(20 points) Each member in a group of N people must independently decide whether
ID: 1157416 • Letter: #
Question
(20 points) Each member in a group of N people must independently decide whether or not to participate in a protest. The individuals value participation differently: person 1 values participating at Vi, person 2 values participating at V2, etc. (the value of protesting might reflect each person's commitment to the cause, etc.). Assume that V1 > V > .. > VN - 0, that is, person 1 attaches the greatest value to protesting, person 2 the next greatest, and so forth to person N, who attaches 0 value. Protesting is costly, e.g. the protest might turn violent. But the more people participate, the smaller each person's cost is. Assume in particlar each person's cost is , where k is the number of people who actually protest, and c> 0. The net payoff to person i is Vi - if she protests, and 0 if she does not. Assume that Vi c. (a) Is it a Nash equilibrium for everyone to protest? (b) Is it a Nash equilibrium for no one to protest? (c) Suppose now the payoff from protesting is kVi - L if k people protest, i.e., the value of protesting grows as more people protest Is it a Nash equilibrium for no one to protest?Explanation / Answer
Answer:
a)
As we know, people will protest if the payoff is greater than zero because he/she will get zero payoff when deciding to not to go to protest. If everyone protest then Vi will become close to zero, so we can say that everyone protesting is not a Nash equilibrium.
b)
Yes, it is a Nash equilibrium because suppose only that person goes to protest than his/her payoff is negative as V1 < c.
c)
Yes, it is a Nash equilibrium for no one to protest, because in this case K now increases faster which will decrease the payoff faster than before (as Vi > c / K2).
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