Question

Sun Yat Sen and Mahatma Ghandi are holding two rallies in London in the year 1910. One hundred and fifty people are trying to choose between attending the two rallies. 350 – 5N is the payoff to attending Dr. Yat Sen’s rally, where N is the number of attendees. 175 – 1/2N is the payoff to attending Ghandi’s rally, where N is the number of attendees.

1. Plot the Payoff Functions.
2. Find all equilibria and show all work.
3. If Winston Churchill were to give a speech at the same time and his listeners got a constant payoff K, what would K have to be in order for him to attract at least 50 attendees.

Answer 1

N = 150

Two Choices are given:

1) Attend Dr. Yat Sen's Rally

2) Attend Gandhi's Rally

Payoffs:

From Dr. Yat Sen's Rally: 350-5N_S

From Gandhi's Rally: 175-0.5N_G

(A)

Lets Plot the Payoff functions:

(B)

Finding the Equilibria:

At equilibrium Payoff from both the rallies should be the same; i.e. There should be no incentive left to attend One or the other's rally

At

U_S = U_G

As we know

In Equilibrium around 45 people will attend Dr. Yat Sen's Rally and Around 105 will attend Gandhi's rally.

(C)

Winston churchill wants to attract at least 50 attendees by giving a constant payoff of k:

Lets say he is able to attract 50 attendees:

Now lets find new equilibrium for Yat sen and Gandhi's Rally

Payoff from attending Gandhi or Yat sen's Rally:

So to attract at least 50 attendees Churchil must give a constant payoff of 145