An online game company has a game that's played by users in two regions that we'll...

 

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An online game company has a game that's played by users in two regions that we'll call X and Y. X has fewer users but they're more interconnected; Y has more users but they're more sparsely connected. In particular, let's suppose that each user in region X has 12 friends in region X who use the game and 4 friends in region Y who use the game. Let's suppose that each user in region Y has 2 friends in region X who use the game and 10 friends in region Y who use the game. (a) The company notices that new features in the game tend to spread over this network of friends, as users learn about the new features from friends who play the game. The company finds that when a new feature starts in region Y (with a sufficient number of initial users in Y), it tends to spread to eveyone in Y and then eventually to everyone in X as well. In contrast, when a new feature starts in region X, it might spread to everyone in X, but it doesn't spread to region Y. The company asks you whether this behavior that they observe is consistent with the threshold model from Chapter 19 operating on the friendship network of users in regions X and Y. In particular, although they don't know what the exact network looks like, they'd like to know whether what they're seeing could potentially arise from a model in which each user adopts a new feature when at least a q fraction of their friends do, for some value of q. If you think this is possible, explain why, including a specific value of q that would be consistent with the information they've provided. If you think this is not possible, explain. why there is no single value of q that could produce the behavior they observe. (b) In addition to studying the spread of new features, the company is also monitoring the spread of certain cheat codes for their game unrecorded sets of instructions that gives users powers in the game that they're not supposed to have. Interestingly, the spread of cheat codes for the game work differently than the spread of new features. When a cheat code is first discovered by a sufficient number of users in region X, it tends to spread to everyone in X and then eventually to everyone in Y as well; but when a cheat code is first discovered by a set of users in region Y, it tends to spread within in Y but then it stops without spreading to anyone in X. As in (a), the company would like to know whether the spread of cheat codes is consistent with the threshold model from Chapter 19 operating on the friendship network of users in regions X and Y. In particular, they'd like to know whether what they're seeing could potentially arise from a model in which each user begins using a cheat code when at least a q fraction of their friends are, for some value of q. If you think this is possible, explain why, including a specific value of q that would be consistent with the information they've provided. If you think this is not possible, explain why there is no single value of q that could produce the behavior they observe.. An online game company has a game that's played by users in two regions that we'll call X and Y. X has fewer users but they're more interconnected; Y has more users but they're more sparsely connected. In particular, let's suppose that each user in region X has 12 friends in region X who use the game and 4 friends in region Y who use the game. Let's suppose that each user in region Y has 2 friends in region X who use the game and 10 friends in region Y who use the game. (a) The company notices that new features in the game tend to spread over this network of friends, as users learn about the new features from friends who play the game. The company finds that when a new feature starts in region Y (with a sufficient number of initial users in Y), it tends to spread to eveyone in Y and then eventually to everyone in X as well. In contrast, when a new feature starts in region X, it might spread to everyone in X, but it doesn't spread to region Y. The company asks you whether this behavior that they observe is consistent with the threshold model from Chapter 19 operating on the friendship network of users in regions X and Y. In particular, although they don't know what the exact network looks like, they'd like to know whether what they're seeing could potentially arise from a model in which each user adopts a new feature when at least a q fraction of their friends do, for some value of q. If you think this is possible, explain why, including a specific value of q that would be consistent with the information they've provided. If you think this is not possible, explain. why there is no single value of q that could produce the behavior they observe. (b) In addition to studying the spread of new features, the company is also monitoring the spread of certain cheat codes for their game unrecorded sets of instructions that gives users powers in the game that they're not supposed to have. Interestingly, the spread of cheat codes for the game work differently than the spread of new features. When a cheat code is first discovered by a sufficient number of users in region X, it tends to spread to everyone in X and then eventually to everyone in Y as well; but when a cheat code is first discovered by a set of users in region Y, it tends to spread within in Y but then it stops without spreading to anyone in X. As in (a), the company would like to know whether the spread of cheat codes is consistent with the threshold model from Chapter 19 operating on the friendship network of users in regions X and Y. In particular, they'd like to know whether what they're seeing could potentially arise from a model in which each user begins using a cheat code when at least a q fraction of their friends are, for some value of q. If you think this is possible, explain why, including a specific value of q that would be consistent with the information they've provided. If you think this is not possible, explain why there is no single value of q that could produce the behavior they observe..

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a ANSWER Yes this behavior is consistent with the threshold model from Chapter 19 operating on the f... View the full answer