ps10_s.gms : Parts Supply Problem w/ 10 Types 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. http://www.grips.ac.jp/r-center/en/discussion_papers/11-27/

**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 :** ps10_s.gms

```
$Title Parts Supply Problem w/ 10 Types & w/ Asymmetric Information (PS10_S,SEQ=368)
* 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://www.grips.ac.jp/r-center/en/discussion_papers/11-27/
Option limcol=0,limrow=0;
* Definition of Set
Set i type of supplier /0*9/;
Alias (i,j);
* Definition of Parameters
Parameter
theta(i) efficiency
p(i) probability of type;
theta(i)=ord(i) /card(i);
p(i) =1 /card(i);
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;
* 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);
* Setting Lower Bounds on Variables to Avoid Division by Zero
x.lo(i)=0.0001;
* Defining and Solving the Model
Model SB_lic /all/;
Solve SB_lic maximizing Util using NLP;
* End of Model
File sol /solution_lic.csv/;
put sol;
sol.pc=5;
sol.pw=32767;
put "type" "x.l" "w.l" "b.l" "prob" "theta"/;
loop(i,
put i.tl x.l(i):20:10 w.l(i):20:10 b.l(i):20:10 p(i):20:10 theta(i):20:10/;
);
put "Util" Util.l:20:10 //;
put "Shadow price of IC(i,j)" /;
put "True type"; put "LICD" /;
loop(i, put i.tl licd.m(i):20:10; put /;);
* end
```