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