Reference no: EM132422755

Problem: Consider a game between two firms, Original Inc. and Copycat Inc. The game proceeds in three stages. At the end of each stage both firms observe what happened during that stage.

• Stage 1: Orinigal Inc. chooses to Develop or Not Develop a new product - invisible earbuds which one can use to listen to music without anyone noticing (these earbuds also have a double noise canceling property, so no one except the person who wear them can hear the music). If Original Inc. chooses to Not Develop, then the game ends and both firms get zero. If Original Inc. chooses to Develop, then it incurs a cost of $15 and the game continues to Stage 2.
• Stage 2: Copycat Inc. chooses to Copy or Not Copy the product. If Copycat Inc. chooses Copy, then it incurs a cost of 5. The game the continues to Stage 3.
• Stage 3: Inverse demand for this new product is p(y) = 10 - y. If Copycat Inc. chose Copy, then both firms are in the market, and they choose quantities simultaneously 3 (Cournot competition). If Copycat Inc. chose Not Copy, then only Original Inc. is in the market, and it chooses its quantity as a monopolist.

Each firm's payoff is its revenue (if any) in the market minus any cost it incurred to develop or copy the product. (There are no variable costs)

(a) Show that there is no Subgame Perfect Nash Equilibrium of this game where Original Inc. develops these invisible earbuds.

Now suppose Stage 1 of the game is modified as follows: In addition to having options Develop and Not Develop, Original Inc. also has a third option: Develop and Patent, which costs $18. If Original Inc. chooses to Develop and Patent, Copycat Inc. can no longer copy the product, and hence Original Inc. will be the monopolist in this market. The rest of the game is the same as before.

(b) Show that in any Subgame Perfect Nash Equilibrium of this game, Original Inc. will choose to Develop and Patent invisible earbuds.