I'd argue no - mainly because there is an incentive for a cartel system to develop, again we are talking about a Ceteris paribus situation and it depends on the particular market in question, for example if the particular market is price sensitive, then accruing costs necessary to support innovation would mean a loss of market share to the other competitor.
This ambiguity in the question means it's hard to be specific but I'd be interested in finding out more about your thought process and perhaps an example and would genuinely enjoy having this discussion with you Revaz Lordkipanidze