% Simulate Hawk-Dove investment game by Cho and Jang (2024)
% This is generated March 28, 2023
% The file is written by Dr. Jang, T.-S.

clear all; close all;

num = 10000;
tt = 1000;
ret_norm = 0.1;
ret_crisis = -1.0;
ret_safe = 0.04;
ret_bar = 0.8;


wealth_int = 1000;

agent_beta = [];

% initial risky asset ratio for individual investors
for ii = 1:num

    agent_beta(ii,1) = ii/num; % initial risky asset
    agent_wealth(ii,1) = wealth_int;

end

average_beta = mean(agent_beta);
disp(average_beta);
wealth_risk = 0;
wealth_safe = 0;

Gam_count = 0;

for jj = 1:tt

    wealth_risk = 0;
    wealth_safe = 0;

    if average_beta < ret_bar

        glob_state = 0;   % normal state
        ret = ret_norm;

    else 
    
        glob_state = 1;   % crisis state
        ret = ret_crisis;
        Gam_count = Gam_count + 1;
        disp(jj);

        %for ii = 1:num

        %    agent_wealth(ii,1) = wealth_int;

        %end

    end


    for ii = 1:num

        agent_wealth(ii,1) = agent_wealth(ii,1)*(agent_beta(ii,1)*(1+ret) + (1-agent_beta(ii,1))*(1+ret_safe));
        wealth_risk = wealth_risk + agent_wealth(ii,1)*agent_beta(ii,1);
        wealth_safe = wealth_safe + agent_wealth(ii,1)*(1-agent_beta(ii,1));

        agent_wealth0(ii,jj) = agent_wealth(ii,1);

    end

    %agent_wealth0(jj,1) = sum(agent_wealth);
    %wealth_risk0(jj,1) = wealth_risk;
    %wealth_safe0(jj,1) = wealth_safe;

    kk(jj,1) = 1 - ((1+ret_norm)/(ret_norm-ret_safe))*(Gam_count/jj);
    gamma0(jj,1) = jj/Gam_count;
   
    average_beta = wealth_risk / (wealth_risk + wealth_safe);    

    beta_hist(jj,1) = average_beta;

end

figure;
subplot(1,2,1); plot(beta_hist); title('Numerical Simulation of Average Beta');
subplot(1,2,2); plot(agent_wealth); title('Wealth Distribution');