## 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:
- 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

$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