Consider a country with 10 citizens. Let V(k) =k denote the value that citizen k attaches...

Consider a country with 10 citizens. Let V(k) =k denote the value that citizen k attaches to protesting. That is, citizen 1 attaches a value of 1, citizen 2 attaches a value of 2 to protesting, and so on with citizen 10 attaching a value of 10 to protesting. There is a cost to protesting, which equals 20/m, where m is the number of citizens protesting. If citizen k protests, her payoff is (k-20/m) where m is the total number of people who protest. Payoff to a citizen who does not protest is zero.

A. How many Nash Equilibria does the game have?

B. Is it Nash Equilibrium if everyone protests?

C. How many people protest in the equilibrium? If there are 2 more Nash Equilibria, write the number of protesters from any one of those Equilibria.

Expert Solution

A. This game has TWO nash equilibria.

B. No. It is not a Nash equilibrium if everyone one protests.

A Nash equilibrium is a strategy profile from which no player has an incentive to deviate. No profitable unilateral deviation is possible.

If everyone protests, the payoff of citizen 1 is equal to 1-20/10 = -1. If the citizen chooses not to protest, he will get a payoff of 0. So, citizen gets better off by deviating.

Therefore, everyone protesting is not a Nash equilibrium.

C. Two Nash equilibria in this game.

In one Nah equilibrium, no one will protest i.e., the number of protestors is 0.

In another Nash equilibrium, 8 citizens will protest. Citizens (3,4,5,6,7,8,9 and 10) will protest.

Rahul Sunny answered 2 years ago

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