README.md

GameTracer.jl

A Julia wrapper for gametracer, providing IPA and GNM Nash equilibrium solvers for GameTheory.jl normal-form games.

Example usage

Consider the following 2x2x2 game with 9 Nash equilibria from McKelvey and McLennan (1996):

using GameTheory, GameTracer, Random
g = NormalFormGame((2, 2, 2))
g[1, 1, 1] = 9, 8, 12
g[2, 2, 1] = 9, 8, 2
g[1, 2, 2] = 3, 4, 6
g[2, 1, 2] = 3, 4, 4
printin(g)

2×2×2 NormalFormGame{3, Float64}:
[:, :, 1] =
 [9.0, 8.0, 12.0]  [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]   [9.0, 8.0, 2.0]

[:, :, 2] =
 [0.0, 0.0, 0.0]  [3.0, 4.0, 6.0]
 [3.0, 4.0, 4.0]  [0.0, 0.0, 0.0]

ipa_solve computes one mixed-action Nash equilibrium with the the iterated polymatrix approximation (IPA) algorithm (Govindan and Wilson, 2004):

ray = [0.11, 0.37, 0.73, 0.19, 0.59, 0.83];
res = ipa_solve(g; ray=ray);

GameTracer.IPAResult{3}(([1.0, 0.0], [1.0, 0.0], [1.0, 0.0]), 1)

gnm_solve computes mixed-action Nash equilibria with the the global Newton method (GNM) algorithm (Govindan and Wilson, 2003):

res = gnm_solve(g, ray=ray)

GameTracer.GNMResult{3}([([0.0, 1.0], [1.0, 0.0], [0.0, 1.0]), 
    ([0.2500000000000622, 0.7499999999999374], [1.0, 0.0], [0.25000000000008304,
     0.7499999999999165]), ([1.0, 0.0], [1.0, 0.0], [1.0, 0.0])], 3)

License

This package is licensed under the GNU General Public License, version 3 or (at your option) any later version. See LICENSE.

It wraps gametracer, originally released under the GNU General Public License, version 2 or (at your option) any later version.