Game ideas don’t always come up through tinkering with code or by mashing up and re-imagining games you liked or by adapting a linear story from another medium.
Try to start from a topic you are passionate about: a real world system, a dynamic, a conflict, a situation that can produce a variety of outcomes.

SimCity was inspired system dynamics, by a little known science fiction story, and a shmup level editor. More importantly it related with Will Wright’s passion for complex systems

Brainstorming tips
With your team mates find a place that is not your habitual working place, away from computers. Bring something to write on, possibly a white board. Don’t make it last more than an hour.

Set a theme or a challenge. You can pick a theme from popular game jams like Ludlum Dare or the Global Game Jam. Stick with it until you run out of ideas.

Write down all of your ideas and worry about their quality later. Do not criticize or ignore your colleagues’ ideas during the brainstorming process. The process should be about free thinking, about building on each other’s thoughts.
A good trick for this is to practice the “yes, and” rule of improvisation: Whenever you want to jump into the conversation, start your sentence with the words “yes, and . . .”. Ideas can be sketches, mind maps, and diagrams as well.

List Creation
One simple form of brainstorming is making lists. List out everything you can think of on a certain topic.
Then create other lists on variations of that topic. The process of writing them down helps you to freely associate and organize at the same time.

Idea Cards
Take a deck of index cards and write a single idea on each one. Then mix them up in a bowl. Now take out
the cards and pair them. For example, “nectar” might appear with “giants.” Perhaps, your next game will include “nectar giants,” whose bodies are fluid and smell like persimmons. You can concatenate sets of cards.

After you come up with a bunch of raw ideas, you can refine them into game premises.
The premise is not the story or the “world” but what ignites the game action and define the player constraints. It also unifies the dramatic and formal aspects of a game.

Portal: the player is trapped in a series of rooms designed by an condescending AI which can only be escaped through the use of a portal gun.

Getting Over It by Bennett Foddy: a guy is stuck in a pot with a hammer and has to climb a mountain?
(Clearly it was generated mechanics-first, it’s actually a remake of an obscure game)

Kentucky Route Zero: a cast of characters discover a secret underground highway in a dreamlike, magical realist Kentucky.

Regardless on whether the development comes from a gameplay or a narrative intuition, the mechanics should support the premise and vice versa.

Once you have a dozen of so of promising game ideas, rank them according to complexity and minimum scope needed. Which ones are the idea that take the most advantage of your team member’s skills?