Question

1. You own a gas station across the street from your friend’s gas station.  If you collude (work together), you each make $800/hr.  If one lowers price of gas, the lower price increases demand such that they make $1500/hr and the original (now higher) price only makes $50/hr.  If you both lower price you each make $500/hr.
   1. Draw the game matrix.
   2. What is the equilibrium?
   3. What is the problem with the equilibrium?

Answer 1

a) The matrix is given as below

Me\Friend	Collude	Low prices
Collude	($800,800)	($50,1500)
Low prices	(1500,50)	(500,500)

b) The vertical part is of me and the horizontal strategies are of the friend.

Given that i have chosen colluding, my friend would be better off if he chooses low prices since the payoff is higher. Similarly if i have chosen low prices, my friend would be better off choosing low prices.

Now if my friend has chosen collude, i would be better off with low prices and if he chooses low prices, i would again be better off with low prices.

Hence the equilibrium is low prices(500,500)

The equilibrium is (low prices, low prices) ie each would earn ($500, $500)

c) The problem is that if they both collude they would each earn more than when they decide to lower the price. This is similar to the case of prisoner of dilemma situation when the prisoners could have cooperated and reduced the jail term rather than confessing and increasing the term.