1. Consider a model of revolutions. Society is made up of N > 1 people. Simultaneously,...

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1. Consider a model of revolutions. Society is made up of N > 1 people. Simultaneously, each person chooses whether or not to participate. If n people participate, the probability the revolution succeeds is . If the revolution succeeds, each member of society receives the benefits of a public good worth B. In addition, each person who participated in the revolution receives a benefit R if the revolution succeeds. (This extra benefit, called a club good, might represent special access to government jobs for people who helped unseat the government once the new government is formed, or it might just represent an expressive benefit of having participated in a victorious revolution.) The cost of participating is c > 0. Assume that R > c and that B+R < N c. (a) Suppose a player believes n other people will participate. What is her expected utility from participating? (b) Suppose a player believes n other people will participate. What is her expected utility from not participating? (c) Write down a player's best response correspondence. game. (d) Identify all of the pure strategy Nash equilibria of this (e) Calculate the utilitarian payoff associated with each equilibrium. (f) Does this game have the potential for a coordination trap? Explain why or why not. (g) What feature of this game makes it a situation that exhibits strategic complementarities? 1. Consider a model of revolutions. Society is made up of N > 1 people. Simultaneously, each person chooses whether or not to participate. If n people participate, the probability the revolution succeeds is . If the revolution succeeds, each member of society receives the benefits of a public good worth B. In addition, each person who participated in the revolution receives a benefit R if the revolution succeeds. (This extra benefit, called a club good, might represent special access to government jobs for people who helped unseat the government once the new government is formed, or it might just represent an expressive benefit of having participated in a victorious revolution.) The cost of participating is c > 0. Assume that R > c and that B+R < N c. (a) Suppose a player believes n other people will participate. What is her expected utility from participating? (b) Suppose a player believes n other people will participate. What is her expected utility from not participating? (c) Write down a player's best response correspondence. game. (d) Identify all of the pure strategy Nash equilibria of this (e) Calculate the utilitarian payoff associated with each equilibrium. (f) Does this game have the potential for a coordination trap? Explain why or why not. (g) What feature of this game makes it a situation that exhibits strategic complementarities?