You've got limited time and limited resources. Instead of thinking about the market at large, think about the market segments and companies where you have the highest probability of generating a deal. Use LinkedIn and other social media tools to find connections with anyone you can find at the companies you are contemplating, then narrow the field down to a reasonable number of target companies. Use your connections to get introductions, and just ask basic questions like, "Hey, who in your company would be the right person to talk to about a branded game?" In my experience people generally want to help, as long as you're gracious and respectful of their time.
It took me a long time to realize that transactions between businesses aren't really transactions between businesses. They're transactions between individuals. But transactions don't occur out of the blue. They are an outgrowth of the process of getting to know each other, getting comfortable with each other, and ultimately trusting each other. So once you find the right person inside each of your target companies, give them a little something up front as a gesture of good faith. Maybe that's a detailed demo specifically tailored to their brand. Whatever it is, establish that you're not just trying to come to them with your great idea, seeking to cash in on their brand. Show that person you're interested in helping them win at whatever their job is inside the organization, that you see this as a win-win.
I'm not a lawyer, but I can tell you that in my experience anything beyond an NDA is only going to slow down the process. Too much involvement from their legal department up front will put your contact on guard and give him or her the impression that you're more interested in guarding your interests than in helping them out. If your idea is good enough, it will almost always be faster and easier to work with you than to take off with your idea and have someone else do it. A lot of entrepreneurs focus on the risk associated with working with large companies and fail to recognize just how slow and cumbersome the big guys really are.
- Pick a small number of target companies that you think you can actually get inside
- Find a person inside each company who needs what you provide and has the budget authority to spend on it; work to make the deal advance that person's goals as well as your own
- Worry about missing the opportunity, not about getting screwed
Best of luck!