Fame and Friends: A Game of Connections

You're in a room filled with famous people. The goal? To get closer to those with more fame than you. This is the premise of a new game in network creation, called "celebrity games. " Each player, or "celebrity, " has a different level of fame, or "celebrity weight. " To win, you need to be close to others, especially the superstars. The cost? It depends on how many direct links you make and how many less-famous people you ignore. Interestingly, this game always has a clear winner, known as a "pure Nash equilibrium. " There's even a special kind of game called "star celebrity games, " where everyone connects to one superstar. Scientists have figured out how to measure the game's efficiency, called the "Price of Anarchy" (PoA). The more organized the connections, the better the PoA. Think about it. Real life is full of these games. Politicians, business leaders, even kids in a playground. It's all about connections and influence. But at what cost? And is it really worth ignoring those who are less connected?