Once you get rid of I win = you lose, many new horizons open up. Cooperation can take the form of trade associations, referrals, virtual partnerships, subcontracting arrangements, and more. These are all different ways of achieving the same result: With enough work to go around, you can help each other.
Professional associations offer a number of benefits: sharing resources through joint purchasing power, learning from those who've gone before (from both their successes and their failures or mistakes), building the overall market, or simply having someone you can comfortably talk shop with or ask for advice on a problem client.
If you have too much work, farm some out to your competitors in a subcontractor arrangement. You pay them, the client pays you somewhat more, and you're assured that if you have more work than you can handle, not only do you keep the client but you get the work done by someone you can trust to do it right.
Or create a virtual partnership. Here, you actually join forces with a competitor to do a project together, kind of like a joint venture except that you dissolve the partnership once the job is complete.
Say you're offered a project with a short deadline, too large for you to do completely within your own company. If you can work with other shops to do pieces of it and then assemble the entire project together as a finished whole, everyone ...