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A simple exercise would be a guessing game. Give each member a concept to describe to the rest (without using equivalent words). The rest of the group must try and guess what it could be. But! They must try to break any consensus that starts to form with different ideas that fits the provided description. When the provided concept and only the provided concept remains the exercise is passed.

Success is measured by how succinct and short the successful description of the concept is.

Edit to add an example and a little explanation:

Someone must describe the concept "Red" as in the original post. He tells the others it's a color, they say Green, Brown, Yellow, Red, so he must find more or better ways to describe it. So he says forget what I said, it's what painted on a firetruck, so they say acrylic color, firefighters symbol, the color red, so again, he must redefine his concept. So he says it's the predominant color of firetrucks or he says it's the color of the uppermost light of a traffic light, or he can say it's the color we see when exposed to light in the 700nm length. The faster he reaches a definition that everyone understands and can't find counterexamples for the better his definition is.

This exercise focuses on the core issue here: good communication and concise definition.