Network message passing game

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This game demonstrates ideas about closeness and betweenness centrality. It's related also to small world networks, and the famous six degrees of separation hypothesis, popularized by experiments conducted by psychologist Stanley Milgram.

Rules of the game:

Write letters of the alphabet on slips of paper. Everyone take a unique letter (A, B, C, ...), such that the letters in use are known to all. Each person selects 1-3 class members they connect to (you may vary this connectivity range), by picking letters at random. These will remain fixed throughout one round of the game. Define a "maximum hops" value (suggestion: double the number of people in the class). Place your letter on your desk where it's clearly visible.

Definition: To stamp a message is to add your letter to the end of the stamp sequence.

Procedure:

  • Address a message. On a slip of paper, everyone write the letter of someone in the class they're not directly connected to, and circle it (this is the "address" of the message and will not change), then stamp it (this is the first stamp in the stamp sequence). Then pass it to someone you do connect to by placing it on their desk.
  • When you receive a note on your desk, check who it's for. If it's for you, take it, stamp it, and stop its circulation. The message has succeeded.
  • If it's not for you, stamp it; then if the number of stamps in the stamp sequence exceeds the max hops (you can set this at 10 initially), write X on it (the message failed), and stop its circulation.
  • Otherwise (if the number of stamps does not exceed the maximum hops value), pass it on to anyone you connect to.

The round ends when all messages are stopped.

When everything has stopped, tally the number of messages that reached their destination. What percentage reached the destination? Check their routes by examining the stamp sequence of each. Which person appears on the most paths? These are the statistics for this round.

Now draw the network on the whiteboard. How many components did it contain? Who is most central? (Everyone compute their degree, closeness, betweenness centrality). What is the centralization of the network as a whole?

Play the whole game again from the start, keeping track of the statistics computed at each round. Try varying the connectivity range (initially set at 1-3). What happens if everyone is allowed to connect to just one other person?

Try the same with "random" routing of one neighbor (every time you pass a message, pick anyone at random to give it to). What happens in this case?