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 xed cost of$50million. 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. If an operator announces it is closing down it does not incur the xed 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 payo and no satellite service is supplied or sold in that market for the current year and every year thereafter.1If 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 erce price competition for subscribers, leading both operators to charge a subscription fee for the year of$100that is equal to theircommon and constantmarginal cost of providing one years worth of service to a subscriber. Hence in this case subscription fees generate no variable prot to oset the xed cost of$50million, leading both to experience a loss of$50million (that is, a payo of$50million).

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$200million ($250operating profit less the$50million fixed cost). It achieves this by setting a subscription fee of$600for one year of service.

1. (a)[5 point]Derive the unique Nash equilibrium for the subgame following Ozstar announc- ing it will be operating this year and Wolftel announcing it is closing down.
2. (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.
3. (c)[10 points]Using your answers from parts(a)and(b), nd 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.]