Two satellite TV operators, Ozstar (O) and Wolftel (W), compete in the same market and play the following game. At the beginning of the year, they each simultaneously announce whether they will continue to provide their pay-TV service for the year or close down.

If an operator announces it will be continuing to provide its satellite TV service that year, it incurs a fixed cost of $50 million. This cost does not depend on how many subscribers it eventually has, but it is sunk once it has announced it is to continue operating for that year. 2

If an operator announces it is closing down it does not incur the fixed cost and it does not incur any operating cost. However, the announcement to close down is irreversible and the operator cannot resume service in future years. If both operators decide to close down then they each get a zero payoff and no satellite service is supplied or sold in that market for the current year and every year thereafter.

If both operators decide to continue providing its satellite TV service then, since viewers in the market regard the two services as essentially equivalent, a potential subscriber will only ever sign up to at most one service and if he does decide to subscribe will choose the one with the lower annual subscription fee. In the case where their subscription fees are equal he will randomly choose between them (with equal probability).

This results in fierce price competition for subscribers, leading both operators to charge a subscription fee for the year of $100 that is equal to their common and constant marginal cost of providing one years worth of service to a subscriber. Hence in this case subscription fees generate no variable profit to offset the fixed cost of $50 million, leading both to experience a loss of $50 million (that is, a payoff of $50 million).

If only one operator decides to close down, then the remaining operator becomes a monopolist provider of satellite TV. The maximum profit per year (that is, payoff per year) it can earn is $200 million ($250 operating profit less the $50 million fixed cost). It achieves this by setting a subscription fee of $600 for one year of service.

For parts (a), (b) and (c) assume the game ends after only one year, no matter what actions the two satellite TV operators take.

(a) [5 point] Derive the unique Nash equilibrium for the subgame following Ozstar announcing it will be operating this year and Wolftel announcing it is closing down.

(b) [5 points] In the subgame following both Ozstar and Wolftel announcing they will be operating their satellite TV services this year, explain why the unique Nash equilibrium is for both to set their subscription fees equal to $100.

(c) [10 points] Using your answers from parts (a) and (b), Find all the subgame perfect equilibria of the one-year game. [HINT: Do not forget about the equilibrium that entails both operators randomizing over their choice between deciding to operate this year or deciding to close down.]

For the rest of the question, assume the game now has an infinite horizon and both satellite TV operators have a common discount factor 0.8. Notice that the payoff from having the market to oneself is equal to the net present value of a profit stream of $200 million every year, that is, $200 million/(1-0.8) = $1000 million.

(d) [15 points] Construct the symmetric 'war-of-attrition' stationary equilibrium for this infinite horizon game.

Denote by Swat the strategy you were asked to derive in part (d).

(e) [10 points] Show that both operators playing the following strategy constitutes a subgame perfect equilibrium in which along the equilibrium path in every year both announce they will operate and both set a subscription fee equal to $600.

Description of strategy:

Year 1: Announce 'we will operate' and then set subscription fee equal at $600 (irrespective of what your competitor has announced it will do).

Year t: (where t > 1) IF, in all previous years, both operators have announced they will operate and have set their subscription fees at $600, or in some previous year, the other operator ceased operating; THEN, announce we will operateand set subscription fee at $600; ELSE, play the stationary 'war-of-attrition' strategy Swat.