m n matrix A matrix B
eg. the file game is for a game with m=3 n=2:
3 2 0 6 2 5 3 3 1 0 0 2 4 3
% setupnash game game1 game2
produces two H-representations, game1 and game2, one for each player. To get the equilibria, run
% nash game1 game2
or
% 2nash game1 game2
Each row beginning 1 is a strategy for the row player yielding a NE with each row beginning 2 listed immediately above it.The payoff for player 2 is the last number on the line beginning 1, and vice versa. Eg: first two lines of output: player 1 uses row probabilities 2/3 2/3 0 resulting in a payoff of 2/3 to player 2.Player 2 uses column probabilities 1/3 2/3 yielding a payoff of 4 to player 1. If both matrices are nonnegative and have no zero columns, you may instead use setupnash2:
% setupnash2 game game1 game2
Now the polyhedra produced are polytopes. The output of nash in this case is a list of unscaled probability vectors x and y. To normalize, divide each vector by v = 1^T x and u=1^T y.u and v are the payoffs to players 1 and 2 respectively. In this case, lower bounds on the payoff functions to either or both players may be included. To give a lower bound of r on the payoff for player 1 add the options to file game2 (yes that is correct!)To give a lower bound of r on the payoff for player 2 add the options to file game1
minimize 0 1 1 ... 1 (n entries to begiven) bound 1/r; ( note: reciprocal of r)
If you do not wish to use the 2-cpu program 2nash, please read the following. If m is greater than n then nash usually runs faster by transposing the players. This is achieved by running:
% nash game2 game1
If you wish to construct the game1 and game2 files by hand, see the m[blue]lrslib user manualm[][1]
For information on H-representation file formats, see the man page for lrslib or the m[blue]lrslib user manualm[][2]
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