README-work.md

Math::GameTheory

The package provides descriptions and data of different games amenable for Game Theory experiments and studies.

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Installation

From Zef ecosystem:

zef install Math::GameTheory

From GitHub:

zef install https://github.com/antononcube/Raku-Math-GameTheory

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Game Theory data

All games known by the package "Math::GameTheory":

use Math::GameTheory;

say "Total number of known games: {game-theory-data().elems}";
say game-theory-data();

Games and their classes:

my @dsGames = game-theory-data(Whatever, property => "Classes").map({ $_.key X $_.value.Array }).flat(1).map({ <name property> Z=> $_  })».Hash;
@dsGames.elems

Here is a summary:

use Data::Summarizers;

sink records-summary(@dsGames)

Here is a "taxonomy tree" like breakdown:

use ML::TriesWithFrequencies;

my %cat = <2Player 3Player NPlayer MatrixGame TreeGame Symmetric> Z=> (^7);

game-theory-data(Whatever, property => "Classes").values
==> { .map({ %cat.keys (&) $_ }) }()
==> { $_.map({ $_ ?? $_.keys !! 'Other' })».sort({ %cat{$_} })».List }()
==> trie-create()
==> trie-form()

Here is a property vs. game cross tabulation:

use Data::Reshapers;
use Data::Translators;

cross-tabulate(@dsGames, 'property', 'name')
==> { $_.map({ %( property => $_.key, |$_.value) }).sort(*<property>).List }()
==> to-dataset()
==> to-html(field-names => ['property', |game-theory-data()], :vertical-header-names)
==> { .subst('1', '⏺', :g) }()
==> { .subst(/ ['<th' .+? '>' property '</th>'] /,  '<th>property</th>') }()

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Two player games

Get the game "Chicken" (provided by the package):

my $obj = game-theory-data('Chicken')

Here is a description of the game:

$obj.description

Here is game's table:

$obj.html

Here is a gray-scale version of the dataset can be obtained with $obj.html(theme => 'gray-scale').

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Three player games

Get the game "3Coordination" (provided by the package):

my $obj = game-theory-data('3Coordination')

$obj.description

Here is game's table:

$obj.html

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Zero sum games

Represent a Rock Paper Scissors game as a directed graph:

use Graph;
my $g = Graph.new(edges => [Rock => "Scissors", Scissors => "Paper", Paper => "Rock"]):d;
#$g.dot(engine => 'neato', :2size, vertex-font-size => 8):svg

Create a Rock Paper Scissors game:

use Data::Reshapers;

my @payoff-array = ($g.adjacency-matrix <<->> transpose($g.adjacency-matrix)).deepmap(-> Int:D $p { [$p, -$p] });
my $game = Math::GameTheory::MatrixGame.new(:@payoff-array, game-action-labels => ($g.vertex-list xx 2))

Here is game's table:

$game.html(theme => 'default')

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TODO

• TODO Implementation
  • TODO Retrieval and creation of games
    • DONE Games data JSON file and corresponding retrieval (multi-)sub
    • TODO Retrieving games using regexes
    • TODO Using properties with any case
  • TODO Matrix games
    • DONE MatrixGame class
    • DONE HTML format of matrix game dataset
    • DONE Wolfram Language (WL) representation
    • TODO Payoff functions
      • TODO Expectation
      • TODO MarginalDistribution
      • TODO MultivariateDistribution
      • TODO Variance
      • TODO Simulation
    • TODO Simpler zero-sum games initialization
  • TODO Tree games
    • TODO TreeGame class
    • TODO Creation using WL's tree game input format
    • TODO Special tree-game plots
• TODO Documentation
  • DONE Complete README
  • TODO Basic usage notebook
  • TODO Blog post
  • TODO Video demo