Stan has an idea for a new iPhone app. However, Calvin is a notorious stealer of new products, and if Stan creates the app, Calvin can choose to copy it (and sell it on his own) or not. Investing in the development of the app will cost Stan 10 thousand dollars. If Stan creates the app, it will cost Calvin 35 thousand dollars to copy it (he is not as skilled as Stan).

Suppose that the total revenue the app will generate is 100 thousand dollars. If Calvin chooses to copy the app, the two products will be indistinguishable, so that the revenue will be shared equally among Stan and Calvin. However, if Calvin does copy the app, Stan can sue him for patent infringement. If Stan does sue, both Stan and Calvin must pay 15 thousand dollars in lawyers fees. Stan and Calvin both know that it will be difficult for Stan to win the lawsuit. In particular, there is a5%chance that Stan wins the lawsuit, in which case Calvin must reimburse Stan for all lost revenue (i.e., he must pay Stan 50 thousand dollars). If Stan loses the lawsuit, both Stan and Calvin keep any revenue generated from the sale of the app.

Assume both Stan and Calvin seek to maximize their expected income (revenues minus any development/legal costs).

(a) Draw this as an extensive form game, specifying who moves at each decision node and the payoffs for each player at each terminal node.

(b) Write down all of Stan's possible strategies, and all of Calvin's possible strategies. (Recall the discussion in lecture about how to describe a strategy in sequential games.)

(c) Solve for a subgame perfect Nash equilibrium.

(d) Is there a Nash equilibrium in which Stan sues Calvin? Is this equilibrium subgame perfect? Why or why not?