ps3_s_mn.gms : Parts Supply Problem w/ 3 Types w/ Monotonicity Constraint

**Description**

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. <a href="http://r-center.grips.ac.jp/DiscussionPapersDetails/247/#">http://r-center.grips.ac.jp/DiscussionPapersDetails/247/#</a>

**References**

- Hashimoto, H, Hamada, K, and Hosoe, N, A Numerical Approachto the Contract Theory: The Case of Adverse Selection. GRIPS Discussion Papers, National Graduate Institute for Policy Studies, 2012.
- Itoh, H, A Course in Contract Theory. Yuhikaku, Tokyo, 2003.

**Small Model of Type :** NLP

**Category :** GAMS Model library

**Main file :** ps3_s_mn.gms

$Title Parts Supply Problem w/ 3 Types w/ Monotonicity Constraint (PS3_S_MN,SEQ=366) * 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 licd(i) incentive compatibility constraint mn(i) monotonicity 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; licd(i)..w(i)-theta(i)*x(i) =g= w(i+1)-theta(i)*x(i+1); mn(i).. x(i) =g= x(i+1); * Setting Lower Bounds on Variables to Avoid Division by Zero x.lo(i)=0.0001; * Defining and Solving the Model Model SB4 /all/; Solve SB4 maximizing Util using NLP; * The Case w/ alternative p(i) p("0") =0.30; p("1") =0.10; p("2") =0.60; Solve SB4 maximizing Util using NLP; * The Case w/ alternative theta(i) * Assumning the original p(i) p("0") =0.20; p("1") =0.50; p("2") =0.30; * Assumning alternative theta(i) theta("0")=0.10; theta("1")=0.30; theta("2")=0.31; Solve SB4 maximizing Util using NLP; * End of Model