Question

Consider a country withncitizens whereviis the value to citizeniof protesting against their government. We number the citizens in order ofthese values. Thusv1> v2> :::vn. Wheremis the number of protesters,the cost of protesting isc=m, and thus the payo from protesting for citizeni would bevicm. Assume thatvn= 0 and thatv1c <0. The payo fromnot protesting is assumed to be 0 for everyone.

A) Can there be a Nash equilibrium where everybody protests? Explain.

B) Provide an example with four citizens that satis es the assumptionsof this problem and where the costs and values are such that the only Nashequilibrium has nobody protesting. (An example consists of speci ed valuesforcand forv1; v2; v3andv4)

C) Provide an example with four citizens such that there are two Nashequilibria, one in which exactly two citizens protest and one in which nobodyprotests.

Answer 1

1) the only Nash equilibrium is nobody will protest. Because only the Vn person has an value to be equal to 0. So by the inequality mentioned above everyone else is having a negative value and also to protest they will have to incur a cost of m as specified above. So in total everyone is getting a negative value so no one would protest. As a rational individual is strictly better off with a zero amount rather than getting a negative amount.

2)if I specify the values as -3=v1,-2=v2,-1=v3 and v4=0. So everyone is getting negative value except v4 also if m=2 say so now everyone will surely get a negative value as they have to incur the cost.

3)if we define the values of v4 and v3 be positive and greater than or equal to m then in such a hypothetical society exactly two people will protest against govt and two will not. The other example has been given in 2).