PS4.pdf - HE3002 Game Theory(Sem 1 AY2019\/20 Problem Set 4(for tutorial on 24 Sep 2019 1 Consider the following game played by a monopolist supplier of

# PS4.pdf - HE3002 Game Theory(Sem 1 AY2019/20 Problem Set...

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HE3002: Game Theory (Sem 1, AY2019/20) Problem Set 4 (for tutorial on 24 Sep 2019) 1. Consider the following game played by a monopolist supplier of oil (Player 1) and a monopolist producer of electricity using oil-fired generator (Player 2). They simultaneously choose their actions: the oil company (Player 1) decides whether to raise the price of oil (action R) or not (action NR), and the electricity company (Player 2) chooses whether to build (action B) a new power plant which uses gas instead of oil or not (action NB). Player 1’s payoff is dependent only on the two players’ action while player 2’s payoff is dependent on the actions as well as the the cost of building the plant. There are two possible costs and the payoff of each scenario is summarized in the following payoff matrix: High Cost H: Player 2 B NB Player 1 R - 1 , 0 1 , 2 NR 0 , 2 0 , 3 Low Cost L: Player 2 B NB Player 1 R - 1 , 3 1 , 2 NR 0 , 5 0 , 3 The type of cost (H or L) is known only to Player 2. Player 1 does not know it, but he knows it is H with probability p . (a) Model this static Bayesian game as a dynamic game with imperfect information (i.e. state the players, their strategies and draw the extensive form game, carefully labeling the payoffs).

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