# ICE Project: "An Optimal Rule of Thumb for Pollution Permits Allocation"  
# by Mar Reguant and Eva Dardati
# August, 2008
#
# Questions or comments to mreguant@mit.edu
#
# References: Please, have a look at Sven Leyffer, Todd Munson and Karl Schmedders tutorials
# Model based on "Cournot Game with Learning and Investment" in K. Schmedders slides and
# "Incorporating oligopoly, CO2 emissions trading and green certificates into a
# power generation expansion model" by Pedro Linares et al, Automatica.

reset;
#option log_file "planner_knitro.log";

# KNITRO
model planner_knitro.mod;
option solver knitroampl;
fix rho := 1.5;
solve;
unfix rho;
solve;

display rho;
display W[10,10];

# PRINTING
# printf "" > q.out;
# printf "" > x.out;
# printf "" > Pi.out;
# for{i in firms, (v,w) in states} {
	# printf "%d , %d , %d , %f \n", i, v, w, q[i,v,w] >> q.out;
	# printf "%d , %d , %d , %f \n", i, v, w, x[i,v,w] >> x.out;
	# printf "%d , %d , %d , %f \n", i, v, w, Pi[i,v,w] >> Pi.out;
# }

# GRID EVALUATION OF WELFARE FUNCTION
# set eval := 1 .. 60;
# param Wrule{eval};

# for {m in eval} {
	# fix rho := m*0.05;
	# solve;
	# let Wrule[m] := W[10,10];
# }

# display Wrule;
# printf "" > Wrule.out;
# for{m in eval} {
	# printf "%f , %f  \n", m*0.05, Wrule[m] >> Wrule.out;
# }

# CHECKING SOC CONDITIONS
# We already know they hold for q
# For x:
# var d2Pr{i in firms, (v,w) in states, t in transitions} =
		# (if t = -1 then 2*(theta[i,v,w]-2)*(theta[i,v,w]^2)/(theta[i,v,w]*x[i,v,w]-theta[i,v,w]+2)^3) +
		# (if t = 0 then  2*(theta[i,v,w]^2)/(theta[i,v,w]*x[i,v,w]-theta[i,v,w]+2)^3) +
		# (if t = 1 then  2*(1-theta[i,v,w])*(theta[i,v,w]^2)/(theta[i,v,w]*x[i,v,w]-theta[i,v,w]+2)^3) ;
# var soc{i in firms, (v,w) in states} =
	# -2*d + delta*sum{t in transitions, k in transitions} d2Pr[i,v,w,t]*Pr[nextw(i),w,v,k]*V[i,v + t,w + k];
# display soc;