107/replication_package/Code/run_simulations.m

function run_simulations()
% Runs simulations of commitment contract game for different populations

% NOTE: If you start a MATLAB session by opening this file, your current
% folder will typically default to the Code subfolder. If that is not the
% case, MATLAB will usually prompt you to change it to that folder when you
% run this file. You can also edit the code below to manually choose the
% correct location. 
% cd '/Users/Your Name/Downloads/Who_Chooses_Commitment_Replication/Code'

% declare global
global OUTPUT; 
OUTPUT = '../Output';

% add path to intermediate files
addpath('MATLAB');

% delete old output file
numbersfile = [OUTPUT '/simulations.tex'];
if (exist(numbersfile,'file')), delete(numbersfile); end 


%% Set game properties

% Game properties from experimental design
props12.a_star = 12;
props12.T = 28;
props12.p = 80;

% Alternate contract threshold properties
props8 = props12;
props8.a_star = 8;
props16 = props12;
props16.a_star = 16;

% Game properties with no penalty (equivalent to no contract)
props12NoP = props12;
props12NoP.p = 0;
props8NoP = props8;
props8NoP.p = 0;
props16NoP = props16;
props16NoP.p = 0;

% Set lower bound on support of cost distribution
minC = 0;


%% Instantiate games for attendance comparisons

% chose 12+ visit contract
params12 = load_parameters('commit12');
game12 = gymGame(props12, params12, minC, 'chose 12+ contract');
mu12 = params12.mu; % store share of pop. in chose 12+ contract group

% add heterogeneity along past attendance (below vs. above median)
params12AM = load_parameters('amcommit');
game12AM = gymGame(props12, params12AM, minC, 'chose 12+, above med. att.');
params12BM = load_parameters('bmcommit');
game12BM = gymGame(props12, params12BM, minC, 'chose 12+, below med. att.');

% add heterogeneity along past attendance (quartiles)
params12Q1 = load_parameters('qfstcommit');
game12Q1 = gymGame(props12, params12Q1, minC, 'chose 12+, q1 att.');
params12Q2 = load_parameters('qsndcommit');
game12Q2 = gymGame(props12, params12Q2, minC, 'chose 12+, q2 att.');
params12Q3 = load_parameters('qthdcommit');
game12Q3 = gymGame(props12, params12Q3, minC, 'chose 12+, q3 att.');
params12Q4 = load_parameters('qfthcommit');
game12Q4 = gymGame(props12, params12Q4, minC, 'chose 12+, q4 att.');

% add heterogeneity along past attendance (median) & info treatment
params12AMInfo = load_parameters('aminfocommit');
game12AMInfo = gymGame(props12, params12AMInfo, minC, 'chose 12+, above med. att., info treat');
params12AMControl = load_parameters('amctrlcommit');
game12AMControl = gymGame(props12, params12AMControl, minC, 'chose 12+, above med. att., control');
params12BMInfo = load_parameters('bminfocommit');
game12BMInfo = gymGame(props12, params12BMInfo, minC, 'chose 12+, below med. att., info treat');
params12BMControl = load_parameters('bmctrlcommit');
game12BMControl = gymGame(props12, params12BMControl, minC, 'chose 12+, below med. att., control');

% add heterogeneity along past attendance (quartiles) & info treatment
params12Q1Info = load_parameters('qfstinfocommit');
game12Q1Info = gymGame(props12, params12Q1Info, minC, 'chose 12+, q1 att., info treat');
params12Q1Control = load_parameters('qfstctrlcommit');
game12Q1Control = gymGame(props12, params12Q1Control, minC, 'chose 12+, q1 att., control');
params12Q2Info = load_parameters('qsndinfocommit');
game12Q2Info = gymGame(props12, params12Q2Info, minC, 'chose 12+, q2 att., info treat');
params12Q2Control = load_parameters('qsndctrlcommit');
game12Q2Control = gymGame(props12, params12Q2Control, minC, 'chose 12+, q2 att., control');
params12Q3Info = load_parameters('qthdinfocommit');
game12Q3Info = gymGame(props12, params12Q3Info, minC, 'chose 12+, q3 att., info treat');
params12Q3Control = load_parameters('qthdctrlcommit');
game12Q3Control = gymGame(props12, params12Q3Control, minC, 'chose 12+, q3 att., control');
params12Q4Info = load_parameters('qfthinfocommit');
game12Q4Info = gymGame(props12, params12Q4Info, minC, 'chose 12+, q4 att., info treat');
params12Q4Control = load_parameters('qfthctrlcommit');
game12Q4Control = gymGame(props12, params12Q4Control, minC, 'chose 12+, q4 att., control');

% add no penalty versions of the above games
% note: the no penalty contracts are equivalent to no contract being 
% assigned due to these populations' rejection of the contract
game12NoP = gymGame(props12NoP, params12, minC, 'chose 12+, no penalty');
game12AMNoP = gymGame(props12NoP, params12AM, minC, 'chose 12+, above med. att., no penalty');
game12BMNoP = gymGame(props12NoP, params12BM, minC, 'chose 12+, below med. att., no penalty');
game12Q1NoP = gymGame(props12NoP, params12Q1, minC, 'chose 12+, q1 att., no penalty');
game12Q2NoP = gymGame(props12NoP, params12Q2, minC, 'chose 12+, q2 att., no penalty');
game12Q3NoP = gymGame(props12NoP, params12Q3, minC, 'chose 12+, q3 att., no penalty');
game12Q4NoP = gymGame(props12NoP, params12Q4, minC, 'chose 12+, q4 att., no penalty');
game12AMInfoNoP = gymGame(props12NoP, params12AMInfo, minC, ...
    'chose 12+, above med. att., info treat, no penalty');
game12AMControlNoP = gymGame(props12NoP, params12AMControl, minC, ...
    'chose 12+, above med. att., control, no penalty');
game12BMInfoNoP = gymGame(props12NoP, params12BMInfo, minC, ...
    'chose 12+, below med. att., info treat, no penalty');
game12BMControlNoP = gymGame(props12NoP, params12BMControl, minC, ...
    'chose 12+, below med. att., control, no penalty');
game12Q1InfoNoP = gymGame(props12NoP, params12Q1Info, minC, ...
    'chose 12+, q1 att., info treat, no penalty');
game12Q1ControlNoP = gymGame(props12NoP, params12Q1Control, ...
    minC, 'chose 12+, q1 att., control, no penalty');
game12Q2InfoNoP = gymGame(props12NoP, params12Q2Info, minC, ...
    'chose 12+, q2 att., info treat, no penalty');
game12Q2ControlNoP = gymGame(props12NoP, params12Q2Control, minC, ...
    'chose 12+, q2 att., control, no penalty');
game12Q3InfoNoP = gymGame(props12NoP, params12Q3Info, minC, ...
    'chose 12+, q3 att., info treat, no penalty');
game12Q3ControlNoP = gymGame(props12NoP, params12Q3Control, minC, ...
    'chose 12+, q3 att., control, no penalty');
game12Q4InfoNoP = gymGame(props12NoP, params12Q4Info, minC, ...
    'chose 12+, q4 att., info treat, no penalty');
game12Q4ControlNoP = gymGame(props12NoP, params12Q4Control, minC, ...
    'chose 12+, q4 att., control, no penalty');


%% Compare attendance outcomes across different simulated populations

% chose 12+ visit contract
mc(1) = game12;
mc(1).mu = 1; % homogeneous population
mcnp(1) = game12NoP;
mcnp(1).mu = 1; % homogeneous population
simulate_attendance(mc,mcnp,'all')

% with hetereogenity along past attendance (above vs. below median)
mc = [game12AM game12BM];
mcnp = [game12AMNoP game12BMNoP];
simulate_attendance(mc,mcnp,'matt')

% with hetereogenity along past attendance (quartile)
mc = [game12Q1 game12Q2 game12Q3 game12Q4];
mcnp = [game12Q1NoP game12Q2NoP game12Q3NoP game12Q4NoP];
simulate_attendance(mc,mcnp,'qatt')

% with heterogeneity along past attendance (median) & info treatment
mc = [game12AMInfo game12AMControl game12BMInfo game12BMControl];
mcnp = [game12AMInfoNoP game12AMControlNoP game12BMInfoNoP game12BMControlNoP];
simulate_attendance(mc,mcnp,'mattinfo')

% with heterogeneity along past attendance (quartile) & info treatment
mc = [game12Q1Info game12Q1Control game12Q2Info game12Q2Control ...
    game12Q3Info game12Q3Control game12Q4Info game12Q4Control];
mcnp = [game12Q1InfoNoP game12Q1ControlNoP game12Q2InfoNoP game12Q2ControlNoP ...
    game12Q3InfoNoP game12Q3ControlNoP game12Q4InfoNoP game12Q4ControlNoP];
simulate_attendance(mc,mcnp,'qattinfo')


%% Instantiate games for welfare/efficiency comparisons
% with heterogeneity along past attendance (median) & info treatment

% add 8+ contract versions (with & without penalty)
params8AMInfo = load_parameters('aminfocommite');
game8AMInfo = gymGame(props8, params8AMInfo, minC, 'chose 8+, above med. att., info treat');
game8AMInfoNoP = gymGame(props8NoP, params8AMInfo, minC, ...
    'chose 8+, above med. att., info treat, no penalty');
params8AMControl = load_parameters('amctrlcommite');
game8AMControl = gymGame(props8, params8AMControl, minC, 'chose 8+, above med. att., control');
game8AMControlNoP = gymGame(props8NoP, params8AMControl, minC, ...
    'chose 8+, above med. att., control, no penalty');
params8BMInfo = load_parameters('bminfocommite');
game8BMInfo = gymGame(props8, params8BMInfo, minC, 'chose 8+, below med. att., info treat');
game8BMInfoNoP = gymGame(props8NoP, params8BMInfo, minC, ...
    'chose 8+, below med. att., info treat, no penalty');
params8BMControl = load_parameters('bmctrlcommite');
game8BMControl = gymGame(props8, params8BMControl, minC, 'chose 8+, below med. att., control');
game8BMControlNoP = gymGame(props8NoP, params8BMControl, minC, ...
    'chose 8+, below med. att., control, no penalty');

% add 16+ contract versions (with & without penalty)
params16AMInfo = load_parameters('aminfocommits');
game16AMInfo = gymGame(props16, params16AMInfo, minC, 'chose 16+, above med. att., info treat');
game16AMInfoNoP = gymGame(props16NoP, params16AMInfo, minC, ...
    'chose 16+, above med. att., info treat, no penalty');
params16AMControl = load_parameters('amctrlcommits');
game16AMControl = gymGame(props16, params16AMControl, minC, 'chose 16+, above med. att., control');
game16AMControlNoP = gymGame(props16NoP, params16AMControl, minC, ...
    'chose 16+, above med. att., control, no penalty');
params16BMInfo = load_parameters('bminfocommits');
game16BMInfo = gymGame(props16, params16BMInfo, minC, 'chose 16+, below med. att., info treat');
game16BMInfoNoP = gymGame(props16NoP, params16BMInfo, minC, ...
    'chose 16+, below med. att., info treat, no penalty');
params16BMControl = load_parameters('bmctrlcommits');
game16BMControl = gymGame(props16, params16BMControl, minC, 'chose 16+, below med. att., control');
game16BMControlNoP = gymGame(props16NoP, params16BMControl, minC, ...
    'chose 16+, below med. att., control, no penalty');

% add versions for those who rejected the commitment contracts
paramsNo12AMInfo = load_parameters('aminfonocommit');
gameNo12AMInfo = gymGame(props12NoP, paramsNo12AMInfo, minC, ...
    'rejected 12+, above med. att., info treat');
paramsNo12AMControl = load_parameters('amctrlnocommit');
gameNo12AMControl = gymGame(props12NoP, paramsNo12AMControl, minC, ...
    'rejected 12+, above med. att., control');
paramsNo12BMInfo = load_parameters('bminfonocommit');
gameNo12BMInfo = gymGame(props12NoP, paramsNo12BMInfo, minC, ...
    'rejected 12+, below med. att., info treat');
paramsNo12BMControl = load_parameters('bmctrlnocommit');
gameNo12BMControl = gymGame(props12NoP, paramsNo12BMControl, minC, ...
    'rejected 12+, below med. att., control');
paramsNo8AMInfo = load_parameters('aminfonocommite');
gameNo8AMInfo = gymGame(props8NoP, paramsNo8AMInfo, minC, ...
    'rejected 8+, above med. att., info treat');
paramsNo8AMControl = load_parameters('amctrlnocommite');
gameNo8AMControl = gymGame(props8NoP, paramsNo8AMControl, minC, ...
    'rejected 8+, above med. att., control');
paramsNo8BMInfo = load_parameters('bminfonocommite');
gameNo8BMInfo = gymGame(props8NoP, paramsNo8BMInfo, minC, ...
    'rejected 8+, below med. att., info treat');
paramsNo8BMControl = load_parameters('bmctrlnocommite');
gameNo8BMControl = gymGame(props8NoP, paramsNo8BMControl, minC, ...
    'rejected 8+, below med. att., control');
paramsNo16AMInfo = load_parameters('aminfonocommits');
gameNo16AMInfo = gymGame(props16NoP, paramsNo16AMInfo, minC, ...
    'rejected 16+, above med. att., info treat');
paramsNo16AMControl = load_parameters('amctrlnocommits');
gameNo16AMControl = gymGame(props16NoP, paramsNo16AMControl, minC, ...
    'rejected 16+, above med. att., control');
paramsNo16BMInfo = load_parameters('bminfonocommits');
gameNo16BMInfo = gymGame(props16NoP, paramsNo16BMInfo, minC, ...
    'rejected 16+, below med. att., info treat');
paramsNo16BMControl = load_parameters('bmctrlnocommits');
gameNo16BMControl = gymGame(props16NoP, paramsNo16BMControl, minC, ...
    'rejected 16+, below med. att., control');

% store share of population that chose each contract
params8 = load_parameters('commit8');
mu8 = params8.mu; 
params16 = load_parameters('commit16');
mu16 = params16.mu; 


%% Compare welfare/efficiency outcomes across different contracts/incentives
% with heterogeneity along past attendance (median) & info treatment

% under the 12+ visit contract
mc = [game12AMInfo game12AMControl game12BMInfo game12BMControl];
mnc = [gameNo12AMInfo gameNo12AMControl gameNo12BMInfo gameNo12BMControl];
mcnp = [game12AMInfoNoP game12AMControlNoP game12BMInfoNoP game12BMControlNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu12;
    mcnp(m).mu = mcnp(m).mu .* mu12;
    mnc(m).mu = mnc(m).mu .* (1 - mu12);
end
Results12 = compute_efficiency(mc,mnc,mcnp);

% under the 8+ visit contract
mc = [game8AMInfo game8AMControl game8BMInfo game8BMControl];
mnc = [gameNo8AMInfo gameNo8AMControl gameNo8BMInfo gameNo8BMControl];
mcnp = [game8AMInfoNoP game8AMControlNoP game8BMInfoNoP game8BMControlNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu8;
    mcnp(m).mu = mcnp(m).mu .* mu8;
    mnc(m).mu = mnc(m).mu .* (1 - mu8);
end
Results8 = compute_efficiency(mc,mnc,mcnp);

% under the 16+ visit contract
mc = [game16AMInfo game16AMControl game16BMInfo game16BMControl];
mnc = [gameNo16AMInfo gameNo16AMControl gameNo16BMInfo gameNo16BMControl];
mcnp = [game16AMInfoNoP game16AMControlNoP game16BMInfoNoP game16BMControlNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu16;
    mcnp(m).mu = mcnp(m).mu .* mu16;
    mnc(m).mu = mnc(m).mu .* (1 - mu16);
end
Results16 = compute_efficiency(mc,mnc,mcnp);

% export results
export_efficiency_results(Results8, Results12, Results16, 'het');


%% Instantiate games for welfare/efficiency comparisons
% with homogeneity & heterogeneity along past attendance & treatment

% add 8+ contract versions (with & without penalty)
% with homogeneity
params8 = load_parameters('commit8');
game8 = gymGame(props8, params8, minC, 'chose 8+ contract');
game8NoP = gymGame(props8NoP, params8, minC, 'chose 8+ contract, no penalty');
% with heterogeneity along past attendance (below vs. above median)
params8AM = load_parameters('amcommite');
game8AM = gymGame(props8, params8AM, minC, 'chose 8+, above med. att.');
game8AMNoP = gymGame(props8NoP, params8AM, minC, 'chose 8+, above med. att., no penalty');
params8BM = load_parameters('bmcommite');
game8BM = gymGame(props8, params8BM, minC, 'chose 8+, below med. att.');
game8BMNoP = gymGame(props8NoP, params8BM, minC, 'chose 8+, below med. att., no penalty');
% add heterogeneity along past attendance (quartiles)
params8Q1 = load_parameters('qfstcommite');
game8Q1 = gymGame(props8, params8Q1, minC, 'chose 8+, q1 att.');
game8Q1NoP = gymGame(props8NoP, params8Q1, minC, 'chose 8+, q1 att., no penalty');
params8Q2 = load_parameters('qsndcommite');
game8Q2 = gymGame(props8, params8Q2, minC, 'chose 8+, q2 att.');
game8Q2NoP = gymGame(props8NoP, params8Q2, minC, 'chose 8+, q2 att., no penalty');
params8Q3 = load_parameters('qthdcommite');
game8Q3 = gymGame(props8, params8Q3, minC, 'chose 8+, q3 att.');
game8Q3NoP = gymGame(props8NoP, params8Q3, minC, 'chose 8+, q3 att., no penalty');
params8Q4 = load_parameters('qfthcommite');
game8Q4 = gymGame(props8, params8Q4, minC, 'chose 8+, q4 att.');
game8Q4NoP = gymGame(props8NoP, params8Q4, minC, 'chose 8+, q4 att., no penalty');

% add 16+ contract versions (with & without penalty)
% with homogeneity
params16 = load_parameters('commit16');
game16 = gymGame(props16, params16, minC, 'chose 16+ contract');
game16NoP = gymGame(props16NoP, params16, minC, 'chose 16+ contract, no penalty');
% with heterogeneity along past attendance (below vs. above median)
params16AM = load_parameters('amcommits');
game16AM = gymGame(props16, params16AM, minC, 'chose 16+, above med. att.');
game16AMNoP = gymGame(props16NoP, params16AM, minC, 'chose 16+, above med. att., no penalty');
params16BM = load_parameters('bmcommits');
game16BM = gymGame(props16, params16BM, minC, 'chose 16+, below med. att.');
game16BMNoP = gymGame(props16NoP, params16BM, minC, 'chose 16+, below med. att., no penalty');
% add heterogeneity along past attendance (quartiles)
params16Q1 = load_parameters('qfstcommits');
game16Q1 = gymGame(props16, params16Q1, minC, 'chose 16+, q1 att.');
game16Q1NoP = gymGame(props16NoP, params16Q1, minC, 'chose 16+, q1 att., no penalty');
params16Q2 = load_parameters('qsndcommits');
game16Q2 = gymGame(props16, params16Q2, minC, 'chose 16+, q2 att.');
game16Q2NoP = gymGame(props16NoP, params16Q2, minC, 'chose 16+, q2 att., no penalty');
params16Q3 = load_parameters('qthdcommits');
game16Q3 = gymGame(props16, params16Q3, minC, 'chose 16+, q3 att.');
game16Q3NoP = gymGame(props16NoP, params16Q3, minC, 'chose 16+, q3 att., no penalty');
params16Q4 = load_parameters('qfthcommits');
game16Q4 = gymGame(props16, params16Q4, minC, 'chose 16+, q4 att.');
game16Q4NoP = gymGame(props16NoP, params16Q4, minC, 'chose 16+, q4 att., no penalty');

% add versions for those who rejected the commitment contracts
% 8+ visits contract
paramsNo8 = load_parameters('nocommit8');
gameNo8 = gymGame(props8NoP, paramsNo8, minC, 'rejected 8+ contract');
paramsNo8AM = load_parameters('amnocommite');
gameNo8AM = gymGame(props8NoP, paramsNo8AM, minC, 'rejected 8+, above med. att.');
paramsNo8BM = load_parameters('bmnocommite');
gameNo8BM = gymGame(props8NoP, paramsNo8BM, minC, 'rejected 8+, below med. att.');
paramsNo8Q1 = load_parameters('qfstnocommite');
gameNo8Q1 = gymGame(props8NoP, paramsNo8Q1, minC, 'rejected 8+, q1 att.');
paramsNo8Q2 = load_parameters('qsndnocommite');
gameNo8Q2 = gymGame(props8NoP, paramsNo8Q2, minC, 'rejected 8+, q2 att.');
paramsNo8Q3 = load_parameters('qthdnocommite');
gameNo8Q3 = gymGame(props8NoP, paramsNo8Q3, minC, 'rejected 8+, q3 att.');
paramsNo8Q4 = load_parameters('qfthnocommite');
gameNo8Q4 = gymGame(props8NoP, paramsNo8Q4, minC, 'rejected 8+, q4 att.');
% 12+ visits contract
paramsNo12 = load_parameters('nocommit12');
gameNo12 = gymGame(props12NoP, paramsNo12, minC, 'rejected 12+ contract');
paramsNo12AM = load_parameters('amnocommit');
gameNo12AM = gymGame(props12NoP, paramsNo12AM, minC, 'rejected 12+, above med. att.');
paramsNo12BM = load_parameters('bmnocommit');
gameNo12BM = gymGame(props12NoP, paramsNo12BM, minC, 'rejected 12+, below med. att.');
paramsNo12Q1 = load_parameters('qfstnocommit');
gameNo12Q1 = gymGame(props12NoP, paramsNo12Q1, minC, 'rejected 12+, q1 att.');
paramsNo12Q2 = load_parameters('qsndnocommit');
gameNo12Q2 = gymGame(props12NoP, paramsNo12Q2, minC, 'rejected 12+, q2 att.');
paramsNo12Q3 = load_parameters('qthdnocommit');
gameNo12Q3 = gymGame(props12NoP, paramsNo12Q3, minC, 'rejected 12+, q3 att.');
paramsNo12Q4 = load_parameters('qfthnocommit');
gameNo12Q4 = gymGame(props12NoP, paramsNo12Q4, minC, 'rejected 12+, q4 att.');
% 16+ visits contract
paramsNo16 = load_parameters('nocommit16');
gameNo16 = gymGame(props16NoP, paramsNo16, minC, 'rejected 16+ contract');
paramsNo16AM = load_parameters('amnocommits');
gameNo16AM = gymGame(props16NoP, paramsNo16AM, minC, 'rejected 16+, above med. att.');
paramsNo16BM = load_parameters('bmnocommits');
gameNo16BM = gymGame(props16NoP, paramsNo16BM, minC, 'rejected 16+, below med. att.');
paramsNo16Q1 = load_parameters('qfstnocommits');
gameNo16Q1 = gymGame(props16NoP, paramsNo16Q1, minC, 'rejected 16+, q1 att.');
paramsNo16Q2 = load_parameters('qsndnocommits');
gameNo16Q2 = gymGame(props16NoP, paramsNo16Q2, minC, 'rejected 16+, q2 att.');
paramsNo16Q3 = load_parameters('qthdnocommits');
gameNo16Q3 = gymGame(props16NoP, paramsNo16Q3, minC, 'rejected 16+, q3 att.');
paramsNo16Q4 = load_parameters('qfthnocommits');
gameNo16Q4 = gymGame(props16NoP, paramsNo16Q4, minC, 'rejected 16+, q4 att.');


%% Compare welfare/efficiency outcomes across different contracts/incentives
% with homogeneity & heterogeneity along past attendance & treatment

% HOMOGENEITY
% under the 12+ visit contract
mc = game12;
mnc = gameNo12;
mcnp = game12NoP;
Results12 = compute_efficiency(mc,mnc,mcnp);

% under the 8+ visit contract
mc = game8;
mnc = gameNo8;
mcnp = game8NoP;
Results8 = compute_efficiency(mc,mnc,mcnp);

% under the 16+ visit contract
mc = game16;
mnc = gameNo16;
mcnp = game16NoP;
Results16 = compute_efficiency(mc,mnc,mcnp);

% export results
export_efficiency_results(Results8, Results12, Results16, 'hom');


% HETEROGENEITY ALONG PAST ATTENDANCE (MEDIAN)
% under the 12+ visit contract
mc = [game12AM game12BM];
mnc = [gameNo12AM gameNo12BM];
mcnp = [game12AMNoP game12BMNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu12;
    mcnp(m).mu = mcnp(m).mu .* mu12;
    mnc(m).mu = mnc(m).mu .* (1 - mu12);
end
Results12 = compute_efficiency(mc,mnc,mcnp);

% under the 8+ visit contract
mc = [game8AM game8BM];
mnc = [gameNo8AM gameNo8BM];
mcnp = [game8AMNoP game8BMNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu8;
    mcnp(m).mu = mcnp(m).mu .* mu8;
    mnc(m).mu = mnc(m).mu .* (1 - mu8);
end
Results8 = compute_efficiency(mc,mnc,mcnp);

% under the 16+ visit contract
mc = [game16AM game16BM];
mnc = [gameNo16AM gameNo16BM];
mcnp = [game16AMNoP game16BMNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu16;
    mcnp(m).mu = mcnp(m).mu .* mu16;
    mnc(m).mu = mnc(m).mu .* (1 - mu16);
end
Results16 = compute_efficiency(mc,mnc,mcnp);

% export results
export_efficiency_results(Results8, Results12, Results16, 'med');


% HETEROGENEITY ALONG PAST ATTENDANCE (QUARTILE)
% under the 12+ visit contract
mc = [game12Q1 game12Q2 game12Q3 game12Q4];
mnc = [gameNo12Q1 gameNo12Q2 gameNo12Q3 gameNo12Q4];
mcnp = [game12Q1NoP game12Q2NoP game12Q3NoP game12Q4NoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu12;
    mcnp(m).mu = mcnp(m).mu .* mu12;
    mnc(m).mu = mnc(m).mu .* (1 - mu12);
end
Results12 = compute_efficiency(mc,mnc,mcnp);

% under the 8+ visit contract
mc = [game8Q1 game8Q2 game8Q3 game8Q4];
mnc = [gameNo8Q1 gameNo8Q2 gameNo8Q3 gameNo8Q4];
mcnp = [game8Q1NoP game8Q2NoP game8Q3NoP game8Q4NoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu8;
    mcnp(m).mu = mcnp(m).mu .* mu8;
    mnc(m).mu = mnc(m).mu .* (1 - mu8);
end
Results8 = compute_efficiency(mc,mnc,mcnp);

% under the 16+ visit contract
mc = [game16Q1 game16Q2 game16Q3 game16Q4];
mnc = [gameNo16Q1 gameNo16Q2 gameNo16Q3 gameNo16Q4];
mcnp = [game16Q1NoP game16Q2NoP game16Q3NoP game16Q4NoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu16;
    mcnp(m).mu = mcnp(m).mu .* mu16;
    mnc(m).mu = mnc(m).mu .* (1 - mu16);
end
Results16 = compute_efficiency(mc,mnc,mcnp);

% export results
export_efficiency_results(Results8, Results12, Results16, 'qrt');


%% Plot the average probability of attending each day

% generate plot for 12+ visit contract
mc = [game12AMInfo game12AMControl game12BMInfo game12BMControl];
plot_att_prob(mc,'daily_att_prob_commit12');


%% Results with a minimal cost draw of $10

% Set lower bound on support of cost distribution
minC = 10;

% INSTANTIATE GAMES
% chose 12+ visit contract
params12 = load_parameters('commit12X');
game12 = gymGame(props12, params12, minC, 'chose 12+ contract');

% add heterogeneity along past attendance (below vs. above median)
params12AM = load_parameters('amcommitX');
game12AM = gymGame(props12, params12AM, minC, 'chose 12+, above med. att.');
params12BM = load_parameters('bmcommitX');
game12BM = gymGame(props12, params12BM, minC, 'chose 12+, below med. att.');

% add heterogeneity along past attendance (quartiles)
params12Q1 = load_parameters('qfstcommitX');
game12Q1 = gymGame(props12, params12Q1, minC, 'chose 12+, q1 att.');
params12Q2 = load_parameters('qsndcommitX');
game12Q2 = gymGame(props12, params12Q2, minC, 'chose 12+, q2 att.');
params12Q3 = load_parameters('qthdcommitX');
game12Q3 = gymGame(props12, params12Q3, minC, 'chose 12+, q3 att.');
params12Q4 = load_parameters('qfthcommitX');
game12Q4 = gymGame(props12, params12Q4, minC, 'chose 12+, q4 att.');

% add heterogeneity along past attendance (median) & info treatment
params12AMInfo = load_parameters('aminfocommitX');
game12AMInfo = gymGame(props12, params12AMInfo, minC, ...
    'chose 12+, above med. att., info treat');
params12AMControl = load_parameters('amctrlcommitX');
game12AMControl = gymGame(props12, params12AMControl, minC, ...
    'chose 12+, above med. att., control');
params12BMInfo = load_parameters('bminfocommitX');
game12BMInfo = gymGame(props12, params12BMInfo, minC, ...
    'chose 12+, below med. att., info treat');
params12BMControl = load_parameters('bmctrlcommitX');
game12BMControl = gymGame(props12, params12BMControl, minC, ...
    'chose 12+, below med. att., control');

% add heterogeneity along past attendance (quartiles) & info treatment
params12Q1Info = load_parameters('qfstinfocommitX');
game12Q1Info = gymGame(props12, params12Q1Info, minC, 'chose 12+, q1 att., info treat');
params12Q1Control = load_parameters('qfstctrlcommitX');
game12Q1Control = gymGame(props12, params12Q1Control, minC, 'chose 12+, q1 att., control');
params12Q2Info = load_parameters('qsndinfocommitX');
game12Q2Info = gymGame(props12, params12Q2Info, minC, 'chose 12+, q2 att., info treat');
params12Q2Control = load_parameters('qsndctrlcommitX');
game12Q2Control = gymGame(props12, params12Q2Control, minC, 'chose 12+, q2 att., control');
params12Q3Info = load_parameters('qthdinfocommitX');
game12Q3Info = gymGame(props12, params12Q3Info, minC, 'chose 12+, q3 att., info treat');
params12Q3Control = load_parameters('qthdctrlcommitX');
game12Q3Control = gymGame(props12, params12Q3Control, minC, 'chose 12+, q3 att., control');
params12Q4Info = load_parameters('qfthinfocommitX');
game12Q4Info = gymGame(props12, params12Q4Info, minC, 'chose 12+, q4 att., info treat');
params12Q4Control = load_parameters('qfthctrlcommitX');
game12Q4Control = gymGame(props12, params12Q4Control, minC, 'chose 12+, q4 att., control');

% add no penalty versions of the above games
game12NoP = gymGame(props12NoP, params12, minC, 'chose 12+, no penalty');
game12AMNoP = gymGame(props12NoP, params12AM, minC, 'chose 12+, above med. att., no penalty');
game12BMNoP = gymGame(props12NoP, params12BM, minC, 'chose 12+, below med. att., no penalty');
game12Q1NoP = gymGame(props12NoP, params12Q1, minC, 'chose 12+, q1 att., no penalty');
game12Q2NoP = gymGame(props12NoP, params12Q2, minC, 'chose 12+, q2 att., no penalty');
game12Q3NoP = gymGame(props12NoP, params12Q3, minC, 'chose 12+, q3 att., no penalty');
game12Q4NoP = gymGame(props12NoP, params12Q4, minC, 'chose 12+, q4 att., no penalty');
game12AMInfoNoP = gymGame(props12NoP, params12AMInfo, minC, ...
    'chose 12+, above med. att., info treat, no penalty');
game12AMControlNoP = gymGame(props12NoP, params12AMControl, minC, ...
    'chose 12+, above med. att., control, no penalty');
game12BMInfoNoP = gymGame(props12NoP, params12BMInfo, minC, ...
    'chose 12+, below med. att., info treat, no penalty');
game12BMControlNoP = gymGame(props12NoP, params12BMControl, minC, ...
    'chose 12+, below med. att., control, no penalty');
game12Q1InfoNoP = gymGame(props12NoP, params12Q1Info, minC, ...
    'chose 12+, q1 att., info treat, no penalty');
game12Q1ControlNoP = gymGame(props12NoP, params12Q1Control, minC, ...
    'chose 12+, q1 att., control, no penalty');
game12Q2InfoNoP = gymGame(props12NoP, params12Q2Info, minC, ...
    'chose 12+, q2 att., info treat, no penalty');
game12Q2ControlNoP = gymGame(props12NoP, params12Q2Control, minC, ...
    'chose 12+, q2 att., control, no penalty');
game12Q3InfoNoP = gymGame(props12NoP, params12Q3Info, minC, ...
    'chose 12+, q3 att., info treat, no penalty');
game12Q3ControlNoP = gymGame(props12NoP, params12Q3Control, minC, ...
    'chose 12+, q3 att., control, no penalty');
game12Q4InfoNoP = gymGame(props12NoP, params12Q4Info, minC, ...
    'chose 12+, q4 att., info treat, no penalty');
game12Q4ControlNoP = gymGame(props12NoP, params12Q4Control, minC, ...
    'chose 12+, q4 att., control, no penalty');

% add 8+ contract versions (with & without penalty)
params8AMInfo = load_parameters('aminfocommiteX');
game8AMInfo = gymGame(props8, params8AMInfo, minC, ...
    'chose 8+, above med. att., info treat');
game8AMInfoNoP = gymGame(props8NoP, params8AMInfo, minC, ...
    'chose 8+, above med. att., info treat, no penalty');
params8AMControl = load_parameters('amctrlcommiteX');
game8AMControl = gymGame(props8, params8AMControl, minC, ...
    'chose 8+, above med. att., control');
game8AMControlNoP = gymGame(props8NoP, params8AMControl, minC, ...
    'chose 8+, above med. att., control, no penalty');
params8BMInfo = load_parameters('bminfocommiteX');
game8BMInfo = gymGame(props8, params8BMInfo, minC, ...
    'chose 8+, below med. att., info treat');
game8BMInfoNoP = gymGame(props8NoP, params8BMInfo, minC, ...
    'chose 8+, below med. att., info treat, no penalty');
params8BMControl = load_parameters('bmctrlcommiteX');
game8BMControl = gymGame(props8, params8BMControl, minC, ...
    'chose 8+, below med. att., control');
game8BMControlNoP = gymGame(props8NoP, params8BMControl, minC, ...
    'chose 8+, below med. att., control, no penalty');

% add 16+ contract versions (with & without penalty)
params16AMInfo = load_parameters('aminfocommitsX');
game16AMInfo = gymGame(props16, params16AMInfo, minC, ...
    'chose 16+, above med. att., info treat');
game16AMInfoNoP = gymGame(props16NoP, params16AMInfo, minC, ...
    'chose 16+, above med. att., info treat, no penalty');
params16AMControl = load_parameters('amctrlcommitsX');
game16AMControl = gymGame(props16, params16AMControl, minC, ...
    'chose 16+, above med. att., control');
game16AMControlNoP = gymGame(props16NoP, params16AMControl, minC, ...
    'chose 16+, above med. att., control, no penalty');
params16BMInfo = load_parameters('bminfocommitsX');
game16BMInfo = gymGame(props16, params16BMInfo, minC, ...
    'chose 16+, below med. att., info treat');
game16BMInfoNoP = gymGame(props16NoP, params16BMInfo, minC, ...
    'chose 16+, below med. att., info treat, no penalty');
params16BMControl = load_parameters('bmctrlcommitsX');
game16BMControl = gymGame(props16, params16BMControl, minC, ...
    'chose 16+, below med. att., control');
game16BMControlNoP = gymGame(props16NoP, params16BMControl, minC, ...
    'chose 16+, below med. att., control, no penalty');

% add versions for those who rejected the commitment contracts
paramsNo12AMInfo = load_parameters('aminfonocommitX');
gameNo12AMInfo = gymGame(props12NoP, paramsNo12AMInfo, minC, ...
    'rejected 12+, above med. att., info treat');
paramsNo12AMControl = load_parameters('amctrlnocommitX');
gameNo12AMControl = gymGame(props12NoP, paramsNo12AMControl, minC, ...
    'rejected 12+, above med. att., control');
paramsNo12BMInfo = load_parameters('bminfonocommitX');
gameNo12BMInfo = gymGame(props12NoP, paramsNo12BMInfo, minC, ...
    'rejected 12+, below med. att., info treat');
paramsNo12BMControl = load_parameters('bmctrlnocommitX');
gameNo12BMControl = gymGame(props12NoP, paramsNo12BMControl, minC, ...
    'rejected 12+, below med. att., control');
paramsNo8AMInfo = load_parameters('aminfonocommiteX');
gameNo8AMInfo = gymGame(props8NoP, paramsNo8AMInfo, minC, ...
    'rejected 8+, above med. att., info treat');
paramsNo8AMControl = load_parameters('amctrlnocommiteX');
gameNo8AMControl = gymGame(props8NoP, paramsNo8AMControl, minC, ...
    'rejected 8+, above med. att., control');
paramsNo8BMInfo = load_parameters('bminfonocommiteX');
gameNo8BMInfo = gymGame(props8NoP, paramsNo8BMInfo, minC, ...
    'rejected 8+, below med. att., info treat');
paramsNo8BMControl = load_parameters('bmctrlnocommiteX');
gameNo8BMControl = gymGame(props8NoP, paramsNo8BMControl, minC, ...
    'rejected 8+, below med. att., control');
paramsNo16AMInfo = load_parameters('aminfonocommitsX');
gameNo16AMInfo = gymGame(props16NoP, paramsNo16AMInfo, minC, ...
    'rejected 16+, above med. att., info treat');
paramsNo16AMControl = load_parameters('amctrlnocommitsX');
gameNo16AMControl = gymGame(props16NoP, paramsNo16AMControl, minC, ...
    'rejected 16+, above med. att., control');
paramsNo16BMInfo = load_parameters('bminfonocommitsX');
gameNo16BMInfo = gymGame(props16NoP, paramsNo16BMInfo, minC, ...
    'rejected 16+, below med. att., info treat');
paramsNo16BMControl = load_parameters('bmctrlnocommitsX');
gameNo16BMControl = gymGame(props16NoP, paramsNo16BMControl, minC, ...
    'rejected 16+, below med. att., control');


% store share of population that chose each contract
params8 = load_parameters('commit8X');
mu8 = params8.mu; 
params12 = load_parameters('commit12X');
mu12 = params12.mu; 
params16 = load_parameters('commit16X');
mu16 = params16.mu;


% GENERATE ATTENDANCE RESULTS
% chose 12+ visit contract
mc = game12;
mc.mu = 1; % homogeneous population
mcnp = game12NoP;
mcnp.mu = 1; % homogeneous population
simulate_attendance(mc,mcnp,'allX')

% with hetereogenity along past attendance (above vs. below median)
mc = [game12AM game12BM];
mcnp = [game12AMNoP game12BMNoP];
simulate_attendance(mc,mcnp,'mattX')

% with hetereogenity along past attendance (quartile)
mc = [game12Q1 game12Q2 game12Q3 game12Q4];
mcnp = [game12Q1NoP game12Q2NoP game12Q3NoP game12Q4NoP];
simulate_attendance(mc,mcnp,'qattX')

% with heterogeneity along past attendance (median) & info treatment
mc = [game12AMInfo game12AMControl game12BMInfo game12BMControl];
mcnp = [game12AMInfoNoP game12AMControlNoP game12BMInfoNoP game12BMControlNoP];
simulate_attendance(mc,mcnp,'mattinfoX')

% with heterogeneity along past attendance (quartile) & info treatment
mc = [game12Q1Info game12Q1Control game12Q2Info game12Q2Control ...
    game12Q3Info game12Q3Control game12Q4Info game12Q4Control];
mcnp = [game12Q1InfoNoP game12Q1ControlNoP game12Q2InfoNoP game12Q2ControlNoP ...
    game12Q3InfoNoP game12Q3ControlNoP game12Q4InfoNoP game12Q4ControlNoP];
simulate_attendance(mc,mcnp,'qattinfoX')


% GENERATE WELFARE/EFFICIENCY RESULTS
% under the 12+ visit contract
mc = [game12AMInfo game12AMControl game12BMInfo game12BMControl];
mnc = [gameNo12AMInfo gameNo12AMControl gameNo12BMInfo gameNo12BMControl];
mcnp = [game12AMInfoNoP game12AMControlNoP game12BMInfoNoP game12BMControlNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu12;
    mcnp(m).mu = mcnp(m).mu .* mu12;
    mnc(m).mu = mnc(m).mu .* (1 - mu12);
end
Results12 = compute_efficiency(mc,mnc,mcnp);

% under the 8+ visit contract
mc = [game8AMInfo game8AMControl game8BMInfo game8BMControl];
mnc = [gameNo8AMInfo gameNo8AMControl gameNo8BMInfo gameNo8BMControl];
mcnp = [game8AMInfoNoP game8AMControlNoP game8BMInfoNoP game8BMControlNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu8;
    mcnp(m).mu = mcnp(m).mu .* mu8;
    mnc(m).mu = mnc(m).mu .* (1 - mu8);
end
Results8 = compute_efficiency(mc,mnc,mcnp);

% under the 16+ visit contract
mc = [game16AMInfo game16AMControl game16BMInfo game16BMControl];
mnc = [gameNo16AMInfo gameNo16AMControl gameNo16BMInfo gameNo16BMControl];
mcnp = [game16AMInfoNoP game16AMControlNoP game16BMInfoNoP game16BMControlNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu16;
    mcnp(m).mu = mcnp(m).mu .* mu16;
    mnc(m).mu = mnc(m).mu .* (1 - mu16);
end
Results16 = compute_efficiency(mc,mnc,mcnp);

% export results
export_efficiency_results(Results8, Results12, Results16, 'hetX');


%% Results with a minimal cost draw of -$5

% Set lower bound on support of cost distribution
minC = -5;

% INSTANTIATE GAMES
% chose 12+ visit contract
params12 = load_parameters('commit12V');
game12 = gymGame(props12, params12, minC, 'chose 12+ contract');

% add heterogeneity along past attendance (below vs. above median)
params12AM = load_parameters('amcommitV');
game12AM = gymGame(props12, params12AM, minC, 'chose 12+, above med. att.');
params12BM = load_parameters('bmcommitV');
game12BM = gymGame(props12, params12BM, minC, 'chose 12+, below med. att.');

% add heterogeneity along past attendance (quartiles)
params12Q1 = load_parameters('qfstcommitV');
game12Q1 = gymGame(props12, params12Q1, minC, 'chose 12+, q1 att.');
params12Q2 = load_parameters('qsndcommitV');
game12Q2 = gymGame(props12, params12Q2, minC, 'chose 12+, q2 att.');
params12Q3 = load_parameters('qthdcommitV');
game12Q3 = gymGame(props12, params12Q3, minC, 'chose 12+, q3 att.');
params12Q4 = load_parameters('qfthcommitV');
game12Q4 = gymGame(props12, params12Q4, minC, 'chose 12+, q4 att.');

% add heterogeneity along past attendance (median) & info treatment
params12AMInfo = load_parameters('aminfocommitV');
game12AMInfo = gymGame(props12, params12AMInfo, minC, ...
    'chose 12+, above med. att., info treat');
params12AMControl = load_parameters('amctrlcommitV');
game12AMControl = gymGame(props12, params12AMControl, minC, ...
    'chose 12+, above med. att., control');
params12BMInfo = load_parameters('bminfocommitV');
game12BMInfo = gymGame(props12, params12BMInfo, minC, ...
    'chose 12+, below med. att., info treat');
params12BMControl = load_parameters('bmctrlcommitV');
game12BMControl = gymGame(props12, params12BMControl, minC, ...
    'chose 12+, below med. att., control');

% add heterogeneity along past attendance (quartiles) & info treatment
params12Q1Info = load_parameters('qfstinfocommitV');
game12Q1Info = gymGame(props12, params12Q1Info, minC, 'chose 12+, q1 att., info treat');
params12Q1Control = load_parameters('qfstctrlcommitV');
game12Q1Control = gymGame(props12, params12Q1Control, minC, 'chose 12+, q1 att., control');
params12Q2Info = load_parameters('qsndinfocommitV');
game12Q2Info = gymGame(props12, params12Q2Info, minC, 'chose 12+, q2 att., info treat');
params12Q2Control = load_parameters('qsndctrlcommitV');
game12Q2Control = gymGame(props12, params12Q2Control, minC, 'chose 12+, q2 att., control');
params12Q3Info = load_parameters('qthdinfocommitV');
game12Q3Info = gymGame(props12, params12Q3Info, minC, 'chose 12+, q3 att., info treat');
params12Q3Control = load_parameters('qthdctrlcommitV');
game12Q3Control = gymGame(props12, params12Q3Control, minC, 'chose 12+, q3 att., control');
params12Q4Info = load_parameters('qfthinfocommitV');
game12Q4Info = gymGame(props12, params12Q4Info, minC, 'chose 12+, q4 att., info treat');
params12Q4Control = load_parameters('qfthctrlcommitV');
game12Q4Control = gymGame(props12, params12Q4Control, minC, 'chose 12+, q4 att., control');

% add no penalty versions of the above games
game12NoP = gymGame(props12NoP, params12, minC, 'chose 12+, no penalty');
game12AMNoP = gymGame(props12NoP, params12AM, minC, 'chose 12+, above med. att., no penalty');
game12BMNoP = gymGame(props12NoP, params12BM, minC, 'chose 12+, below med. att., no penalty');
game12Q1NoP = gymGame(props12NoP, params12Q1, minC, 'chose 12+, q1 att., no penalty');
game12Q2NoP = gymGame(props12NoP, params12Q2, minC, 'chose 12+, q2 att., no penalty');
game12Q3NoP = gymGame(props12NoP, params12Q3, minC, 'chose 12+, q3 att., no penalty');
game12Q4NoP = gymGame(props12NoP, params12Q4, minC, 'chose 12+, q4 att., no penalty');
game12AMInfoNoP = gymGame(props12NoP, params12AMInfo, minC, ...
    'chose 12+, above med. att., info treat, no penalty');
game12AMControlNoP = gymGame(props12NoP, params12AMControl, minC, ...
    'chose 12+, above med. att., control, no penalty');
game12BMInfoNoP = gymGame(props12NoP, params12BMInfo, minC, ...
    'chose 12+, below med. att., info treat, no penalty');
game12BMControlNoP = gymGame(props12NoP, params12BMControl, minC, ...
    'chose 12+, below med. att., control, no penalty');
game12Q1InfoNoP = gymGame(props12NoP, params12Q1Info, minC, ...
    'chose 12+, q1 att., info treat, no penalty');
game12Q1ControlNoP = gymGame(props12NoP, params12Q1Control, minC, ...
    'chose 12+, q1 att., control, no penalty');
game12Q2InfoNoP = gymGame(props12NoP, params12Q2Info, minC, ...
    'chose 12+, q2 att., info treat, no penalty');
game12Q2ControlNoP = gymGame(props12NoP, params12Q2Control, minC, ...
    'chose 12+, q2 att., control, no penalty');
game12Q3InfoNoP = gymGame(props12NoP, params12Q3Info, minC, ...
    'chose 12+, q3 att., info treat, no penalty');
game12Q3ControlNoP = gymGame(props12NoP, params12Q3Control, minC, ...
    'chose 12+, q3 att., control, no penalty');
game12Q4InfoNoP = gymGame(props12NoP, params12Q4Info, minC, ...
    'chose 12+, q4 att., info treat, no penalty');
game12Q4ControlNoP = gymGame(props12NoP, params12Q4Control, minC, ...
    'chose 12+, q4 att., control, no penalty');

% add 8+ contract versions (with & without penalty)
params8AMInfo = load_parameters('aminfocommiteV');
game8AMInfo = gymGame(props8, params8AMInfo, minC, ...
    'chose 8+, above med. att., info treat');
game8AMInfoNoP = gymGame(props8NoP, params8AMInfo, minC, ...
    'chose 8+, above med. att., info treat, no penalty');
params8AMControl = load_parameters('amctrlcommiteV');
game8AMControl = gymGame(props8, params8AMControl, minC, ...
    'chose 8+, above med. att., control');
game8AMControlNoP = gymGame(props8NoP, params8AMControl, minC, ...
    'chose 8+, above med. att., control, no penalty');
params8BMInfo = load_parameters('bminfocommiteV');
game8BMInfo = gymGame(props8, params8BMInfo, minC, ...
    'chose 8+, below med. att., info treat');
game8BMInfoNoP = gymGame(props8NoP, params8BMInfo, minC, ...
    'chose 8+, below med. att., info treat, no penalty');
params8BMControl = load_parameters('bmctrlcommiteV');
game8BMControl = gymGame(props8, params8BMControl, minC, ...
    'chose 8+, below med. att., control');
game8BMControlNoP = gymGame(props8NoP, params8BMControl, minC, ...
    'chose 8+, below med. att., control, no penalty');

% add 16+ contract versions (with & without penalty)
params16AMInfo = load_parameters('aminfocommitsV');
game16AMInfo = gymGame(props16, params16AMInfo, minC, ...
    'chose 16+, above med. att., info treat');
game16AMInfoNoP = gymGame(props16NoP, params16AMInfo, minC, ...
    'chose 16+, above med. att., info treat, no penalty');
params16AMControl = load_parameters('amctrlcommitsV');
game16AMControl = gymGame(props16, params16AMControl, minC, ...
    'chose 16+, above med. att., control');
game16AMControlNoP = gymGame(props16NoP, params16AMControl, minC, ...
    'chose 16+, above med. att., control, no penalty');
params16BMInfo = load_parameters('bminfocommitsV');
game16BMInfo = gymGame(props16, params16BMInfo, minC, ...
    'chose 16+, below med. att., info treat');
game16BMInfoNoP = gymGame(props16NoP, params16BMInfo, minC, ...
    'chose 16+, below med. att., info treat, no penalty');
params16BMControl = load_parameters('bmctrlcommitsV');
game16BMControl = gymGame(props16, params16BMControl, minC, ...
    'chose 16+, below med. att., control');
game16BMControlNoP = gymGame(props16NoP, params16BMControl, minC, ...
    'chose 16+, below med. att., control, no penalty');

% add versions for those who rejected the commitment contracts
paramsNo12AMInfo = load_parameters('aminfonocommitV');
gameNo12AMInfo = gymGame(props12NoP, paramsNo12AMInfo, minC, ...
    'rejected 12+, above med. att., info treat');
paramsNo12AMControl = load_parameters('amctrlnocommitV');
gameNo12AMControl = gymGame(props12NoP, paramsNo12AMControl, minC, ...
    'rejected 12+, above med. att., control');
paramsNo12BMInfo = load_parameters('bminfonocommitV');
gameNo12BMInfo = gymGame(props12NoP, paramsNo12BMInfo, minC, ...
    'rejected 12+, below med. att., info treat');
paramsNo12BMControl = load_parameters('bmctrlnocommitV');
gameNo12BMControl = gymGame(props12NoP, paramsNo12BMControl, minC, ...
    'rejected 12+, below med. att., control');
paramsNo8AMInfo = load_parameters('aminfonocommiteV');
gameNo8AMInfo = gymGame(props8NoP, paramsNo8AMInfo, minC, ...
    'rejected 8+, above med. att., info treat');
paramsNo8AMControl = load_parameters('amctrlnocommiteV');
gameNo8AMControl = gymGame(props8NoP, paramsNo8AMControl, minC, ...
    'rejected 8+, above med. att., control');
paramsNo8BMInfo = load_parameters('bminfonocommiteV');
gameNo8BMInfo = gymGame(props8NoP, paramsNo8BMInfo, minC, ...
    'rejected 8+, below med. att., info treat');
paramsNo8BMControl = load_parameters('bmctrlnocommiteV');
gameNo8BMControl = gymGame(props8NoP, paramsNo8BMControl, minC, ...
    'rejected 8+, below med. att., control');
paramsNo16AMInfo = load_parameters('aminfonocommitsV');
gameNo16AMInfo = gymGame(props16NoP, paramsNo16AMInfo, minC, ...
    'rejected 16+, above med. att., info treat');
paramsNo16AMControl = load_parameters('amctrlnocommitsV');
gameNo16AMControl = gymGame(props16NoP, paramsNo16AMControl, minC, ...
    'rejected 16+, above med. att., control');
paramsNo16BMInfo = load_parameters('bminfonocommitsV');
gameNo16BMInfo = gymGame(props16NoP, paramsNo16BMInfo, minC, ...
    'rejected 16+, below med. att., info treat');
paramsNo16BMControl = load_parameters('bmctrlnocommitsV');
gameNo16BMControl = gymGame(props16NoP, paramsNo16BMControl, minC, ...
    'rejected 16+, below med. att., control');


% store share of population that chose each contract
params8 = load_parameters('commit8V');
mu8 = params8.mu; 
params12 = load_parameters('commit12V');
mu12 = params12.mu; 
params16 = load_parameters('commit16V');
mu16 = params16.mu;


% GENERATE ATTENDANCE RESULTS
% chose 12+ visit contract
mc = game12;
mc.mu = 1; % homogeneous population
mcnp = game12NoP;
mcnp.mu = 1; % homogeneous population
simulate_attendance(mc,mcnp,'allV')

% with hetereogenity along past attendance (above vs. below median)
mc = [game12AM game12BM];
mcnp = [game12AMNoP game12BMNoP];
simulate_attendance(mc,mcnp,'mattV')

% with hetereogenity along past attendance (quartile)
mc = [game12Q1 game12Q2 game12Q3 game12Q4];
mcnp = [game12Q1NoP game12Q2NoP game12Q3NoP game12Q4NoP];
simulate_attendance(mc,mcnp,'qattV')

% with heterogeneity along past attendance (median) & info treatment
mc = [game12AMInfo game12AMControl game12BMInfo game12BMControl];
mcnp = [game12AMInfoNoP game12AMControlNoP game12BMInfoNoP game12BMControlNoP];
simulate_attendance(mc,mcnp,'mattinfoV')

% with heterogeneity along past attendance (quartile) & info treatment
mc = [game12Q1Info game12Q1Control game12Q2Info game12Q2Control ...
    game12Q3Info game12Q3Control game12Q4Info game12Q4Control];
mcnp = [game12Q1InfoNoP game12Q1ControlNoP game12Q2InfoNoP game12Q2ControlNoP ...
    game12Q3InfoNoP game12Q3ControlNoP game12Q4InfoNoP game12Q4ControlNoP];
simulate_attendance(mc,mcnp,'qattinfoV')


% GENERATE WELFARE/EFFICIENCY RESULTS
% under the 12+ visit contract
mc = [game12AMInfo game12AMControl game12BMInfo game12BMControl];
mnc = [gameNo12AMInfo gameNo12AMControl gameNo12BMInfo gameNo12BMControl];
mcnp = [game12AMInfoNoP game12AMControlNoP game12BMInfoNoP game12BMControlNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu12;
    mcnp(m).mu = mcnp(m).mu .* mu12;
    mnc(m).mu = mnc(m).mu .* (1 - mu12);
end
Results12 = compute_efficiency(mc,mnc,mcnp);

% under the 8+ visit contract
mc = [game8AMInfo game8AMControl game8BMInfo game8BMControl];
mnc = [gameNo8AMInfo gameNo8AMControl gameNo8BMInfo gameNo8BMControl];
mcnp = [game8AMInfoNoP game8AMControlNoP game8BMInfoNoP game8BMControlNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu8;
    mcnp(m).mu = mcnp(m).mu .* mu8;
    mnc(m).mu = mnc(m).mu .* (1 - mu8);
end
Results8 = compute_efficiency(mc,mnc,mcnp);

% under the 16+ visit contract
mc = [game16AMInfo game16AMControl game16BMInfo game16BMControl];
mnc = [gameNo16AMInfo gameNo16AMControl gameNo16BMInfo gameNo16BMControl];
mcnp = [game16AMInfoNoP game16AMControlNoP game16BMInfoNoP game16BMControlNoP];
for m = 1:length(mc) % rescale mu's as a share of whole population
    mc(m).mu = mc(m).mu .* mu16;
    mcnp(m).mu = mcnp(m).mu .* mu16;
    mnc(m).mu = mnc(m).mu .* (1 - mu16);
end
Results16 = compute_efficiency(mc,mnc,mcnp);

% export results
export_efficiency_results(Results8, Results12, Results16, 'hetV');


%% Helper functions

function parameters = load_parameters(title)
    % reads in parameters estimated in Stata

    file = strcat(OUTPUT,'/parameter_estimates/',title,'.csv');

    % read file into vector
    P = readmatrix(file);

    % set parameter values from vector
    parameters.lambda = P(1);
    parameters.beta = P(2);
    parameters.betatilde = P(3);
    parameters.b = P(4);
    parameters.mu = P(5);

end

function simulate_attendance(commit_models, no_p_commit_models, name)
    % simulate attendance with & without the commitment contract
    
    % average change in attendance
    DaC = 0;
    for i = 1:length(commit_models)
       
        DaC = DaC + commit_models(i).mu .* (commit_models(i).avg_att - ...
            no_p_commit_models(i).avg_att);
        
    end
    
    % average probabilities of success with & without the contract
    prob_c = 0;
    prob_nop = 0;
    for i = 1:length(commit_models)
        
        prob_c = prob_c + commit_models(i).mu .* ...
            commit_models(i).prob_success;
        
        prob_nop = prob_nop + no_p_commit_models(i).mu .* ...
            no_p_commit_models(i).prob_success;
        
    end
    prob_diff = prob_c - prob_nop;
    
    % export results
    latex_command(strcat('DaC',name),DaC,'%1.2f');
    latex_command(strcat('probc',name),prob_c,'%1.2f');
    latex_command(strcat('probnop',name),prob_nop,'%1.2f');
    latex_command(strcat('Dprob',name),prob_diff,'%1.2f'); 
        
end

function export_efficiency_results(results8, results12, results16, name)
    % exports welfare/efficiency outcomes
    
    % for the optimal piece-rate incentive (12+ visit contract)
    latex_command(strcat('Ropt',name),results12.r_opt,'currency');
    latex_command(strcat('DaRopt',name),results12.delta_att_r_opt,'%3.2f');
    latex_command(strcat('DsurplusRopt',name),results12.delta_surplus_r_opt,'currency');
    latex_command(strcat('DbenefitsRopt',name),results12.delta_benefits_r_opt,'currency');
    latex_command(strcat('DcostsRopt',name),results12.delta_costs_r_opt,'currency');
    latex_command(strcat('DeffRopt',name),results12.U_E_r_opt,'currency');
    
    % for the 12+ visit contract
    latex_command(strcat('DaCT',name),results12.avg_delta_a_C,'%3.2f');
    latex_command(strcat('DcommitsurplusCT',name),results12.commit_delta_surplus,'currency');
    latex_command(strcat('DsurplusCT',name),results12.avg_delta_surplus,'currency');
    latex_command(strcat('DbenefitsCT',name),results12.avg_delta_benefits,'currency');
    latex_command(strcat('DcostsCT',name),results12.avg_delta_costs,'currency');
    latex_command(strcat('DeffCT',name),results12.V_E,'currency');
    
    % for the attendance-equivalent incentive (12+ visit contract)
    latex_command(strcat('RattT',name),results12.r_att,'currency');
    latex_command(strcat('DaRattT',name),results12.delta_att_r_att,'%3.2f');
    latex_command(strcat('DsurplusRattT',name),results12.delta_surplus_r_att,'currency');
    latex_command(strcat('DbenefitsRattT',name),results12.delta_benefits_r_att,'currency');
    latex_command(strcat('DcostsRattT',name),results12.delta_costs_r_att,'currency');
    latex_command(strcat('DeffRattT',name),results12.U_E_r_att,'currency');
    
    % for the 8+ visit contract
    latex_command(strcat('DaCE',name),results8.avg_delta_a_C,'%3.2f');
    latex_command(strcat('DcommitsurplusCE',name),results8.commit_delta_surplus,'currency');
    latex_command(strcat('DsurplusCE',name),results8.avg_delta_surplus,'currency');
    latex_command(strcat('DbenefitsCE',name),results8.avg_delta_benefits,'currency');
    latex_command(strcat('DcostsCE',name),results8.avg_delta_costs,'currency');
    latex_command(strcat('DeffCE',name),results8.V_E,'currency');
    
    % for the attendance-equivalent incentive (8+ visit contract)
    latex_command(strcat('RattE',name),results8.r_att,'currency');
    latex_command(strcat('DaRattE',name),results8.delta_att_r_att,'%3.2f');
    latex_command(strcat('DsurplusRattE',name),results8.delta_surplus_r_att,'currency');
    latex_command(strcat('DbenefitsRattE',name),results8.delta_benefits_r_att,'currency');
    latex_command(strcat('DcostsRattE',name),results8.delta_costs_r_att,'currency');
    latex_command(strcat('DeffRattE',name),results8.U_E_r_att,'currency');
    
    % for the 16+ visit contract
    latex_command(strcat('DaCS',name),results16.avg_delta_a_C,'%3.2f');
    latex_command(strcat('DcommitsurplusCS',name),results16.commit_delta_surplus,'currency');
    latex_command(strcat('DsurplusCS',name),results16.avg_delta_surplus,'currency');
    latex_command(strcat('DbenefitsCS',name),results16.avg_delta_benefits,'currency');
    latex_command(strcat('DcostsCS',name),results16.avg_delta_costs,'currency');
    latex_command(strcat('DeffCS',name),results16.V_E,'currency');
    
    % for the attendance-equivalent incentive (16+ visit contract)
    latex_command(strcat('RattS',name),results16.r_att,'currency');
    latex_command(strcat('DaRattS',name),results16.delta_att_r_att,'%3.2f');
    latex_command(strcat('DsurplusRattS',name),results16.delta_surplus_r_att,'currency');
    latex_command(strcat('DbenefitsRattS',name),results16.delta_benefits_r_att,'currency');
    latex_command(strcat('DcostsRattS',name),results16.delta_costs_r_att,'currency');
    latex_command(strcat('DeffRattS',name),results16.U_E_r_att,'currency');
     
end

function plot_att_prob(commit_models, name)
    % plot the average probability of attending each day
        
    % contract threshold
    a_star = commit_models(1).a_star;
    
     % average probability for each day over all naive groups
     probs = zeros(commit_models(1).T,1);
     for i = 1:length(probs)
     
         p = 0;
         for j = 1:length(commit_models)
             
             p = p + commit_models(j).mu .* ...
                 commit_models(j).prob_att_day(i);
             
         end
         probs(i) = p;
     
     end
     
     % average probability without the contract or present bias
     noc_prob = 0;
     noc_nopb_prob = 0;
     for j = 1:length(commit_models)
             
         noc_prob = noc_prob + commit_models(j).mu .* ...
             commit_models(j).F(commit_models(j).beta .* commit_models(j).b);
         
         noc_nopb_prob = noc_nopb_prob + commit_models(j).mu .* ...
             commit_models(j).F(commit_models(j).b);
             
     end
     
     plot(repmat(noc_prob,length(probs),1),'LineStyle','--', ...
         'Color','#D95319');
     hold on
     plot(probs,'LineStyle','-','Color','#0072BD');
     hold on
     plot(repmat(noc_nopb_prob,length(probs),1),'LineStyle','-.', ...
         'Color','#EDB120');
     xticks(linspace(0,28,15));
     xlim([0 28])
     ylim([0 1]);
     xlabel('Day');
     label2 = "With " + num2str(a_star) + "+ visits contract";
     ylabel('Probability of going to the gym');
     legend({'Baseline',label2, 'First best'}, ...
          'location','northwest');
     set(gcf,'color','w');
     fpath = [OUTPUT '/' name '.pdf'];
     fig = gcf;
     fig.PaperPositionMode = 'auto';
     fig_pos = fig.PaperPosition;
     fig.PaperSize = [fig_pos(3) fig_pos(4)];
     print(fig,fpath,'-dpdf');
     close;
        
end

function latex_command(name, value, format)
    % outputs figures to a tex file
    
    if strcmp(format, 'currency')
        curr = java.util.Locale.CANADA; % preserves negative sign
        j = java.text.NumberFormat.getCurrencyInstance(curr); % format
        value = char(j.format(value));
        value = strrep(value,'$','\$');
    else
        value = compose(format, value);
    end
    
    if ismac
        input = strcat('\\\newcommand{\\',name,'}{',value,'}');
    else
        input = strcat('\\newcommand{\',name,'}{',value,'}');

    end

  

    file = [OUTPUT '/simulations.tex'];

    command = strcat('echo ',input,'  >> ',file);

    system(char(command));



end



end