Professor Phobos said:
There isn't, not from my perspective or experience. The GM can't "win", so he's not participating in any kind of friendly competition.
Maybe, but the players can certainly "lose."
The most obvious situation being the default D&D setup: players outfit a team of adventurers who have a limited set of resources (abilities, items, points) that they pit against challenges posed to them by the DM, often in pursuit of an overarching goal, which may be as simple as "survive and level up in order to do it again." Assuming the DM is not rigging the game in order to insure any given outcome (be it a TPK or total Monty Haul PCs-can't-die play), they essentially serve the role of thwarting the PCs. Not accomplishing their goal, or more simply, death, is a very obvious "lose" condition. So is accomplishing the goal, yet paying a higher price than expected, e.g., too many resources spent, sacrifices made, etc.
Ergo, there can certainly be friendly competition. If anything, it's the most traditional mode of play. Look at any game where the players start to sweat when a combat goes south, or when the DM stares in dismay at a carefully planned encounter that PCs breeze through.
EDIT: I think it's important to note that "adversarial" doesn't necessarily map to "win"/"lose". In most RPG play, everyone at the table generally knows that yes, we will make it to the end of the module no matter what. The question is usually. "What's it going to take to get there?" The GM's role is generally not to just happily walk the players through to the end; there's no game then. The GM's job is to get in the players' way, i.e., serve as an adversary. Without conflict, you have neither challenge nor drama, i.e., "fun." Ergo, even if the sole end goal is "fun," that doesn't mean that the GM and players don't hammer on each other en route.