function []=Pure_Games(W,s,MaxT)
%
% Pure_Games(W, s0, MaxTime)
%    where W is a 2x2 matrix of the payoff to the two strategies.
%    s0 is the initial ratio of strategy 1 in the population
%    MaxTime is the duration of the dynamics.
%

if nargin<3
    MaxT=100;
    if nargin<2
        s=1e-3;
        if nargin<1
            W=[1 0; 1.5 0.7];
        end
    end
end

[T P]=ode45( @(t,y)diff_equations(t,y,W), [0 MaxT], s);

subplot(2,1,1);
plot(T,P,'k','linewidth',1);
xlabel 'Time'
ylabel 'Proportion of strategy s in population'

subplot(2,1,2);
h=plot(T,P.*P*W(1,1)+P.*(1-P)*W(1,2)+(1-P).*P*W(2,1)+(1-P).*(1-P)*W(2,2),'b','LineWidth',1); 
xlabel 'Time'
ylabel 'Mean population payoff'

end

function [ds]=diff_equations(t,s,W)

ds=s*(1-s)*(s*W(1,1)+(1-s)*W(1,2) - s*W(2,1) - (1-s)*W(2,2));

end