Suppose that a group of co-workers are each members of one of two possible messaging systems,...

 

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Suppose that a group of co-workers are each members of one of two possible messaging systems, A or B. A is generally an easier system to use than B; and also, two workers have an easier time communicating when they are on the same system than when they are on different systems. But the two systems are compatible, so any two workers are able to communicate regardless of which systems they're on; it's just that the experience may be better or worse. We'll represent the quality of the experience for two co-workers v and w using the following payoff matrix, which shows the payoffs received by u and w respectively when they each use A or B. A B A 5,5 2,1 B 1,2 3,3 Figure 3: Payoffs for communicating using A or B v Note that unlike the main model that we use in class and Chapter 19, vand w still receive positive payoffs even if they communicate using opposite platforms (since we want to represent the idea that communication is still possible in this case, just a worse experience). It turns out that even with this richer payoff structure, the type of threshold rule we saw in Chapter 19 still applies, but adapted to handle these new payoffs. Specifically, suppose that a person u in the network is trying to decide whether to use system A or system B. Let z be the fraction of u's neighbors in the network who are using A. (So a 1 - z fraction of u's neighbors are using B.) Specify a number q so that u should choose A if x > q, and should choose B if x < q. (You should find that your choice of q has the property that if x = q, then u is indifferent; our convention in these cases has been that u chooses A, but that's not crucial for the current question.) Give an explanation for your answer, including how you derived the value of q. Suppose that a group of co-workers are each members of one of two possible messaging systems, A or B. A is generally an easier system to use than B; and also, two workers have an easier time communicating when they are on the same system than when they are on different systems. But the two systems are compatible, so any two workers are able to communicate regardless of which systems they're on; it's just that the experience may be better or worse. We'll represent the quality of the experience for two co-workers v and w using the following payoff matrix, which shows the payoffs received by u and w respectively when they each use A or B. A B A 5,5 2,1 B 1,2 3,3 Figure 3: Payoffs for communicating using A or B v Note that unlike the main model that we use in class and Chapter 19, vand w still receive positive payoffs even if they communicate using opposite platforms (since we want to represent the idea that communication is still possible in this case, just a worse experience). It turns out that even with this richer payoff structure, the type of threshold rule we saw in Chapter 19 still applies, but adapted to handle these new payoffs. Specifically, suppose that a person u in the network is trying to decide whether to use system A or system B. Let z be the fraction of u's neighbors in the network who are using A. (So a 1 - z fraction of u's neighbors are using B.) Specify a number q so that u should choose A if x > q, and should choose B if x < q. (You should find that your choice of q has the property that if x = q, then u is indifferent; our convention in these cases has been that u chooses A, but that's not crucial for the current question.) Give an explanation for your answer, including how you derived the value of q.

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The number q that should be chosen in this case is q 05 This is because if q 05 then the payoff for using A will be equal to the payoff for using B so the person u in the network will be indifferent b... View the full answer