Matt Leacock is a game designer probably best known for creating the very popular game Pandemic. His most critically acclaimed game is undisputedly the Pandemic Legacy series (particularly Season 1 which was number one on BGG for a long while).

Pandemic Legacy is a co-operative campaign game, with an overarching story-arc played through 12-24 sessions, depending on how well your group does at the game. At the beginning, the game starts very similar to basic Pandemic, in which your team of disease-fighting specialists races against the clock to travel around the world, treating disease hotspots while researching cures for each of four plagues before they get out of hand. During the campaign, new rules and components will be introduced. These will sometimes require you to permanently alter the components of the game; this includes writing on cards, ripping up cards, and placing permanent stickers on components. Your characters can gain new skills, or detrimental effects. A character can even be lost entirely, at which point it's no longer available for play.

So this way of playing games where there are changes to the rules and components of a game is called a legacy system – think of it as a “choose your own adventure” type game where there are permanent repercussions to every single decision the players make when you play a game. So if you want to teach your team about strategic choices and the effects of change, this would be a fantastic game to play.