A catch-up mechanism is a rule in a board game that tends to help whoever's currently losing, to help make sure that nobody falls hopelessly behind and that the game stays interesting and competitive for everyone. They can be tricky to get right! Power Grid probably has the most intrusive catch-up example of any popular game; whoever has the lowest score gets first pick of the new power plants and new commodities each turn. Settlers of Catan also has a minor catch-up mechanism because of the robber; players tend to send the robber to steal from the richest players, which gives the poorer players a chance to accumulate more resources. Risk, on the other hand, has a negative catchup mechanism; once you get a bit of a lead, the game gives you disproportionately more armies, and so you're likely to win all at once and crush your enemies into the dust as soon as you get your first significant advantage.
One interesting feature of a catchup mechanism is that they tend to exist for the benefit of the winners at least as much as the losers -- it's fun to win, but unless you're startlingly immature, it's not much fun to keep playing a game when everyone already knows you're going to win. It's more fun to have a modest advantage that still leaves your opponents with a sporting chance.
I mention all this because Lawrence H. Summers, former President of Harvard University, has written a surprisingly humble, fair, and insightful book review of Picketty's Capital in the Twenty-First Century. If you're interested in how we could make sure that people who aren't born wealthy have a chance to catch up with their peers, but don't have time to slog through Picketty's treatise, you should check this out.
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