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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.
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.
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