Ramsey policy, osr or else can solve optimization problem if there is only one objective. Is it possible to solve the optimization problem if there are two objectives, like a NE problem with two players?

In one way, I set up a lagrangian equation for each player and put in dynare the FOCs wrt variables and lagrangian multipliers. However, I had a problem in finding the steady state. I am worried the more equations I code, the harder to find the steady state. So I was wondering if there is some other ways to solve a problem with simultaneous several optimization objectives. Cheers!

There is not automated routine for things like this. The way you suggest seems correct to me. Finding the steady state is always one of the hardest parts. You should try to compute an analytical steady state if possible. If that is impossible, try the unstable version with

Also, run model_diagnostics on the simple version to see if there are any obvious problems.

Thanks for the kind advice. Just to follow up, how is solve_algo=4 special from other approaches, since I only found algo = 1,2,3 in the user guide?

It is a different algorithm (trust-region) implemented in the unstable version (to be released in 4.5). You cannot fund it in the user guide as the user guide was written before it was added to Dynare. It is not “special” but often shows a good performance.