What software libraries exist for finding the optimal solution in game theory?

Question

Python

Hello.
In the future, I will have a payoff matrix from game theory. I will need to find the optimal solution for this matrix.
I used to search for the best solution using the Solve Finder add-in in Microsoft Excel. But I suspect that there may be special functions in Python or R programming libraries that allow you to find the optimal solution faster than Excel does. It's just that this time I will have a large matrix, and the time it takes to calculate it can be large.
What are the functions in software libraries (for programming languages ​​Python or R) designed to find the optimal solution in game theory?

Answer 1

Solver:
GLPK (GNU Linear Programming Kit)
COIN
CPLEX
GUROBI
Revised Simplex Method
Interior Point Methods
Interior-Point-Legacy Linear Programming
Active-Set linprog Algorithm
- SciPy (tutorial video )
- PyOMO
- PuLP (tutorial video )
Source: video .

Answer 2

I searched but didn't find it. Not sure if there is an efficient algorithm for this at all. The proof of the existence of the Nash equilibrium is based on the fixed point theorem, the proof of which is not constructive. In the case of a horse table, you can solve a linear programming problem with parameters, and then make the optimization according to these parameters something like gradient descent, but I'm afraid this will slow down a lot.