If an organization has a philanthropist that agreed to match every dollar donated.
If you give $100, and he matches your $100. Do you get reward for $200 or $100?
Had you not given your $100, neither would he...(unless some else donated $100)
I'm going to have to step WAY back, because this answer depends on adjusting one of the assumptions behind the question and ask you to visit the answer I gave to "Weighing mitzvot/aveirot".
I wrote "Yishmael was repaid in terms of 'ba'asher hu sham -- as he was there'. The way your soul stands at that moment is the direct cause of reward or punishment." And "The greater the effort and sacrifice, the bigger the change in "ba'asher hu sham -- as you are there", when being judged."
So it depends on how the matching funds change your experience, which in turn shapes the act's impact on your soul.
As the mishnah puts it, "be [as] aware of a "light" mitzvah as with a weighty one, for you don't know the reward for [each of the] mitzvos." (Avos 2:1)