Let\'s Play a Game of Evolution We play on a rectangular M × N gaine board, wher

Question

Let's Play a Game of Evolution We play on a rectangular M × N gaine board, where each entry represents a player. Each player is either loyal (denoted L), or a traitor (denoted T). Each square plays the prisoners dilemma with its 8 neighbors and itself, and receives as it's score the sum of the years of freedom gained in its 9 games. Prisoners dilema game ·Lvs Leach receives a score of 1. L vs T, player L receive a score of 0 and player T receives a score of b. . T vs T, each receives a score of 0. Since, in our game, each square plays 9 games, the score in our game is the sum of the 9 scores. So for example, if b 2, then the gameboard 2 4 4 TLL has as it's scores 6 5 4 3 5 4 Since this is a game of evolution, the players at each square evolve. Each player sees whether its neighbor fared better than itself. We will assume that, as rational players, each one assumes the strategy of its most successful neighbor. Thus, the next evolution of that 3 x 3 grid would be TTL TTL TTL We will then illustrate the state and movement of the board as follows: . Illustrate each square as blue if L remains L . Illustrate each square as red if T remains T . Illustrate each square as yellow if L becomes T. Illustrate each square as green if T becomes L. We will assume that players on the edge have as it's neighbors the entries in the corresponding entries of the opposite side, as if the board was wrapped into a cylinder in the north-south direction and the east-west direction. Opposite corners are neighbors of opposite corners.

Explanation / Answer

function playerstruct = IPDshell(varargin)
%
% playerstruct = IPDshell
% playerstruct = IPDshell('nodisp')
%
% GENERAL:
% IPDshell (iterated prisoner dilemma) runs the prisoner's dilemma game
% between two personalities at a time, 20 times. Each personality is a
% MATLAB function that must take the form:
%
% function response = personalityname(n,p)
%
% The shell passes the personality function the current iteration, n,
% (i.e. the number of times that the two personalities have been playing
% the game +1) and the amount of points scored by their opponent on the
% previous iteration, p. On the first iteration, p = -1.
% (From the number of points scored, it can be inferred both what your
% personality did, and what the opponent personality did.)
%
% The personality is required to respond when called with either of two
% strings:
% 'cooperate' or 'defect'
% The string must be the only output of the function.
%
% Note: The more personalities that are used, the better the gauge of the
% actual validity of all the personalities. Some personalities are
% highly exploitable, so small sample sizes can skew results.
%
% SETUP:
% (1) Place the file IPDshell.m into an empty directory.
% (2) Each player places a folder in this directory, and the name of this
% folder will be the player's name.
% (3) In each player's folder they should place as many personality
% functions as they wish, but only personality functions may be
% placed in the player's folder. (see INSTRUCTIONS on how to create
% an appropriate personality function)
% (4) Once SETUP(1-3) is complete, run IPDshell in the command window.
%
% >> IPDshell;
%
% (IPDshell will return the structure containing all the player data
% after the matches are completed.)
%
% Also, displayed to the command window will be all of the matches
% played and the scoring after each round. To supress this display,
% as it may be cumbersome when playing large competitions, use the
% command:
%
% >> IPDshell('nodisp');
%
% RULES:
% Each personality tries to score the most number of points against each
% opponent personality during each match. P1 (a personality that is in
% the match) will say 'cooperate' or 'defect', as will P2. Points are
% then awarded to P1 and P2 based on the combination of their answers.
% Below is the chart the scoring is based on:
%
% P2
% cooperate defect
%
% cooperate 3 - 3 0 - 5
% P1
% defect 5 - 0 1 - 1
%
%
% The scoring rubric gives points according to (P1 - P2). The decision to
% cooperate or defect will be made by both parties 20 times in
% succession. Each time a decision must be made, the personality is
% supplied with two pieces of information that may be used to make their
% decision, or that may be ignored. (1)The number of times they have
% played the game with this particular opponent, and (2)The number of
% points their opponent scored the last time they played.
%
% The maximum score in a competition for any personality is 100 points,
% earning 5 points during each of the 20 decisions by defecting when the
% opponent cooperates.
%
% Games are played 20 times between two personalities, which constitutes
% a match. Matches are played between every personality available,
% however, personalities made by the same player do not play matches
% against each other to avoid collusion.
%
% Deciding the competition winner:
% The personality that scores the most average points per match is the
% most successful, and so the player who employs that personality is
% declared the winner.
%
% v1.02
% %%% ZCD 2006 %%%

% Build player structure
[playerstruct] = BuildPlayerStruct;
% Get the schedules of personalities that will be playing against each
% other in an array, schedule.
schedule = BuildMatchSchedule(playerstruct);
schedsize = size(schedule); % BUGFIX: Must use # of rows in case of 1 match

% ============= Begin the competition: ==============
for mn=1:schedsize(1) % number of matches (mn = match number)
  
% reset scoring matrix
ScoreMat = [-1 -1];
  
% Pick out the appropriate match from schedule.
match = schedule(mn,:);
  
% Begin particular match
for n=1:20 % 20 rounds
  
% Evaluate each player personality. Do not use the last 2 characters of
% the personality name, '.m' This is where the personality makes
% the decision to cooperare or defect, and their function is
% called.
% ----
response{1} = eval( [playerstruct(match(1)).personality(1:end-2),'(n,ScoreMat(end,2))'] );
response{2} = eval( [playerstruct(match(2)).personality(1:end-2),'(n,ScoreMat(end,1))'] );
% ----

% score the outcomes:
if isequal('cooperate',response{1}) & isequal('cooperate',response{2})
ScoreMat(n,1)=3; ScoreMat(n,2)=3;
elseif isequal('defect',response{1}) & isequal('cooperate',response{2})
ScoreMat(n,1)=5; ScoreMat(n,2)=0;
elseif isequal('cooperate',response{1}) & isequal('defect',response{2})
ScoreMat(n,1)=0; ScoreMat(n,2)=5;
elseif isequal('defect',response{1}) & isequal('defect',response{2})
ScoreMat(n,1)=1; ScoreMat(n,2)=1;
else
error(' ======= There is an uncooperative personality. ======= ');
end

end % end round
  
% keep score for each personality, and track number of matches played
playerstruct(match(1)).score = sum(ScoreMat(:,1)) + playerstruct(match(1)).score;
playerstruct(match(1)).nummatches = playerstruct(match(1)).nummatches + 1;
playerstruct(match(2)).score = sum(ScoreMat(:,2)) + playerstruct(match(2)).score;
playerstruct(match(2)).nummatches = playerstruct(match(2)).nummatches + 1;
  
% Allow user to turn off display
if isempty(varargin)
GraphicDisplay(playerstruct,ScoreMat,match);
elseif isequal(varargin{1},'nodisp')
% Supress match scores display to command window.
else
error('=== Invalid input to IPDshell ===');
end
  
end % end match
% ============= END COMPETITION ===============

% Display final results.
Results(playerstruct);

  

% -----------------------------------------------------
function [playerstruct] = BuildPlayerStruct
%
% Builds the structure containing player names and personalities from the
% player files. File names are player names and function names are
% personality names. Each index in playerstruct corrisponds to a
% personality. Each index in playerstruct has the following fields:
%
% playerstruct
% .playername : name of the player that this personality belongs to
% .playerdir : directory path that the personality is in
% .personality : name of the personality
% .score : total number of points earned by this personality
% .nummatches : number of matches that this personality played
%
%
% %%% ZCD 2006 %%%

% Put all contents of the directory into 'files'
files = dir(cd);
% Count the number of total personalities (equal to length(playerstruct)
% once the playerstruct is built.
np = 0;
% Count the number of players.
nplayer = 0; % as of v1.01 this is unused

% Obtain the contents of the player directories, search for player
% directories, and load player names and player personalities into the
% structure playerstruct.
for n=1:length(files)
% if the entry in files is a directory and not a path...
if (files(n).isdir) & (files(n).name(1)~='.')
% We found another player
nplayer = nplayer+1;
  
% Obtain all personalities in the player's file
playerfiles = dir( strcat(cd,'',files(n).name,'*m') );
  
for k=1:length(playerfiles)
np = np+1; % We found another personality
% Get the player's name (same as their folder's name)
playerstruct(np).playername = files(n).name;
playerstruct(np).playerdir = strcat(cd,'',playerstruct(np).playername);

% Put all the names of the personalities in the field
% 'personality'
playerstruct(np).personality = playerfiles(k).name;
  
% Keep fields for scores and total number of games played
playerstruct(np).score = 0;
playerstruct(np).nummatches = 0;

end
% Empty out playerfiles for the next player
clear playerfiles

% Add the player folders to the MATLAB path
addpath(playerstruct(np).playerdir);
end
end

% -----------------------------------------------------
function GraphicDisplay(playerstruct,ScoreMat,match)
%
fprintf(' %s %s ',playerstruct(match(1)).playername,...
playerstruct(match(2)).playername);
fprintf(' %s %s ', playerstruct(match(1)).personality(1:end-2),...
playerstruct(match(2)).personality(1:end-2));
disp(ScoreMat);

% -----------------------------------------------------
function schedule = BuildMatchSchedule(playerstruct)
%
% This builds the schedule of matches to be played. It checks each
% personality against each other, looking for weather the playername
% is the same. If playernames are the same, the corrisponding match is not
% placed into schedule.
% Schedule is a nx2 array where each row is one match to be played, and
% each column is the index in playerstruct of the two personalities playing.
%
%
% %%% ZCD 2006 %%%

% Initialize schedule variable
schedule = [];

for h = 1:length(playerstruct)
% Don't recount any of the personalities, they have been checked
% already by the i loop in the past h iteration. So, now we can start
% checking from h+1. This also avoids repeat matches.
for i = (h+1) : length(playerstruct)
% if the h player's maker is not the same as the i players maker...
if ~strcmp(playerstruct(h).playername , playerstruct(i).playername)
  
% ...they should play each other
schedule(end+1,:) = [h i];
end
end
end
  
% -----------------------------------------------------
function Results(playerstruct)
%
% This function displays the results of the competition in a bar graph,
% sorted from highest scoring personality to lowest. If there are more than
% 6 personalities only the top 5 appear in the bar graph, the rest apear as
% names and scores only. If there are more than 20, only the top 20 are
% shown.
%
% This function takes the argument, playerstruct, created in function
% BuildPlayerStruct.
%
% %%% ZCD 2006 %%%

h1 = figure('name','IPD RESULTS','NumberTitle','off');

% Calculate average score and assign it to Y. Assign the corrisponding name
% and assign it to X.
for i=1:length(playerstruct)
Y(i) = playerstruct(i).score / playerstruct(i).nummatches;
X{i} = [playerstruct(i).playername,': ',playerstruct(i).personality(1:end-2)];
end
% Total number of competitors in cnum
cnum = length(Y);

% Sort Y, but retain the corrisponding name in Xsrt.
[Ysrt IX] = sort( Y, 'descend' );
for i=1:length(Y)
indsort = IX(i);
Xsrt(i) = X(indsort);
end

if length(Y)<=6
bar(Y)
colormap summer   
set( gca, 'XTickLabel', X );   
else   
Ym = [Ysrt(1:5) 0];
Xm = Xsrt(1:5); Xm{6} = 'Field';
bar(Ym)
colormap summer
set( gca, 'XTickLabel', Xm );
for i=6:length(Y)
% Define placement of text string
text( 5.6, Ysrt(1)-(i-6.5)*(Ysrt(1)/15),...
[ Xsrt{i} ' - ' num2str(Ysrt(i)) ],...
'BackGroundColor', 'w', 'FontWeight', 'bold' );
if i==20
cnum = i;
break
end
end
set( gcf, 'Position', [70 373 1502 547] );
end

if length(Y)<21
title( [ 'Rank Order and Score of All ', num2str(cnum), ' Competitors' ] );
else
title( [ 'Rank Order and Score of Top ', num2str(cnum), ' Competitors' ] );
end

ylabel('Average Points Earned by Personality');
grid on;

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