"I want our team to work our hardest and do our best." "I want our team to win the contract." Are these two statements the same thing? I don't think so. There are so many ways a team can win a contract but stating "I want us to win" puts the situation into a win/lose category.
There are two (probably more) ways for the "win the contract" scenario to come about. The first is that your team wins. The other is that the other team loses.
There can be a concentration on hoping the other team does things such that they lose and ways to make the other team lose. The focus is a negative one and energy is spent concerning the other team.
Their lead worker gets hurt, an important paper gets mislaid, your team steals important confidential information from them that gives you an edge, your team gives false information about the other team that influences the purchaser's opinion and decisions, you promise things you cannot fulfill knowing that the other team wouldn't make such promises, and so forth.
These may be "skills" and "techniques" that you can use many times in the future, but they do not make your team better. They do not make your product better. It may improve your "bottom line" in the short-term but they do not make your team continue to improve for the long haul.
How about the other way -- "I want our team to work our hardest and do our best." First, it may still end up being a win/lose but it does not preclude the possibility of win/win. Next, how do you achieve these goals? The goals of "working our hardest and doing our best"? You are now concentrating on your own team efforts. That doesn't mean you close your eyes and ears to what the competition is doing -- that is a legitimate part of work. But you are concentrating on your own team. Keeping realistic work/life balance in mind and the reality that overextending is counter-productive, you try to make each 8 hours of work include 8 hours of useful work. And, within that work time, you want to help your team function at their best. People work according to their strengths, overhead is minimized, obstacles are removed, and coordination and communication is made as directly useful as possible.
You can, of course, substitute in the words appropriate for other competitive situations in life -- personal, business, political, and so on.
At the end of the period, you will have gotten the contract or not. But if you have worked hard and done your best then you won't have any regrets. You can shake the hands of your competitors, smile, and say "Congratulations. Wait until next time." And sleep well.