Suppose a firm 'Mega Airlines' holds a monopoly on the Melbourne to Cairns airline route, but is concerned about the possible entry of another firm 'Leopard Airlines'. Mega Airlines must decide whether to charge a high price or a low price for its tickets. Meanwhile Leopard Airlines is deliberating over whether to enter the market and service the Melbourne to Cairns airline route. Assume each firm cares only about its own profit and knows all possible profit outcomes from its decisions.

Mega Airlines is presently charging high prices and earning profits of $20 million on the route. If Leopard Airlines enters the market they will share the market - Mega Airlines will earn profits of $12 million and Leopard Airlines profits of $8 million. If Mega Airlines switches to charge low prices and Leopard Airlines enters the market, Mega Airlines will earn profits of $10 million and Leopard Airlines will make a loss of $6 million.If Mega Airlines charges low prices and Leopard Airlines doesn't enter, Mega Airlines will earn profits of $16 million.

a) (5 marks) Suppose Mega Airlines and Leopard Airlines must make their decisions simultaneously; that is, Mega Airlines chooses to charge a high price or a low price, and Leopard Airlines chooses to enter or not enter the market.

i] Does either player have a dominant strategy? Explain your answer. (2.5 marks)

ii] What is the Nash equilibrium? Explain your answer. (2.5 marks)

b) (5 marks) Now assume Leopard Airlines moves first by deciding whether to enter the market or not and Mega Airlines, having observed Leopard's choice, then decides on whether to charge a high price or low price.

i] What choices of actions constitute a strategy for each player? (2 marks)

ii]What is the 'rollback equilibrium' for this game? Explain how you derived the 'rollback equilibrium'. (2 marks)

iii] One manager at Mega Airlines argues that a successful strategy to deter entry into the market by Leopard Airlines is to charge a high price now, but publicly announce that it would set a low price if Leopard Airlines was ever to enter.

How successful would such a strategy be in deterring entry by Leopard Airlines? (1 mark)

c) (5 marks) Now assume Mega Airlines moves first to choose its price and Leopard Airlines, having observed Mega Airline's choice, then makes its decision on whether to enter.

i] What choices of actions constitute a strategy for each player? (2 marks)

ii]What is the 'rollback equilibrium' for this game? Explain how you derived the 'rollback equilibrium'. (2 marks)

iii] Another manager at Mega Airlines argues that a more successful strategy to deter entry by Leopard Airlines is for Mega Airlines to commit to a low price in advance of any entry decision of Leopard Airlines.

How successful would such a strategy be in deterring entry by Leopard Airlines? (1 mark)