ps2_f_s.gms : Parts Supply Problem w/ 2 Types w/o and w/ Asymmetric Information

**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 :** ps2_f_s.gms

$Title Parts Supply Problem w/ 2 Types w/o & w/ Asymmetric Information (PS2_F_S,SEQ=358) * 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 /eff, inf/; Alias (i,j); * Definition of Parameters Parameter theta(i) efficiency /eff 0.2 inf 0.3/ p(i) probability of type /eff 0.2 inf 0.8/; 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 ic(i,j) incentive compatibility 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; ic(i,j)..w(i)-theta(i)*x(i) =g= w(j)-theta(i)*x(j); * Setting Lower Bounds on Variables to Avoid Division by Zero x.lo(i)=0.0001; * Defining and Solving the Model Model FB1 /obj,rev,pc/; Solve FB1 maximizing Util using NLP; Model SB1 /obj,rev,pc,ic/; Solve SB1 maximizing Util using NLP; * End of Model