In most systems, there are varying degrees and types of cooperation and competition. There is a difference between a system in which cooperation happens merely within a framework of competition, and a system in which competition occurs only within a framework of cooperation.
In the first type of system, where competition is dominant, we have examples like warfare and corporations fighting for market share. In these examples, groups of people cooperate, but only within their own groups. Their groups then compete with one another, attempting to destroy the other group. Cooperation within each group (whether the army or the company) makes that group stronger, and more able to outcompete their rival. However, because competition is dominant, the resulting system is that many of those involved (the soldiers killed or the employees laid off) will end up suffering.
On the other hand, attempts can be made to build a system where cooperation is dominant, without harming any individuals. Take memetic competition, for example: societies with different memeplexes have different levels of success. When you have competition at the memeplex level and cooperation at the individual level, it doesn't hurt individuals, merely memeplexes. The memeplexes that work poorly are simply allowed to go extinct, but individuals are taught / converted to the various more successful memeplexes.
Similarly, it is possible to create competition between products, while maintaining cooperation between producers. In other words, producers share technology and "trade secrets" but they are free to produce different products. The products then compete for consumers - the ones nobody likes are allowed to go extinct. However, the benefits to society or industry resulting from the better products are given to all the producers, thus giving them an incentive to continue to cooperate, rather than hide their trade secrets or trying to sabotage their competition.