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ps3_f.gms : Parts Supply Problem w/ 3 Types w/o Asymmetric Information


Hideo Hashimoto, Kojun Hamada, and Nobuhiro Hosoe, "A Numerical Approach
  to the Contract Theory: the Case of Adverse Selection", GRIPS Discussion
  Paper 11-27, National Graduate Institute for Policy Studies, Tokyo, Japan,
  March 2012.

 http://r-center.grips.ac.jp/DiscussionPapersDetails/247/#

References:
Small Model of Type: NLP
$Title Parts Supply Problem w/ 3 Types w/o Asymmetric Information (PS3_F,SEQ=363) * Hideo Hashimoto, Kojun Hamada, and Nobuhiro Hosoe, "A Numerical Approach * to the Contract Theory: the Case of Adverse Selection", GRIPS Discussion * Paper 11-27, National Graduate Institute for Policy Studies, Tokyo, Japan, * March 2012. * * http://r-center.grips.ac.jp/DiscussionPapersDetails/247/# Option limcol=0,limrow=0; * Definition of Set Set i type of supplier /0,1,2/; Alias (i,j); * Definition of Parameters Parameter theta(i) efficiency /0 0.1 1 0.2 2 0.3/ p(i) probability of type /0 0.2 1 0.5 2 0.3/; Scalar ru reservation utility /0/; * Definition of Primal/Dual Variables Positive Variable x(i) quality b(i) maker's revenue w(i) price; Variable Util maker's utility; Equation obj maker's utility function rev(i) maker's revenue function pc(i) participation constraint; * Specification of Equations obj.. Util =e= sum(i, p(i)*(b(i)-w(i))); rev(i)..b(i) =e= x(i)**(0.5); pc(i).. w(i)-theta(i)*x(i) =g= ru; * Setting Lower Bounds on Variables to Avoid Division by Zero x.lo(i)=0.0001; * Defining and Solving the Model Model FB3 /all/; Solve FB3 maximizing Util using NLP; * End of Model