Many of us have a habit of walking on the right. Imagine you're about the ascend a staircase as fast as possible, following the norm of staying on your right, when some other person will turn the corner and descend. Let p be the probability (between 0 and 1) the descender also follows the same "on the right side" norm so (1 p) is the probability they do the opposite and you collide. Using p, a (a positive number representing the benefit of successfully ascending without collision), and b (a negative number representing the pain of collision) we can think of the expected value of our trip up the stairs using the right side as:

right = pa + (1 p)b

6a. Come up with the equation for left, i.e. walking on the left side.

6b. Graph both on the same graph with p on the horizontal and the respective values on the vertical.

6c. Find the value of p that sets the expected value of climbing the stairs on the right (right) with the left (left).

6d. Interpret your answer to part c. Does it make sense? Is it an equilibrium?