Game studios do not allow this, even if they are using a commercial engine such as Unity 3D which can convert from any tool to their own format.
The reason being that assets need to be shared between artists and it doesn’t make sense for half of them to be in 3D Studio Max and the other half in Maya. Every artist is required to stick to the same tool.
I went to a conference talk by one of Epic's character artists, and he spoke of having the choice of using Max/Maya/Mudbox/ZBrush in his work, and how different staff did use different tools on the same project.
many artists on boards full of them talk about having all the major programs installed (since they are all owned by Autodesk now), and being able to use whatever they like
Yes, it's common for a company to mandate either Max or Maya for efficiency's sake, but there are also companies that do give their artists the choice.
When I worked at a very large developer, we used Max, Maya and even XSI, but the choice was made per-project by the lead artist. Some projects were done in Max and others were done in Maya. Of course with a system this flexible, there were exceptions to this rule, such as when you re-used assets from other teams, or borrowed a staff member from another team to help out for a few days -- meaning that even on the "Max projects" there were still some Maya assets, etc...
N.B. there's still always small exceptions, e.g. at the above company, even on a "Max only project", there was still a small amount of work done in XSI because it was better suited. Or, at my last job, the whole company was "Maya only", but a few small bits of isolated work were done in Blender. Also, at that "maya only" company, most of the artists really resented the fact that they had been forced to switch from Max, which they liked better (a decision made by an incompetent manager), so there's no real objectively better tool.
On my current project, I'm only supporting XSI at the moment, because my artist prefers it over Max/Maya, and when I get time I might add support for Blender, for modders.
The inefficiency with allowing multiple DCC tools is mainly just that your engine department has to maintain more plugins/tools... but if you're making a huge engine that you want to be able to sell to a diverse range of customers, like Epic, you need to do that work anyway. In my case, our engine-staff were subsidised by tax-breaks, while game-staff weren't, so we had an absolutely massive engine team
In a lot of games, sharing of assets between artists doesn't happen that often -- if someone is assigned to create a character, then they're the only one that needs to edit the source file.
 to clarify, the large company I worked for always planned to license their massive engine, like Epic does (but never actually did), so they did have a reason to go through that trouble [/edit]