Solves random zero-sum matrix games using Fictitious play, Counterfactual Regret Minimization and CFR+.

#####Building

make

#####Parameters

• -h show help
• -a <id> algorithm
  • -a 0 Fictitious play
  • -a 1 CFR
  • -a 2 CFR+ (default)
• -s <n> matrix dimensions (n-by-n) (default 1000)
• -distribution <id> random number distribution
  • -distribution 0 uniform [-1, 1] (default)
  • -distribution 1 normal (sigma 0.5)
  • -distribution 2 cauchy (gamma 0.02)
• -e <epsilon> epsilon (default 0.0001)
• -n <n> number of times to run
• -all run all algorithms (used together with -n)
• -dump print payoffs and strategies when done
• -delay <n> CFR+ averaging delay in number of iterations (default 0)
• -w <id> CFR+ weighting mode
  • -w 0 constant (like in CFR)
  • -w 1 linear (default)
  • -w 2 quadratic (often faster than linear but can get stuck in small games)

#####Examples

./CFRPlusMatrix -a 0 -s 10 -e 0.001

Use algorithm 0 (Fictitious play) to find an epsilon-equilibrium with epsilon of 0.001 in a 10x10 game.

./CFRPlusMatrix -a 1 -s 100 -e 0.0001

Use algorithm 1 (CFR) to find an epsilon-equilibrium with epsilon of 0.0001 in a 100x100 game.

./CFRPlusMatrix -a 2 -s 1000 -e 0.00001

Use algorithm 2 (CFR+) to find an epsilon-equilibrium with epsilon of 0.00001 in a 1000x1000 game.

./CFRPlusMatrix -s 10 -e 0.0001 -n 50 -all

Compare algorithms. It will output something like this:

Matrix size: 10x10
Epsilon: 0.000100
N: 50
Fictitious play  | min 9500 | max 1690341 | avg 597456.7
CFR              | min 3483 | max 49694  | avg 17850.9
CFR+             | min 127  | max 3657   | avg 968.6

See http://jeskola.net/cfr/ for more stuff.