Profile

NASH

NASH

NAME

nash - find nash equilibria of two person noncooperative games

SYNOPSIS

setupnash input game1.ine game2.ine
setupnash2 input game1.ine game2.ine
nash game1.ine game2.ine
2nash game1.ine game2.ine

DESCRIPTION

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
  

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]

SEE ALSO

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

NOTES

1.
lrslib user manual
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Nash%20Equilibria
2.
lrslib user manual
http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#File%20Formats

H-representation
Latest Tech News
Your Notes

Sign in/Sign up

Signing in to our system allows you to post your contributions and vote on the contributions of others. It will also allow you to get extra perts like having your favorites in the cloud and having your persistent personal notes wherever you go. More will be added as we scale up our services.

By signing in to our system, you agree our Member Terms and Conditions


Sign-in with one of the following services

Almost finished!

Please select a screen name for NET SOUP.



 Please send me news and special offers from NET SOUP.

 I have read and accept the Terms of Use.

COMPLIMENTARY EXAMPLES

We have no example yet for this entry


Your Name
Now

Community Contributions and Discussions

Modify your search

View Documentation

Jobs from Indeed