Question

The widget market is currently monopolized by Widgets R Us (or simply Widgets), but another firm (Wadgets) is deciding whether to enter that market. If Wadgets stays out of the market, Widgets will earn $100 million profit. However, if Wadgets enters, Widgets can either share the market, in which case the two companies enjoy a total $20 million in profit, or wage a ruinous price war, in which case both companies lose big and go bankrupt (call this $0 profit for concreteness). The only sane choice for Widgets is to share the market, but before Wadgets chooses whether to enter, the Widgets Board of Directors has the opportunity to hire a new CEO—and this new CEO might just be crazy enough to wage a price war!

(a) Draw the game table for this game, where the relevant players are Wadgets, which decides whether to enter the market, and the Widgets Board, which decides whether to hire a crazy CEO who will wage a price war if Wadgets enters or hire a sane CEO who will share the market if Wadgets enters. (Assume that Wadgets has no way of knowing if the newly hired Widgets CEO is crazy or sane, making this a simultaneousmove game.)

(b) In this game, the Widgets Board views Hire a Sane CEO as a _______ strategy. Fill in the blank with one of the following answers: “superdominant,” “strictly dominant (but not superdominant),” “weakly dominant (but not strictly dominant),” or “not dominant.” Explain your answer.

(c) Find all pure-strategy Nash equilibria of this game.

(d) Suppose that, in addition to wanting to maximize profits and avoid bankruptcy, the Widgets Board would prefer not to have a crazy CEO. How does this extra consideration change your answer to part (b), and how does it change the set of pure-strategy Nash equilibria relative to part (c)? Explain your answers.

Answer 1