A style of dialog or debate in which the objective of each person is to have ''their'' idea win, with as little modification as possible.

One example of this style of debate is (American) high school and college debating.

I have read that managers sometimes set up this type of debate among their underlings, to explore an issue.

When someone plays devil's advocate, they are using this style of debate.

This is one of the AlternativesToPositiveDialog.  In positive dialog (I think) the objective is to come to a civil consensus.  There are advantages and disadvantages to both styles of dialog/debate.

I suppose we can apply this term (SurvivalOfTheFittestDebate) to a single conversation, lasting an hour or two, or to a longer battle between ideas, lasting years or decades.

The below comments seem to address both the style of debate, and the mindset behind it.

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Assumptions:
 
1) An existing idea is better and the new idea can't possibly work, and if it does, it is less desirable. The better, already existing idea wins, as is, or by adjusting only the minimum amount needed to survive. 

2) The ideas must compete. The alternative ideas must prove in trials and tests that there exists a preference based on performance and effectiveness and that the preferred deserves to be used over its alternative(s).

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Propositions for Opponents of the new Idea: 

1) If an idea is an improvement or enhancement of an old idea that has components or areas that threaten an existing component or area, it is to be resisted and opposed for reasons of self preservation. Those whose vested interests are at stake are to employ opposition based not on opposing its strengths, but by emphasizing and amplifying its weaknesses.

2) If an idea is dependent on support from artifacts in the control of its opponents, support should be modified as to make the new idea inoperative or inferior. 

3) If an idea is such a radical change that its adoption has more negative results due to its usage affecting existing ideas which are not in competition, encourage opposition from those idea proponents. Do not reveal any features of the idea that would enhance or improve the non-competitive ideas and allow support from that quarter.

4) If the idea has support from areas over which you have some influence, discourage that support by any means that might be effective.
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See PropositionsForProponents