Forecasting with game theory? Im familiar with sequential games in game theory. Specifically Im interested in if one can forecast using such a method?

what specific models I should know about if I can forecast using game theory?
As @denesp has pointed out making real precise predictions with game theory is difficult because it is hard to gather data on payoffs and behavior under uncertainty, not to mention the fact that game theory typically assumes individual rationality (although the behavioral game theory referenced by @HerrK above loosens some of those requirements)
Of course that has never stopped people from trying. At least in environmental and resource economics there are plenty of papers looking into dynamic games that are calibrated to make some general (but perhaps not very accurate) predictions. This overview paper from Hannesson includes a lot of references to such papers in fisheries, a similar but older overview paper on transboundary polution was written by Finus.
Given what you're interested in, I'd look into repeated games with sequential moves. In a very simple set-up it could work out like this: each period the employers make an offer, and the unions then decide to either go on strike (hurting the employers and employees and moving to another round) or accept (which ends the game). As said, I don't think it will give you an accurate prediction, but it would perhaps give you some insights in the motives at work.
The problem with such a game set-up is that

I'd expect both the employers and unions to fall for sunk cost arguments (can't quit now, we've gone so far...), which a rational player wouldn't do
Repeated games in the presence of uncertainty often have multiple equilibria that can be supported by trigger strategies. Although these trigger strategies are subgame perfect, they are also non-renegotiation proof, and that is probably exactly what you're interested in.

Hope that helps.