'on the market' is acceptable here? If any native speaker could answer I'd be grateful.
That ("on the market") sounds odd to me, like competition is something you could buy. Even though I speak British English I agree with the American usage described here: http://www.merriam-webster.com/dictionary/market
You need to use 'in' here. "On the market" is used as a phrase meaning "for sale."
This sentence could also be "We need to have competition in the marketplace."
Good point, Oinophilos, but Duo wouldn't accept "market place." (Which is another way of writing "marketplace.") I'm reporting.
What about "we need to compete in the market "?
I was thrown by the idea. I guess it must be a government regulator talking about a wished-for situation.
what about "--- at the market"?
"in" sounds odd to me ....
I think "at" would only be applicable when speaking about an actual marketplace, like a farmer's market with vegetable stalls, for example.
It's funny that 'concorrência' means 'competition', because 'concurrence' means 'agreement' in English.
"To have" is not necessary in English