Game matrices and trees can be hard to interpret and reason about. This is not only true for people who may be new to game theory (like young experiment participants), but even for those familiar with it. It normally isn't a problem because most lab experiments focus on one or two familiar games and can explain them with arbitrarily great care. But it could be a problem for experiments that use unfamiliar games or that expose participants to many different games in a session.
One way around this is to use practice rounds to give participants experience with the various outcomes, but, additionally, there must be a general intuitive approach to the materials that can present simple games in a way that highlights their different contingencies and incentives.
At present, for a 2x2 game, I imagine I'd use the classic game matrix supplemented with some equivalent textual description: "If you select strategy Left, the other player will either select Top (earning each of you 1 and 4, respectively) or Bottom (earning each of you 2 and 2, respectively). If you select strategy Right ...." But even that isn't so clear, and it wouldn't scale well to larger games; I'm sure there's a better way.
Is anyone familiar with research that tests, or at least uses, some unconventional intuitive format for visually communicating the different outcomes of a range of economic games? Without resorting to "cover story" narratives?