Hi all,
We have a problem and appreciate if you guys could help us implementing it. Long story short, this is a GNEP (Generalized Nash Equilibrium Problem) in which each player tries to maximize its own profit subject to some constraints. Player k would maximize the following problem :
Max π_k =∑_r∑_s ∑_c∑_p f_(r,s,p.c) *((L_(p.k)^rs)/(L_p^rs ))
Subject to:
∑_c∑_p f(r,s,p,c) =Q(r,s) ∀r,s
∑_s∑_r∑_c∑_p f_(r,s,p,c)*ε_(r,s,j,p) ≤ C_j^k ∀j,k
f_(r,s,p,c) ≥ 0 ∀r,s,p,c
The problem is to finding optimal f_(r,s,p,c) . As we see above, variables corresponding to other players DO EXIST in both constraints and objective function of player k. To solving this GNEP we write Karush-Kuhn-Tucker (KKT) system of each k player with corresponding Lagrangian multipliers (τ(r,s),η(r,s) ,µ(j,k )). KKT conditions are then transformed into the following Linear Complementary problem(LCP):
0≤F_k (X)⊥ X^k≥0
We coded this problem into GAMS 24.1.2 and solve it using PATH solver.
Our GAMS code is:
positive variables
f(r,s,p,c)
tau(r,s)
eta(r,s)
mu(j,k)
;
equations
co1(r,s,p,k)
co2(r,s)
co3(r,s)
co4(j,k)
;
co1(r,s,p,k) . . (L_(r,s,p,k)/(L_(r,s,p) )-τ(r,s)+η(r,s)-∑_j ϱ_(j,k)* ε_(r,s,j,p) =g= 0 ;
co2(r,s) . . Q(r,s) - ∑_c∑_p f_(r,s,p,c) =g= 0 ;
co3(r,s) . . ∑_c∑_p f_(r,s,p,c) - Q(r,s) =g= 0 ;
co4(j,k) . . C_(j,k) - ∑_s∑_r∑_c∑_p f_(r,s,p,c)* ε_(r,s,j,p) =g= 0 ;
Model GAME /co1.f , co2.tau, co3.eta, co4.mu / ;
option mcp = path ;
solve GAME Using mcp ;
The model status is Locally Infeasible. Do you have any comments on this?
All the best,
Danesh