Question

Suppose n people can choose between going to one of two campgrounds for 4th of July weekend. They can go to either Campground A or Campground B. The payoff to going to Campground A is 100-a, where a is the number of people in Campground A, and the payoff to going to Campground B is 200-2b, where b is the number of people in Campground B, such that a+b=n, and a, b, and n have to be greater than or equal to 0.

a. Is this a tipping game or a congestion game? Explain your reasoning. (2 pts)

b. Suppose only one person is going camping for the 4th of July (i.e. n=1). Which campground would they chose to go to? (3 pts)

c. Suppose n=25. How many people will go to Campground A and how many people will go to Campground B? (3 pts)

d. What is the number n of people such that the n+1 person will be the first person to choose to go to Campground A? (5 pts)

e. What Nash Equilibria exist, if any, when n=52? (3 pts)

f. What Nash Equilibria exist, if any, when n=53? (3 pts)

g. What Nash Equilibria exist, if any, when n=54? (3 pts)

h. What Nash Equilibria exist, if any, when n=55? (3 pts)

i. Bonus: Describe the equilibria that exist when n>51. (5 pts)

Answer 1

a) This is an example of congestion game.  In a Congestion game we define players and resources, where the payoff of each player depends on the resources it chooses and the number of players choosing the same resource. In this game , we can see that the payoff for players going inti the ground depends on the campground chosen and the number of players going in a campground.

b) If only one people  is going to campground, then he will go to campground B because the payoff in that campground will be (200-2) =198 whereas in campground A , the payoff will be (100-1) = 99.

c) People will first go to campground B as the payoff in this campground is more.

If all 25 people go in campground B , the payoff will be 200-(2*25) = 150 , which is more than payoff in campground A even when one person goes to Campground A.

So all the 25 people will go to campground .

d) N will be the number of people when the payoff from the campground B will be equal to the campground A.

When 50 people go to campground A the payoff will be (200-(2*50)) = 100

If the next person goes to groung B the payoff will be 98.

And when the first person goes to ground A , the payoff will be (100-1*1) = 99

So after 50 people go to campground B , the next person will go to campground A

So n=50.