Hello friends
Recently I read a paper written by Xuan Liu and Antonio J. Conejo. In this paper, they have 3 minimization problems. to find the equilibria, they converted these 3 optimization problems to their KKT equivalent and then added one auxiliary optimization. altogether, there would be one optimization problem (the auxiliary) along with the KKT of the former three optimizations.
I can model such a system using PATH solver in GAMS like a Mixed Complementarity Problem (MCP) format, but I am wondering if it is possible to use EMP to find equilibria, instead of the equilibrium.

If I model the 3 optimizations in EMP Equilibrium, does GAMS return any first equilibrium it may encounter? or it returns the equilibria?
In many cases working with ‘EMP equilibrium’ , I have received “other error” message or “Solution found” just by changing the input data! Even sometimes I am sure about the availability of feasible solutions, but still I get “Other error” .is it related to the availability of equilibria or what?

I’m afraid if I model 4 optimizations in the ‘EMP equilibrium’, GAMS there is no way to define which ones are the main problems and which one is the auxiliary.

Thank you very much for your help and consideration

As I understand it, you have 3 follower agents, each of whom solves their own optimization model, and one leader agent, also with an optimization model. You can do this in EMP: you formulate the model as a bilevel program.

In your post you mention several times the search for equilibria vs. an equilibrium. For this problem, the follower models will be reformulated as KKT conditions internally, resulting in an MPEC. The MPEC solvers in GAMS don’t do an exhaustive search to find all equilibria: they will return the first solution point found.

Dear Steve
I’m very grateful for your help. You not only answered my question but also showed a better way to pursue my analysis.
Wish you the best
Iman