Problem 2:

Game Theory.

Suppose cyclists Lance Armstrong and Jan Ulrich are simultaneously deciding whether or not to start doping (i.e.take performance-enhancing drugs) before the Tour de France.If they both dope, they will each earn a $10 million.If neither one dopes, they will each earn a $8 million.If Armstrong dopes and Ulrich does not, Arm-strong earns $12 million and Ulrich earns $5 million.If Ulrich dopes and Armstrong does not, then Ulrich earns $12 million and Armstrong earns $5 million.There is a chance that a cyclist who dopes gets caught, which is given by the probability p.A cyclists earns $0 if caught.

a) What are the expected earnings for each player as a function of p if they both choose to dope?

b) Draw the normal form matrix of this game.Payoffs are in terms of the players expected earnings.

c) Assume p= 0.25.Find all the pure strategy Nash Equilibria of this game.

d) Suppose the Tour de France wants to eliminate doping.To do so, they enhance their screening process, which increases p.What is the lowest value of p where both cyclists choose not to dope in equilibrium?