For the new game solving software GTE, please follow this link

Game Theory Explorer (GTE)

to documentation and program (top-right link on that page). Below is the previous bimatrix game solver.

Solve a Bimatrix Game

 back to homepage example games website history

Please cite as follows:

D. Avis, G. Rosenberg, R. Savani , and B. von Stengel (2010), Enumeration of Nash Equilibria for Two-Player Games. Economic Theory 42, 9-37. Online solver available at http://banach.lse.ac.uk.

Matrix sizes are now capped at 15 x 15.
If you need help to solve larger games feel free to contact me at rahul dot savani at liverpool.ac.uk

Enter dimension of game e.g. 2 3 for 2x3 matrices (max 15x15)

Enter payoff matrix A for player 1, e.g.

1 0 0
0 1 0
0 0 1

Enter type of game:

General m x n game (A,B)

Zerosum m x n game (A,-A)

Symmetric m x m game (A,AT)

For zerosum and symmetric games,
only enter payoff matrix A for player 1.

For symmetric games, m = n.

Enter payoff matrix B for player 2 (not required for zerosum or symmetric games).

This solver uses the excellent lrs - David Avis's implementation of Avis and Fukuda's reverse search algorithm for polyhedral vertex enumeration.

In particular, this uses an interleaved reverse search on two polyhedra, which was introduced in version 4.2 of lrs (see here).

For a description of the method see

D. Avis, G. Rosenberg, R. Savani , and B. von Stengel (2010), Enumeration of Nash Equilibria for Two-Player Games. Economic Theory 42, 9-37.

This page was created and is maintained by Rahul Savani