# nash(1) [debian man page]

```NASH(1) 							   lrslib 0.42b 							   NASH(1)

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 lrslib user manual[1]

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

July 2009							    03/30/2011								   NASH(1)```

## Check Out this Related Man Page

```CRIBBAGE(6)							 BSD Games Manual						       CRIBBAGE(6)

NAME
cribbage -- the card game cribbage

SYNOPSIS
cribbage [-eqr]

DESCRIPTION
cribbage plays the card game cribbage, with the program playing one hand and the user the other.  The program will initially ask the user if
the rules of the game are needed - if so, it will print out the appropriate section from According to Hoyle with more(1).

cribbage options include:

-e      When the player makes a mistake scoring his hand or crib, provide an explanation of the correct score.  (This is especially useful
for beginning players.)

-q      Print a shorter form of all messages - this is only recommended for users who have played the game without specifying this option.

-r      Instead of asking the player to cut the deck, the program will randomly cut the deck.

cribbage first asks the player whether he wishes to play a short game ( ``once around'', to 61) or a long game ( ``twice around'', to 121).
A response of 's' will result in a short game, any other response will play a long game.

At the start of the first game, the program asks the player to cut the deck to determine who gets the first crib.	The user should respond
with a number between 0 and 51, indicating how many cards down the deck is to be cut.  The player who cuts the lower ranked card gets the
first crib.  If more than one game is played, the loser of the previous game gets the first crib in the current game.

For each hand, the program first prints the player's hand, whose crib it is, and then asks the player to discard two cards into the crib.
The cards are prompted for one per line, and are typed as explained below.

After discarding, the program cuts the deck (if it is the player's crib) or asks the player to cut the deck (if it's its crib); in the latter
case, the appropriate response is a number from 0 to 39 indicating how far down the remaining 40 cards are to be cut.

After cutting the deck, play starts with the non-dealer (the person who doesn't have the crib) leading the first card.  Play continues, as
per cribbage, until all cards are exhausted.  The program keeps track of the scoring of all points and the total of the cards on the table.

After play, the hands are scored.	The program requests the player to score his hand (and the crib, if it is his) by printing out the appro-
priate cards (and the cut card enclosed in brackets).  Play continues until one player reaches the game limit (61 or 121).

A carriage return when a numeric input is expected is equivalent to typing the lowest legal value; when cutting the deck this is equivalent
to choosing the top card.

Cards are specified as rank followed by suit.  The ranks may be specified as one of: 'a', '2', '3', '4', '5', '6', '7', '8', '9', 't', 'j',
'q', and 'k', or alternatively, one of: 'ace', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine', 'ten', 'jack', 'queen', and
'king'.  Suits may be specified as: 's', 'h', 'd', and 'c', or alternatively as: 'spades', 'hearts', 'diamonds', and 'clubs'.  A card may be
specified as: ``<rank>   <suit>'', or: ``<rank> of <suit>''.  If the single letter rank and suit designations are used, the space separating
the suit and rank may be left out.  Also, if only one card of the desired rank is playable, typing the rank is sufficient.  For example, if
your hand was ``2H, 4D, 5C, 6H, JC, and KD'' and it was desired to discard the king of diamonds, any of the following could be typed: 'k',
'king', 'kd', 'k d', 'k of d', 'king d', 'king of d', 'k diamonds', 'k of diamonds', 'king diamonds', 'king of diamonds'.

FILES
/usr/games/cribbage
/var/games/criblog
/usr/share/games/cribbage.instr

AUTHORS
Earl T. Cohen wrote the logic.  Ken Arnold added the screen oriented interface.

BSD								   May 31, 1993 							       BSD```
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