Problem 2

BHP and the Chinese Steel Association are negotiating over sales of iron ore by BHP to Chinese steel producers. Iron ore can be sold by long-term contract, or on a spot market. BHP must make choices about whether to seek to sell a 'Small' or 'Large' proportion of its iron ore on the 'spot' market for iron ore, and about whether to seek a 'Low' or 'High' price for the iron ore it sells by long- term contract. The Chinese Steel Association must decide whether to 'Not Allow' or 'Allow' BHP from selling its iron ore on the spot market. Payoffs from this game involving BHP and the Chinese Steel Association are shown in the game table below: Chinese Steel Association Not allow Allow $70billion, $80billion, BHP Small quantity Low price $80billion $40billion $60billion, $40billion Small quantity High price $30billion $60billion $60billion, $120billion, Large quantity Low price $30billion $40billion $40billion, $60billion, Large quantity High price $20billion $10billion$40billion, $60billion, Large quantity High price $20billion $10billion Suppose BHP and the Chinese Steel Association make their choices simultaneously: a) (2 marks) Does either player have a strict dominant strategy? Explain your answer. b) (3 marks) What are the Nash equilibria? Explain your answer. Suppose this game is played sequentially. First, BHP chooses whether to try to sell a 'Small' or 'Large' quantity of iron ore on the spot market. Second, having observed this choice, the Chinese Steel Association decides whether to 'Not allow' or 'Allow' BHP to sell on the spot market. Finally, having observed the choice made by the Chinese Steel Association, BHP decides whether to ask for a 'Low' or 'High' price for long-term contract sales. c) (3 marks) Describe the choices of action that constitute a strategy for each player. d) (5 marks) What is the rollback equilibrium in the sequential version of the game? Explain your answer. e) (2 marks) Explain how and why your answer to part (d) differs from your answer to part (b)