function [m, y, coal] = openrule(n,delta)

% Purpose: Gives the equilibrium outcome for the open rule as
%          described in Baron and Ferejohn (1989), APSR, where
%          n (odd) is the number of players and delta is the
%          discount factor.

% returns: m = number of member in the coalition (excluding the proposer)
%          y = the share to the proposer
%          coal = the share to the other coalition members

% written by:
% Guillaume R. Frechette
% Ohio State University
% Department of Economics
% frechette.6@osu.edu

if n/2==round(n/2), error('n should be odd'); end
if delta<=0, error('delta should be greater than 0'); end
if delta>1, error('delta should be less than or equal to 1'); end

min = ( n - 1 ) / 2;
max = n-1;

argmax = min;
maxV = 0;

for m = min:max;
   B = 1 - ( ( 2*m - n + 2 ) / m )*( 1 - ( m / ( n - 1 ) ) )*...
      delta - ( ( n - m - 2 ) / m )*( 1 - ( ( m + 1 )/( n - 1 ) ) )*...
      ( 1 - ( m / ( n - 1 ) ) )*delta^2;
   gamma = ( delta / B )*( ( m / ( n - 1 ) ) +...
      delta*( 1 - m / ( n - 1 ) )*( ( n - m - 2 ) / m )*( 1 / ( n - 1 ) ) );
   V = ( m / ( n - 1 ) ) / ( 1 + delta*( m^2 / ( n - 1 ) ) -...
      ( delta^2 )*( 1 - m / ( n - 1 ) )*( ( 1 / ( n - 1 ) ) +...
      ( 1 - ( m + 1 )/( n - 1 ) )*gamma ) );
   if V > maxV
      argmax = m;
      maxV = V;
   end
end

m = argmax;
y = 1 - m*delta*maxV;
coal = delta*maxV;