ps2_f_inf.gms : Parts Supply Problem w/ Inefficient Type w/o 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_inf.gms

$Title Parts Supply Problem w/ Inefficient Type w/o Asymmetric Information (PS2_F_inf,SEQ=361)

* 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        /inf/;
* Definition of Parameters
Parameter
        theta(i)        efficiency      /inf    0.3/;
* Definition of Primal/Dual Variables
Positive Variable
        x(i)            quality
        b(i)            maker's revenue
        c(i)            cost;
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, (b(i)-c(i)));
rev(i)..b(i) =e= x(i)**(0.5);
pc(i).. c(i)-theta(i)*x(i) =e= 0;

* Setting Lower Bounds on Variables to Avoid Division by Zero
x.lo(i)=0.0001;

* Defining and Solving the Model
Model FB1 /all/;
Solve FB1 maximizing Util using NLP;

Parameter
                db(i)   derivative of b
                w(i)    price
;
db(i)   =0.5*x.l(i)**(-0.5);
w(i)    =c.l(i);

Display x.l, b.l, c.l, util.l, db, w;
* End of Model