This is less of a full game idea and more of game mechanic idea. In multiplayer mode for any game, there is usually a definite objective such as getting to somewhere faster than everyone else, collecting the most of something or doing a specific task the most times out of all the players. For the latter two it will usually be coupled with a time limit to ensure that rounds are not too long or too short if the players are inexperienced or expert respectively.
This time limit, while sometimes customisable before the round begins, is a constant, allowing know when the round will end. If the players could end the game at whatever time they wanted (with a majority voting system) it could add a whole new dynamic to the gameplay. But rather than the game ending as soon as the majority indicates that they want to end, the game plays on for a certain amount of time afterwards. For instance, if the goal of the game was to collect coins spread out around the map, people could pretend to be bad at collecting coins, offer to end the game then quickly collect a lot before the time runs out, while the opposition is relaxing thinking they have it in the bag. This would almost allow for poker-like tactics of bluffing and double bluffing. This would be coupled with the score being hidden during the final minutes of the game, so as to not alert the opposing side to what you are doing.