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       nash - find nash equilibria of two person noncooperative games


       setupnash input game1.ine game2.ine

       setupnash2 input game1.ine game2.ine

       nash game1.ine game2.ine

       2nash game1.ine game2.ine


       All Nash equilibria (NE) for a two person noncooperative game are
       computed using two interleaved reverse search vertex enumeration steps.
       The input for the problem are two m by n matrices A,B of integers or
       rationals. The first player is the row player, the second is the column
       player. If row i and column j are played, player 1 receives Ai,j and
       player 2 receives Bi,j. If you have two or more cpus available run
       2nash instead of nash as the order of the input games is immaterial. It
       runs in parallel with the games in each order. (If you use nash, the
       program usually runs faster if m is <= n , see below.) The easiest way
       to use the program nash or 2nash is to first run setupnash or (
       setupnash2 see below ) on a file containing:

             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


             %  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 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

             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
       lrslib user manual[1]


       For information on H-representation file formats, see the man page for
       lrslib or the lrslib user manual[2]


        1. lrslib user manual

        2. lrslib user manual