NAME
Game::Theory::TwoPersonMatrix - Analyze a 2 person matrix game
VERSION
version 0.1502
SYNOPSIS
use Game::Theory::TwoPersonMatrix;
$g = Game::Theory::TwoPersonMatrix->new(
1 => { 1 => 0.2, 2 => 0.3, 3 => 0.5 },
2 => { 1 => 0.1, 2 => 0.7, 3 => 0.2 },
payoff => [ [-5, 4, 6],
[ 3,-2, 2],
[ 2,-3, 1] ]
};
$g->row_reduce();
$g->col_reduce();
$p = $g->saddlepoint();
$o = $g->oddments();
$e = $g->expected_payoff();
$c = $g->counter_strategy($player);
$g = Game::Theory::TwoPersonMatrix->new(
1 => { 1 => 0.1, 2 => 0.2, 3 => 0.7 },
2 => { 1 => 0.1, 2 => 0.2, 3 => 0.3, 4 => 0.4 },
payoff1 => [ [5,3,8,2],[6,5,7,1],[7,4,6,0] ],
payoff2 => [ [2,0,1,3],[3,4,4,1],[5,6,8,2] ],
);
$t = $g->mm_tally();
$m = $g->pareto_optimal();
$n = $g->nash();
$e = $g->expected_payoff();DESCRIPTION
A Game::Theory::TwoPersonMatrix analyzes a two person matrix game of player names, strategies and utilities ("payoffs").
The players must have the same number of strategies, and each strategy must have the same size utility vectors as all the others.
Players 1 and 2 are the "row" and "column" players, respectively. This is due to the tabular format of a matrix game:
Player 2
--------
Strategy 0.5 0.5
Player | 0.5 1 -1 < Payoff
1 | 0.5 -1 1 <A non-zero sum game is represented by two payoff profiles, as above in the SYNOPSIS.
METHODS
new()
$g = Game::Theory::TwoPersonMatrix->new(
1 => { 1 => '0.5', 2 => '0.5' },
2 => { 1 => '0.5', 2 => '0.5' },
payoff => [ [1,0],
[0,1] ]
);
$g = Game::Theory::TwoPersonMatrix->new(
payoff1 => [ [2,3],[2,1] ],
payoff2 => [ [3,5],[2,3] ],
);Create a new Game::Theory::TwoPersonMatrix object.
expected_payoff()
$e = $g->expected_payoff();Return the expected payoff value of the game.
s_expected_payoff()
$g = Game::Theory::TwoPersonMatrix->new(
1 => { 1 => '(1 - p)', 2 => 'p' },
2 => { 1 => 1, 2 => 0 },
payoff => [ ['a','b'], ['c','d'] ]
);
$s = $g->s_expected_payoff();Return the expected payoff expression for a non-numeric game.
Using real payoff values, we solve the resulting expression for p in the eg/ examples.
counter_strategy()
$c = $g->counter_strategy($player);Return the counter-strategies for a given player.
saddlepoint()
$p = $g->saddlepoint;If the game is strictly determined, the saddlepoint is returned. Otherwise undef is returned.
oddments()
$o = $g->oddments();Return each player's "oddments" for a 2x2 game.
row_reduce()
$g->row_reduce();Reduce a game by identifying and eliminating strictly dominated rows and their associated player strategies.
col_reduce()
$g->col_reduce();Reduce a game by identifying and eliminating strictly dominated columns and their associated opponent strategies.
mm_tally()
$t = $g->mm_tally();For zero-sum games, return the maximum of row minimums and the minimum of column maximums. For non-zero-sum games, return the maximum of row and column minimums.
pareto_optimal()
$m = $g->pareto_optimal();Return the Pareto optimal outcomes.
nash()
$n = $g->nash();Identify the Nash equilibria.
Given payoff pair (a, b) a is maximum for its column and b is maximum for its row.
SEE ALSO
The eg/ and t/ scripts in this distribution.
"A Gentle Introduction to Game Theory"
http://www.amazon.com/Gentle-Introduction-Theory-Mathematical-World/dp/0821813390
http://books.google.com/books?id=8doVBAAAQBAJ
AUTHOR
Gene Boggs <gene@cpan.org>
COPYRIGHT AND LICENSE
This software is copyright (c) 2014 by Gene Boggs.
This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.