It would be ridiculous for various countries on the earth to let their rivalry get in the way of learning all we can about space as it is our last frontier and one that may save us all in centuries to come. We need to collaborate and put all our scientific knowledge together.
Yes, the space race is a chance for countries to collaborate, because it is very hard and expensive to have a space program in each country. The International Space Station is a good example of that collaboration. As we venture out into the universe, each country will only represent the earth, in the end.
It is true that the race to space gives countries an opportunity to work together toward shared interests, but we should not be fooled by the overall strategies of countries. In what international relations experts refer to as a form Machiavellian realism, countries compete on the national stage for supremacy. The United States has historically been a major player in the space race, and its desire to act as a global hegemon have been openly stated in documents like the Project for the New American Century. Joan Johnson-Freese has pointed out that US is currently on the path to dominate space as well, and so any efforts toward cooperation on international space technologies and efforts should be viewed with a healthy dose of skepticism. In the end, the chance to collaborate is there and breakthroughs in technological and human achievement will certainly result, but if the underlying strategies which nations employ to gain military and economic supremacy over one another is not addressed, then space collaboration will be nothing more than a joint effort to create self serving strategic advantage in an unstable world.
A space race would be an excellent opportunity for countries to collaborate. Most space projects are too large and expensive for a single country to handle, so it would be necessary for many countries to contribute. In this way, countries could collaborate in a peaceful manner that would benefit mankind.
Space race is not a chance for countries to collaborate. It is just an opportunity for countries to show off who has better technology and who can get first to whatever planet or solar system they have on their agenda. To put it in better perspective, space race goes against other countries. The United States used it in the past to prove to the Russians how much more technologically advanced they were.