |
1.5135 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0 |
Weighted Fraction of Eqa |
0 |
Time (sec) |
1800 |
Normalized Time |
1560.87 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.239765 |
Weighted Fraction of Eqa |
0.0375492 |
Time (sec) |
0.687516 |
Normalized Time |
4.65944 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0588235 |
Weighted Fraction of Eqa |
0.0196078 |
Time (sec) |
0.484841 |
Normalized Time |
31.1158 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0909091 |
Weighted Fraction of Eqa |
0.030303 |
Time (sec) |
0.0513456 |
Normalized Time |
1.61668 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.349647 |
Weighted Fraction of Eqa |
0.0554777 |
Time (sec) |
0.966773 |
Normalized Time |
33.8824 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.153897 |
Weighted Fraction of Eqa |
0.0311547 |
Time (sec) |
0.28003 |
Normalized Time |
7.51681 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.732691 |
Weighted Fraction of Eqa |
0.0718566 |
Time (sec) |
6.70744 |
Normalized Time |
124.043 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.464167 |
Weighted Fraction of Eqa |
0.0838261 |
Time (sec) |
0.0184558 |
Normalized Time |
2.28596 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1 |
Time (sec) |
0.000151873 |
Normalized Time |
1 |
Regret Matching¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Random |
0.924928 |
0.64514 |
Pure |
0.515728 |
0.236737 |
Biased |
0.10575 |
0.0276221 |
Role biased |
0.102853 |
0.0250178 |
Uniform |
0.0637684 |
0.0137799 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Multiplicative Weights Stoch |
0.927526 |
0.648969 |
Replicator Dynamics |
0.927218 |
80.6078 |
Fictitious Play Long |
0.926172 |
0.232047 |
Fictitious Play |
0.926072 |
8.98201 |
Multiplicative Weights Bandit |
0.9153 |
1.17789 |
Multiplicative Weights Dist |
0.904918 |
6.74234 |
Regret Minimization |
0.900291 |
559.022 |
Scarf 1 |
0.871919 |
84.6587 |
Scarf 5 |
0.871468 |
35.8871 |
Scarf 30 |
0.871176 |
16.7646 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.555556 |
Time (sec) |
33.8172 |
Normalized Time |
228405 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.304548 |
Weighted Fraction of Eqa |
0.034857 |
Time (sec) |
127.934 |
Normalized Time |
7810.02 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0625 |
Weighted Fraction of Eqa |
0.04 |
Time (sec) |
3.14211 |
Normalized Time |
599.737 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.621495 |
Weighted Fraction of Eqa |
0.391822 |
Time (sec) |
254.72 |
Normalized Time |
19059.1 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0 |
Weighted Fraction of Eqa |
0 |
Time (sec) |
2.96706 |
Normalized Time |
538.77 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1125 |
Time (sec) |
1.53544 |
Normalized Time |
67.9379 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.455498 |
Weighted Fraction of Eqa |
0.0478788 |
Time (sec) |
4.64639 |
Normalized Time |
72.936 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0357143 |
Weighted Fraction of Eqa |
0.00478316 |
Time (sec) |
2.82121 |
Normalized Time |
77.3436 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.145833 |
Weighted Fraction of Eqa |
0.0148201 |
Time (sec) |
5.05215 |
Normalized Time |
176.661 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.130333 |
Weighted Fraction of Eqa |
0.0545 |
Time (sec) |
23.0914 |
Normalized Time |
1201.27 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.385925 |
Weighted Fraction of Eqa |
0.224672 |
Time (sec) |
243.786 |
Normalized Time |
7511.41 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.666667 |
Weighted Fraction of Eqa |
0.366667 |
Time (sec) |
29.9445 |
Normalized Time |
196860 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.525 |
Weighted Fraction of Eqa |
0.0622159 |
Time (sec) |
0.693169 |
Normalized Time |
116.204 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.142857 |
Time (sec) |
19.839 |
Normalized Time |
17.2034 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.305898 |
Weighted Fraction of Eqa |
0.0395527 |
Time (sec) |
5.54689 |
Normalized Time |
37.5924 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0588235 |
Weighted Fraction of Eqa |
0.0117647 |
Time (sec) |
78.2362 |
Normalized Time |
5021 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.363636 |
Weighted Fraction of Eqa |
0.0454545 |
Time (sec) |
1.52629 |
Normalized Time |
48.0573 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.405965 |
Weighted Fraction of Eqa |
0.0664618 |
Time (sec) |
39.8172 |
Normalized Time |
1395.47 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.261022 |
Weighted Fraction of Eqa |
0.0723834 |
Time (sec) |
76.8243 |
Normalized Time |
2062.19 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.760323 |
Weighted Fraction of Eqa |
0.0714043 |
Time (sec) |
2.72771 |
Normalized Time |
50.4443 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.7075 |
Weighted Fraction of Eqa |
0.323323 |
Time (sec) |
33.247 |
Normalized Time |
4118.02 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1 |
Time (sec) |
25.2879 |
Normalized Time |
166507 |
Multiplicative Weights Dist¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Uniform |
0.945395 |
0.845543 |
Biased |
0.163391 |
0.0462799 |
Role biased |
0.160499 |
0.0431626 |
Random |
0.156742 |
0.0466468 |
Pure |
0.0609121 |
0.0172996 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Fictitious Play Long |
0.996554 |
0.0344164 |
Fictitious Play |
0.996255 |
1.33218 |
Replicator Dynamics |
0.994949 |
11.9555 |
Multiplicative Weights Stoch |
0.978448 |
0.0962527 |
Multiplicative Weights Bandit |
0.947091 |
0.1747 |
Regret Minimization |
0.94645 |
82.9121 |
Scarf 1 |
0.892497 |
12.5563 |
Scarf 5 |
0.892045 |
5.32264 |
Scarf 30 |
0.891754 |
2.48646 |
Regret Matching |
0.565745 |
0.148316 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.0555556 |
Time (sec) |
2.92369 |
Normalized Time |
19746.9 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.512942 |
Weighted Fraction of Eqa |
0.160588 |
Time (sec) |
8.43969 |
Normalized Time |
515.22 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5375 |
Weighted Fraction of Eqa |
0.0612103 |
Time (sec) |
2.60122 |
Normalized Time |
496.497 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.373656 |
Weighted Fraction of Eqa |
0.0858021 |
Time (sec) |
4.23339 |
Normalized Time |
316.759 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.8 |
Weighted Fraction of Eqa |
0.0832143 |
Time (sec) |
2.59525 |
Normalized Time |
471.255 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1125 |
Time (sec) |
11.4917 |
Normalized Time |
508.467 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.655801 |
Weighted Fraction of Eqa |
0.122854 |
Time (sec) |
32.0664 |
Normalized Time |
503.358 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.285714 |
Weighted Fraction of Eqa |
0.220557 |
Time (sec) |
1704.14 |
Normalized Time |
46719.1 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.576389 |
Weighted Fraction of Eqa |
0.0670621 |
Time (sec) |
15.1364 |
Normalized Time |
529.282 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.529003 |
Weighted Fraction of Eqa |
0.102581 |
Time (sec) |
16.2656 |
Normalized Time |
846.174 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.337059 |
Weighted Fraction of Eqa |
0.167468 |
Time (sec) |
5.92329 |
Normalized Time |
182.506 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.333333 |
Weighted Fraction of Eqa |
0.0333333 |
Time (sec) |
2.89428 |
Normalized Time |
19027.4 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.558333 |
Weighted Fraction of Eqa |
0.0822159 |
Time (sec) |
2.58478 |
Normalized Time |
433.317 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.142857 |
Time (sec) |
69.3236 |
Normalized Time |
60.1139 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.437487 |
Weighted Fraction of Eqa |
0.108665 |
Time (sec) |
33.4532 |
Normalized Time |
226.719 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.235294 |
Weighted Fraction of Eqa |
0.188235 |
Time (sec) |
4.93074 |
Normalized Time |
316.442 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.454545 |
Weighted Fraction of Eqa |
0.0636364 |
Time (sec) |
5.28843 |
Normalized Time |
166.513 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.445319 |
Weighted Fraction of Eqa |
0.0851808 |
Time (sec) |
5.67596 |
Normalized Time |
198.925 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.326832 |
Weighted Fraction of Eqa |
0.0679519 |
Time (sec) |
4.73046 |
Normalized Time |
126.979 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.796538 |
Weighted Fraction of Eqa |
0.0885722 |
Time (sec) |
30.7712 |
Normalized Time |
569.061 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.380833 |
Weighted Fraction of Eqa |
0.0529392 |
Time (sec) |
2.99483 |
Normalized Time |
370.944 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1 |
Time (sec) |
2.88606 |
Normalized Time |
19003.2 |
Replicator Dynamics¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Uniform |
0.942031 |
0.850344 |
Biased |
0.143336 |
0.0352437 |
Role biased |
0.143326 |
0.0355169 |
Random |
0.142065 |
0.0361951 |
Pure |
0.0752944 |
0.0219619 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Fictitious Play Long |
0.974041 |
0.00287872 |
Fictitious Play |
0.973601 |
0.111429 |
Multiplicative Weights Dist |
0.954491 |
0.0836439 |
Multiplicative Weights Stoch |
0.954236 |
0.00805094 |
Multiplicative Weights Bandit |
0.942476 |
0.0146126 |
Regret Minimization |
0.941664 |
6.93509 |
Scarf 1 |
0.887903 |
1.05025 |
Scarf 5 |
0.887451 |
0.445206 |
Scarf 30 |
0.88716 |
0.207977 |
Regret Matching |
0.556909 |
0.0124058 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.0555556 |
Time (sec) |
0.0477914 |
Normalized Time |
322.788 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.436103 |
Weighted Fraction of Eqa |
0.0885598 |
Time (sec) |
8.00409 |
Normalized Time |
488.628 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5375 |
Weighted Fraction of Eqa |
0.0612103 |
Time (sec) |
0.0729519 |
Normalized Time |
13.9244 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.120139 |
Weighted Fraction of Eqa |
0.0142472 |
Time (sec) |
0.676059 |
Normalized Time |
50.5854 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.8 |
Weighted Fraction of Eqa |
0.0832143 |
Time (sec) |
0.0424278 |
Normalized Time |
7.7042 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1125 |
Time (sec) |
0.219549 |
Normalized Time |
9.7143 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.594784 |
Weighted Fraction of Eqa |
0.0688609 |
Time (sec) |
1.41217 |
Normalized Time |
22.1674 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0535714 |
Weighted Fraction of Eqa |
0.00924745 |
Time (sec) |
46.3598 |
Normalized Time |
1270.96 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.576389 |
Weighted Fraction of Eqa |
0.0670621 |
Time (sec) |
0.463779 |
Normalized Time |
16.2172 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.538898 |
Weighted Fraction of Eqa |
0.116055 |
Time (sec) |
1.25418 |
Normalized Time |
65.2456 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.161206 |
Weighted Fraction of Eqa |
0.0185797 |
Time (sec) |
1.29125 |
Normalized Time |
39.7854 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.333333 |
Weighted Fraction of Eqa |
0.0333333 |
Time (sec) |
0.0478084 |
Normalized Time |
314.299 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.541667 |
Weighted Fraction of Eqa |
0.0655492 |
Time (sec) |
0.0424702 |
Normalized Time |
7.11978 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.142857 |
Time (sec) |
1.69171 |
Normalized Time |
1.46697 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.365775 |
Weighted Fraction of Eqa |
0.0514696 |
Time (sec) |
4.76914 |
Normalized Time |
32.3215 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0 |
Weighted Fraction of Eqa |
0 |
Time (sec) |
7.1365 |
Normalized Time |
458.002 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.454545 |
Weighted Fraction of Eqa |
0.0636364 |
Time (sec) |
0.0791451 |
Normalized Time |
2.49199 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.351567 |
Weighted Fraction of Eqa |
0.0363664 |
Time (sec) |
0.303221 |
Normalized Time |
10.627 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.29407 |
Weighted Fraction of Eqa |
0.0453142 |
Time (sec) |
0.469837 |
Normalized Time |
12.6118 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.781501 |
Weighted Fraction of Eqa |
0.075289 |
Time (sec) |
0.923911 |
Normalized Time |
17.0862 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0 |
Weighted Fraction of Eqa |
0 |
Time (sec) |
0.0532223 |
Normalized Time |
6.59218 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1 |
Time (sec) |
0.0481976 |
Normalized Time |
317.356 |
Fictitious Play¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Uniform |
0.968887 |
0.844597 |
Pure |
0.179452 |
0.0399854 |
Random |
0.177787 |
0.040904 |
Biased |
0.176497 |
0.0375596 |
Role biased |
0.172362 |
0.0357947 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Fictitious Play Long |
0.996304 |
0.0258347 |
Replicator Dynamics |
0.985459 |
8.97436 |
Multiplicative Weights Stoch |
0.970015 |
0.0722521 |
Multiplicative Weights Dist |
0.965673 |
0.75065 |
Regret Minimization |
0.945646 |
62.238 |
Multiplicative Weights Bandit |
0.94078 |
0.131139 |
Scarf 1 |
0.890577 |
9.42536 |
Scarf 5 |
0.890126 |
3.99544 |
Scarf 30 |
0.889834 |
1.86646 |
Regret Matching |
0.564136 |
0.111334 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.0555556 |
Time (sec) |
3.42748 |
Normalized Time |
23149.6 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.376006 |
Weighted Fraction of Eqa |
0.0486926 |
Time (sec) |
7.0972 |
Normalized Time |
433.264 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5375 |
Weighted Fraction of Eqa |
0.0612103 |
Time (sec) |
3.16318 |
Normalized Time |
603.759 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.345037 |
Weighted Fraction of Eqa |
0.0625309 |
Time (sec) |
4.30669 |
Normalized Time |
322.244 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.8 |
Weighted Fraction of Eqa |
0.0832143 |
Time (sec) |
3.1759 |
Normalized Time |
576.692 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1125 |
Time (sec) |
15.0365 |
Normalized Time |
665.315 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.575141 |
Weighted Fraction of Eqa |
0.0639502 |
Time (sec) |
10.5182 |
Normalized Time |
165.108 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0357143 |
Weighted Fraction of Eqa |
0.00478316 |
Time (sec) |
204.126 |
Normalized Time |
5596.11 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.576389 |
Weighted Fraction of Eqa |
0.0670621 |
Time (sec) |
15.187 |
Normalized Time |
531.051 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.453237 |
Weighted Fraction of Eqa |
0.0506665 |
Time (sec) |
18.3005 |
Normalized Time |
952.033 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.193276 |
Weighted Fraction of Eqa |
0.0357827 |
Time (sec) |
4.168 |
Normalized Time |
128.422 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.333333 |
Weighted Fraction of Eqa |
0.0333333 |
Time (sec) |
3.4285 |
Normalized Time |
22539.4 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.525 |
Weighted Fraction of Eqa |
0.0622159 |
Time (sec) |
0.289863 |
Normalized Time |
48.5931 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.142857 |
Time (sec) |
70.5892 |
Normalized Time |
61.2113 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.35141 |
Weighted Fraction of Eqa |
0.0470733 |
Time (sec) |
16.5122 |
Normalized Time |
111.907 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0588235 |
Weighted Fraction of Eqa |
0.0117647 |
Time (sec) |
5.68838 |
Normalized Time |
365.066 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.454545 |
Weighted Fraction of Eqa |
0.0636364 |
Time (sec) |
1.13567 |
Normalized Time |
35.7579 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.385215 |
Weighted Fraction of Eqa |
0.0425868 |
Time (sec) |
1.50801 |
Normalized Time |
52.8512 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.315737 |
Weighted Fraction of Eqa |
0.0726808 |
Time (sec) |
3.85757 |
Normalized Time |
103.548 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.774358 |
Weighted Fraction of Eqa |
0.0788605 |
Time (sec) |
4.29832 |
Normalized Time |
79.4902 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.380833 |
Weighted Fraction of Eqa |
0.0529392 |
Time (sec) |
3.59557 |
Normalized Time |
445.351 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1 |
Time (sec) |
3.43402 |
Normalized Time |
22611.2 |
Fictitious Play Long¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Uniform |
0.968629 |
0.84456 |
Pure |
0.178594 |
0.0403717 |
Biased |
0.176104 |
0.037672 |
Random |
0.173102 |
0.0400963 |
Role biased |
0.172011 |
0.0359403 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Fictitious Play |
0.997874 |
38.7077 |
Replicator Dynamics |
0.985459 |
347.377 |
Multiplicative Weights Stoch |
0.969578 |
2.79671 |
Multiplicative Weights Dist |
0.965337 |
29.0559 |
Regret Minimization |
0.944251 |
2409.09 |
Multiplicative Weights Bandit |
0.940954 |
5.07608 |
Scarf 1 |
0.89096 |
364.834 |
Scarf 5 |
0.890508 |
154.654 |
Scarf 30 |
0.890217 |
72.2465 |
Regret Matching |
0.564378 |
4.30947 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.0555556 |
Time (sec) |
168.961 |
Normalized Time |
1.14118e+06 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.376602 |
Weighted Fraction of Eqa |
0.0492878 |
Time (sec) |
173.48 |
Normalized Time |
10590.5 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5375 |
Weighted Fraction of Eqa |
0.0612103 |
Time (sec) |
73.9022 |
Normalized Time |
14105.8 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.323985 |
Weighted Fraction of Eqa |
0.0460835 |
Time (sec) |
134.481 |
Normalized Time |
10062.4 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.8 |
Weighted Fraction of Eqa |
0.0832143 |
Time (sec) |
87.0887 |
Normalized Time |
15813.9 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1125 |
Time (sec) |
152.084 |
Normalized Time |
6729.21 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.575141 |
Weighted Fraction of Eqa |
0.0639502 |
Time (sec) |
150.813 |
Normalized Time |
2367.37 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0357143 |
Weighted Fraction of Eqa |
0.00478316 |
Time (sec) |
313.31 |
Normalized Time |
8589.39 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.576389 |
Weighted Fraction of Eqa |
0.0670621 |
Time (sec) |
489.299 |
Normalized Time |
17109.5 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.453237 |
Weighted Fraction of Eqa |
0.0506665 |
Time (sec) |
639.256 |
Normalized Time |
33255.6 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.179163 |
Weighted Fraction of Eqa |
0.0236679 |
Time (sec) |
104.171 |
Normalized Time |
3209.66 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.333333 |
Weighted Fraction of Eqa |
0.0333333 |
Time (sec) |
199.545 |
Normalized Time |
1.31183e+06 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.525 |
Weighted Fraction of Eqa |
0.0622159 |
Time (sec) |
0.290636 |
Normalized Time |
48.7227 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.142857 |
Time (sec) |
1886.26 |
Normalized Time |
1635.67 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.34766 |
Weighted Fraction of Eqa |
0.0433233 |
Time (sec) |
266.383 |
Normalized Time |
1805.34 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0588235 |
Weighted Fraction of Eqa |
0.0117647 |
Time (sec) |
186.185 |
Normalized Time |
11948.9 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.454545 |
Weighted Fraction of Eqa |
0.0636364 |
Time (sec) |
25.2319 |
Normalized Time |
794.46 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.385215 |
Weighted Fraction of Eqa |
0.0425868 |
Time (sec) |
22.0073 |
Normalized Time |
771.287 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.291578 |
Weighted Fraction of Eqa |
0.0485217 |
Time (sec) |
102.072 |
Normalized Time |
2739.9 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.774358 |
Weighted Fraction of Eqa |
0.0788605 |
Time (sec) |
4.52731 |
Normalized Time |
83.7249 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.355833 |
Weighted Fraction of Eqa |
0.0493677 |
Time (sec) |
182.412 |
Normalized Time |
22593.7 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1 |
Time (sec) |
190.732 |
Normalized Time |
1.25587e+06 |
Multiplicative Weights Stoch¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Random |
0.159355 |
0.0463557 |
Biased |
0.157019 |
0.0422164 |
Role biased |
0.152887 |
0.0409085 |
Uniform |
0.123094 |
0.0294856 |
Pure |
0.0740799 |
0.0203774 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Multiplicative Weights Bandit |
0.9531 |
1.81502 |
Fictitious Play Long |
0.172797 |
0.357563 |
Fictitious Play |
0.17243 |
13.8404 |
Replicator Dynamics |
0.168424 |
124.209 |
Regret Matching |
0.159336 |
1.54091 |
Multiplicative Weights Dist |
0.146658 |
10.3893 |
Regret Minimization |
0.128161 |
861.401 |
Scarf 1 |
0.0885782 |
130.451 |
Scarf 5 |
0.0881266 |
55.2986 |
Scarf 30 |
0.087835 |
25.8327 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0 |
Weighted Fraction of Eqa |
0 |
Time (sec) |
85.1506 |
Normalized Time |
575117 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.335488 |
Weighted Fraction of Eqa |
0.0522358 |
Time (sec) |
197.324 |
Normalized Time |
12046.1 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.8125 |
Weighted Fraction of Eqa |
0.246419 |
Time (sec) |
0.739706 |
Normalized Time |
141.188 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.329394 |
Weighted Fraction of Eqa |
0.047297 |
Time (sec) |
197.321 |
Normalized Time |
14764.3 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.95 |
Weighted Fraction of Eqa |
0.214464 |
Time (sec) |
0.726422 |
Normalized Time |
131.906 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1125 |
Time (sec) |
2.76868 |
Normalized Time |
122.505 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.593593 |
Weighted Fraction of Eqa |
0.0710435 |
Time (sec) |
15.3826 |
Normalized Time |
241.466 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0892857 |
Weighted Fraction of Eqa |
0.0241284 |
Time (sec) |
73.1534 |
Normalized Time |
2005.5 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.576389 |
Weighted Fraction of Eqa |
0.0670621 |
Time (sec) |
4.79695 |
Normalized Time |
167.737 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.559266 |
Weighted Fraction of Eqa |
0.119028 |
Time (sec) |
24.1546 |
Normalized Time |
1256.58 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.221167 |
Weighted Fraction of Eqa |
0.0503129 |
Time (sec) |
214.367 |
Normalized Time |
6604.98 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.333333 |
Weighted Fraction of Eqa |
0.0333333 |
Time (sec) |
27.8162 |
Normalized Time |
182868 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.541667 |
Weighted Fraction of Eqa |
0.0655492 |
Time (sec) |
6.17225 |
Normalized Time |
1034.73 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.142857 |
Time (sec) |
10.0131 |
Normalized Time |
8.68284 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.37734 |
Weighted Fraction of Eqa |
0.0736149 |
Time (sec) |
21.801 |
Normalized Time |
147.75 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0588235 |
Weighted Fraction of Eqa |
0.0117647 |
Time (sec) |
91.2241 |
Normalized Time |
5854.53 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.363636 |
Weighted Fraction of Eqa |
0.0454545 |
Time (sec) |
14.5183 |
Normalized Time |
457.126 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.389067 |
Weighted Fraction of Eqa |
0.0434497 |
Time (sec) |
69.5512 |
Normalized Time |
2437.56 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.280575 |
Weighted Fraction of Eqa |
0.0560627 |
Time (sec) |
56.8294 |
Normalized Time |
1525.47 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.781501 |
Weighted Fraction of Eqa |
0.075289 |
Time (sec) |
11.4221 |
Normalized Time |
211.233 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.380833 |
Weighted Fraction of Eqa |
0.0529392 |
Time (sec) |
60.4415 |
Normalized Time |
7486.36 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1 |
Time (sec) |
86.3627 |
Normalized Time |
568652 |
Scarf 1¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Uniform |
0.99136 |
0.99136 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Scarf 5 |
0.997329 |
0.423903 |
Scarf 30 |
0.996585 |
0.198026 |
Replicator Dynamics |
0.891199 |
0.95215 |
Multiplicative Weights Bandit |
0.887203 |
0.0139134 |
Multiplicative Weights Stoch |
0.882973 |
0.00766571 |
Regret Minimization |
0.877238 |
6.60325 |
Fictitious Play |
0.875705 |
0.106097 |
Fictitious Play Long |
0.875311 |
0.00274097 |
Multiplicative Weights Dist |
0.875229 |
0.0796415 |
Regret Matching |
0.49575 |
0.0118121 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.0555556 |
Time (sec) |
0.000176191 |
Normalized Time |
1.19002 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.318822 |
Weighted Fraction of Eqa |
0.073497 |
Time (sec) |
3.64492 |
Normalized Time |
222.512 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5375 |
Weighted Fraction of Eqa |
0.0772222 |
Time (sec) |
0.00536712 |
Normalized Time |
1.02443 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.312472 |
Weighted Fraction of Eqa |
0.0581924 |
Time (sec) |
1.6169 |
Normalized Time |
120.983 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.8 |
Weighted Fraction of Eqa |
0.0954167 |
Time (sec) |
0.00701667 |
Normalized Time |
1.27411 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.05 |
Time (sec) |
1.5415 |
Normalized Time |
68.206 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.46131 |
Weighted Fraction of Eqa |
0.060965 |
Time (sec) |
6.22083 |
Normalized Time |
97.6506 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0178571 |
Weighted Fraction of Eqa |
0.00595238 |
Time (sec) |
0.0366912 |
Normalized Time |
1.00589 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.576389 |
Weighted Fraction of Eqa |
0.106637 |
Time (sec) |
0.189967 |
Normalized Time |
6.64268 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.453237 |
Weighted Fraction of Eqa |
0.0686254 |
Time (sec) |
1.63158 |
Normalized Time |
84.8785 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.153815 |
Weighted Fraction of Eqa |
0.0336958 |
Time (sec) |
7.43034 |
Normalized Time |
228.94 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.333333 |
Weighted Fraction of Eqa |
0.0333333 |
Time (sec) |
0.000173092 |
Normalized Time |
1.13793 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.525 |
Weighted Fraction of Eqa |
0.148674 |
Time (sec) |
0.00917681 |
Normalized Time |
1.53842 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0 |
Weighted Fraction of Eqa |
0 |
Time (sec) |
60.0021 |
Normalized Time |
52.0307 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.239765 |
Weighted Fraction of Eqa |
0.0375492 |
Time (sec) |
0.687618 |
Normalized Time |
4.66013 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0588235 |
Weighted Fraction of Eqa |
0.0196078 |
Time (sec) |
0.482798 |
Normalized Time |
30.9847 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0909091 |
Weighted Fraction of Eqa |
0.030303 |
Time (sec) |
0.0517638 |
Normalized Time |
1.62985 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.349647 |
Weighted Fraction of Eqa |
0.0554777 |
Time (sec) |
0.965104 |
Normalized Time |
33.8239 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.153897 |
Weighted Fraction of Eqa |
0.0311547 |
Time (sec) |
0.28036 |
Normalized Time |
7.52566 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.725548 |
Weighted Fraction of Eqa |
0.0711423 |
Time (sec) |
3.22001 |
Normalized Time |
59.5486 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.464167 |
Weighted Fraction of Eqa |
0.0838261 |
Time (sec) |
0.0186894 |
Normalized Time |
2.31489 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1 |
Time (sec) |
0.000180483 |
Normalized Time |
1.18838 |
Multiplicative Weights Bandit¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Random |
0.115048 |
0.0483717 |
Biased |
0.111203 |
0.038484 |
Role biased |
0.106899 |
0.035918 |
Uniform |
0.0676234 |
0.0180948 |
Pure |
0.0614487 |
0.0178271 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Multiplicative Weights Stoch |
0.949729 |
0.550958 |
Regret Matching |
0.148754 |
0.848975 |
Replicator Dynamics |
0.14488 |
68.434 |
Fictitious Play |
0.12992 |
7.6255 |
Fictitious Play Long |
0.128606 |
0.197002 |
Multiplicative Weights Dist |
0.112712 |
5.72408 |
Regret Minimization |
0.108446 |
474.596 |
Scarf 1 |
0.0709794 |
71.8731 |
Scarf 5 |
0.0705277 |
30.4673 |
Scarf 30 |
0.0702361 |
14.2327 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0 |
Weighted Fraction of Eqa |
0 |
Time (sec) |
37.7035 |
Normalized Time |
254653 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.433037 |
Weighted Fraction of Eqa |
0.141674 |
Time (sec) |
45.2721 |
Normalized Time |
2763.74 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.620833 |
Weighted Fraction of Eqa |
0.175863 |
Time (sec) |
5.04106 |
Normalized Time |
962.191 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.207575 |
Weighted Fraction of Eqa |
0.0814147 |
Time (sec) |
61.3869 |
Normalized Time |
4593.21 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.8 |
Weighted Fraction of Eqa |
0.0832143 |
Time (sec) |
2.10556 |
Normalized Time |
382.334 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1125 |
Time (sec) |
1.31277 |
Normalized Time |
58.0854 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.611212 |
Weighted Fraction of Eqa |
0.169466 |
Time (sec) |
16.1931 |
Normalized Time |
254.188 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.125 |
Weighted Fraction of Eqa |
0.0509141 |
Time (sec) |
30.0901 |
Normalized Time |
824.921 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.704167 |
Weighted Fraction of Eqa |
0.167062 |
Time (sec) |
7.22445 |
Normalized Time |
252.621 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.617381 |
Weighted Fraction of Eqa |
0.21696 |
Time (sec) |
20.0386 |
Normalized Time |
1042.45 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.406794 |
Weighted Fraction of Eqa |
0.246532 |
Time (sec) |
75.293 |
Normalized Time |
2319.89 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.333333 |
Weighted Fraction of Eqa |
0.333333 |
Time (sec) |
42.2664 |
Normalized Time |
277865 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.566667 |
Weighted Fraction of Eqa |
0.0717992 |
Time (sec) |
6.16585 |
Normalized Time |
1033.65 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.142857 |
Time (sec) |
3.99676 |
Normalized Time |
3.46578 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.434973 |
Weighted Fraction of Eqa |
0.152492 |
Time (sec) |
15.3441 |
Normalized Time |
103.99 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.411765 |
Weighted Fraction of Eqa |
0.411765 |
Time (sec) |
63.0848 |
Normalized Time |
4048.62 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.363636 |
Weighted Fraction of Eqa |
0.0454545 |
Time (sec) |
6.41273 |
Normalized Time |
201.913 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.725753 |
Weighted Fraction of Eqa |
0.354831 |
Time (sec) |
64.5869 |
Normalized Time |
2263.57 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.28421 |
Weighted Fraction of Eqa |
0.108513 |
Time (sec) |
41.0832 |
Normalized Time |
1102.79 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.781501 |
Weighted Fraction of Eqa |
0.075289 |
Time (sec) |
12.4333 |
Normalized Time |
229.932 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.26 |
Weighted Fraction of Eqa |
0.116534 |
Time (sec) |
41.2253 |
Normalized Time |
5106.21 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0 |
Weighted Fraction of Eqa |
0 |
Time (sec) |
42.6458 |
Normalized Time |
280800 |
Regret Minimization¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Biased |
0.913189 |
0.238037 |
Random |
0.909974 |
0.238086 |
Role biased |
0.905214 |
0.231136 |
Uniform |
0.89146 |
0.222137 |
Pure |
0.105826 |
0.0560536 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Replicator Dynamics |
0.964337 |
0.144194 |
Fictitious Play |
0.954297 |
0.0160674 |
Fictitious Play Long |
0.953767 |
0.000415095 |
Multiplicative Weights Stoch |
0.938871 |
0.0011609 |
Multiplicative Weights Dist |
0.937148 |
0.012061 |
Multiplicative Weights Bandit |
0.929212 |
0.00210706 |
Scarf 1 |
0.879939 |
0.151441 |
Scarf 5 |
0.879487 |
0.0641962 |
Scarf 30 |
0.879196 |
0.0299891 |
Regret Matching |
0.543883 |
0.00178884 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.0555556 |
Time (sec) |
0.0068413 |
Normalized Time |
46.2069 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.520615 |
Weighted Fraction of Eqa |
0.201114 |
Time (sec) |
0.0163808 |
Normalized Time |
1 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5375 |
Weighted Fraction of Eqa |
0.0612103 |
Time (sec) |
0.00654014 |
Normalized Time |
1.24832 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.276208 |
Weighted Fraction of Eqa |
0.0962257 |
Time (sec) |
0.0133647 |
Normalized Time |
1 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.8 |
Weighted Fraction of Eqa |
0.0832143 |
Time (sec) |
0.0055071 |
Normalized Time |
1 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.0625 |
Time (sec) |
0.0226006 |
Normalized Time |
1 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.658149 |
Weighted Fraction of Eqa |
0.205024 |
Time (sec) |
0.063705 |
Normalized Time |
1 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.678571 |
Weighted Fraction of Eqa |
0.662946 |
Time (sec) |
82.0281 |
Normalized Time |
2248.8 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.613889 |
Weighted Fraction of Eqa |
0.162895 |
Time (sec) |
0.028598 |
Normalized Time |
1 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.456218 |
Weighted Fraction of Eqa |
0.0836675 |
Time (sec) |
0.0192225 |
Normalized Time |
1 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.283948 |
Weighted Fraction of Eqa |
0.130335 |
Time (sec) |
0.0324554 |
Normalized Time |
1 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.333333 |
Weighted Fraction of Eqa |
0.0333333 |
Time (sec) |
0.00646641 |
Normalized Time |
42.5111 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.558333 |
Weighted Fraction of Eqa |
0.0822159 |
Time (sec) |
0.0059651 |
Normalized Time |
1 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0 |
Weighted Fraction of Eqa |
0 |
Time (sec) |
1.15321 |
Normalized Time |
1 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.674401 |
Weighted Fraction of Eqa |
0.371161 |
Time (sec) |
0.147553 |
Normalized Time |
1 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.294118 |
Weighted Fraction of Eqa |
0.294118 |
Time (sec) |
0.0155818 |
Normalized Time |
1 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.909091 |
Weighted Fraction of Eqa |
0.518182 |
Time (sec) |
0.0317599 |
Normalized Time |
1 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.502937 |
Weighted Fraction of Eqa |
0.162104 |
Time (sec) |
0.0285332 |
Normalized Time |
1 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.64973 |
Weighted Fraction of Eqa |
0.435108 |
Time (sec) |
0.0372538 |
Normalized Time |
1 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.949546 |
Weighted Fraction of Eqa |
0.24158 |
Time (sec) |
0.0540736 |
Normalized Time |
1 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.4975 |
Weighted Fraction of Eqa |
0.100479 |
Time (sec) |
0.00807355 |
Normalized Time |
1 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1 |
Time (sec) |
0.00644888 |
Normalized Time |
42.4624 |
Scarf 5¶
Initial Profile Rates¶
Starting Type |
Fraction of Eqa |
Weighted Fraction |
|---|---|---|
Uniform |
0.994031 |
0.994031 |
Compared to Other Methods¶
Method |
Fraction of Eqa |
Time Ratio |
|---|---|---|
Scarf 1 |
1 |
2.35903 |
Scarf 30 |
0.999257 |
0.467148 |
Replicator Dynamics |
0.89197 |
2.24615 |
Multiplicative Weights Bandit |
0.88933 |
0.0328221 |
Multiplicative Weights Stoch |
0.8851 |
0.0180836 |
Regret Minimization |
0.879302 |
15.5772 |
Fictitious Play |
0.877925 |
0.250285 |
Fictitious Play Long |
0.877531 |
0.00646603 |
Multiplicative Weights Dist |
0.875799 |
0.187877 |
Regret Matching |
0.49797 |
0.0278652 |
By Game Type¶
Shapley hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.0555556 |
Time (sec) |
0.000164747 |
Normalized Time |
1.11272 |
Rbf¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.331322 |
Weighted Fraction of Eqa |
0.074747 |
Time (sec) |
10.8419 |
Normalized Time |
661.87 |
Chicken¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5375 |
Weighted Fraction of Eqa |
0.0772222 |
Time (sec) |
0.00525931 |
Normalized Time |
1.00385 |
Zero sum¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.312472 |
Weighted Fraction of Eqa |
0.0581924 |
Time (sec) |
1.6158 |
Normalized Time |
120.9 |
Mix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.8 |
Weighted Fraction of Eqa |
0.0954167 |
Time (sec) |
0.00688252 |
Normalized Time |
1.24975 |
Sineagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.5 |
Weighted Fraction of Eqa |
0.05 |
Time (sec) |
1.53476 |
Normalized Time |
67.9077 |
Normagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.464881 |
Weighted Fraction of Eqa |
0.0627507 |
Time (sec) |
26.1881 |
Normalized Time |
411.084 |
Polyagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0178571 |
Weighted Fraction of Eqa |
0.00595238 |
Time (sec) |
0.0364764 |
Normalized Time |
1 |
Local effect¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.576389 |
Weighted Fraction of Eqa |
0.106637 |
Time (sec) |
0.189879 |
Normalized Time |
6.63957 |
Congestion¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.453237 |
Weighted Fraction of Eqa |
0.0686254 |
Time (sec) |
1.63183 |
Normalized Time |
84.8917 |
Covariant¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.153815 |
Weighted Fraction of Eqa |
0.0336958 |
Time (sec) |
19.4318 |
Normalized Time |
598.722 |
Shapley easy¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.333333 |
Weighted Fraction of Eqa |
0.0333333 |
Time (sec) |
0.000152349 |
Normalized Time |
1.00157 |
Prisoners¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.525 |
Weighted Fraction of Eqa |
0.148674 |
Time (sec) |
0.00904394 |
Normalized Time |
1.51614 |
Normagg large¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0 |
Weighted Fraction of Eqa |
0 |
Time (sec) |
300.002 |
Normalized Time |
260.146 |
Sineagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.239765 |
Weighted Fraction of Eqa |
0.0375492 |
Time (sec) |
0.687357 |
Normalized Time |
4.65837 |
Hard¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0588235 |
Weighted Fraction of Eqa |
0.0196078 |
Time (sec) |
0.501494 |
Normalized Time |
32.1846 |
Gambit¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.0909091 |
Weighted Fraction of Eqa |
0.030303 |
Time (sec) |
0.0513351 |
Normalized Time |
1.61635 |
Polymatrix¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.349647 |
Weighted Fraction of Eqa |
0.0554777 |
Time (sec) |
0.965855 |
Normalized Time |
33.8502 |
Random¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.153897 |
Weighted Fraction of Eqa |
0.0311547 |
Time (sec) |
0.2803 |
Normalized Time |
7.52407 |
Polyagg small¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.732691 |
Weighted Fraction of Eqa |
0.0718566 |
Time (sec) |
6.71802 |
Normalized Time |
124.238 |
Roshambo¶
Metric |
Value |
|---|---|
Fraction of Eqa |
0.464167 |
Weighted Fraction of Eqa |
0.0838261 |
Time (sec) |
0.0185103 |
Normalized Time |
2.29271 |
Shapley normal¶
Metric |
Value |
|---|---|
Fraction of Eqa |
1 |
Weighted Fraction of Eqa |
0.1 |
Time (sec) |
0.000156879 |
Normalized Time |
1.03297 |