Offer something they dont have! And lots of advertisement. I know it may be expensive, but it is really important to have people who heard of your video game so it can be credible. Make sure you have great programmers because EA and Activision make amazing games and it's hard to compete with big companies like them, but its very possible. Try to target the newer game consoles and more popular.
Best Wishes on your start-up!
To compete with giants one should focus on the current market trend and develop same products like sports and multiplayer game are a huge hit in market, the next thing to keep in mind is to develop games with high quality video and have a penetrative price in the market, little advertisement is required to make the company's presence felt.