...and encourage him to keep trying until he catches up with us because by slowing down every time he is left behind I am making him less competitive and less prepared for real life scenarios.
You make a couple of assumptions here:
- You assume that competitiveness is an important character trait
- You assume that what happens in video games has a strong influence on someone's behavior in real life
- You assume that it's important that your son starts learning this this when he's three years old.
What should I do?
I'd first give these three assumptions a bit more thought.
Number one is a personal belief; other people have other priorities. So it's not right or wrong, it depends on how important this is to you. But think about what they teach kids in kindergarden.
Number two is a much debated question, but from what I've read, it seems clear that expressed like this, it's much too simple. Video games do not have such a strong influence on everyone's real life behavior. If they did, we'd be absolutely swamped by teenagers and young men running amok with guns. It seems like what video games mostly teach is fast reaction times and an ability to quickly prioritize objectives.
Finally, number three gives me a bit of pause. I'd think that at this age, it's much more important for your son just to have you there to play with to develop a range of different skills. These skills range from social skills over emotional development to motor skills. Personally, competitiveness doesn't strike me as something that's very important to develop at age 3 or 4. Also, video games are severely limited in the range of skills they can help develop. Real-life human interaction is much, much more broad.
So I'd forget about thinking what kinds of skills or character traits a computer game will or will not develop, and just use the games for having a bit of fun together. I really wouldn't worry one way or the other about the influence of staying behind with him or racing ahead on his competitiveness. But I'd make sure that video game sessions are, while fun, fairly short at least at his age, and just one of lots of activities you do together.