\$title Parts Supply Problem w/ 2 Types w/o & w/ Asymmetric Information (PS2_F_S,SEQ=358) \$onText 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/ Keywords: nonlinear programming, contract theory, principal-agent problem, adverse selection, parts supply problem \$offText option limCol = 0, limRow = 0; Set i 'type of supplier' / eff, inf /; Alias (i,j); 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"; 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; Model FB1 / obj, rev, pc / SB1 / obj, rev, pc, ic /; solve FB1 maximizing Util using nlp; solve SB1 maximizing Util using nlp;