Test 2016, answers PDF

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Econ228 (2016-17): SSG Econ228: Game Theory Feedback: Coursework Test 2016-17

Question 1 (25 marks) Some students have done the analysis considering 1, 2 or 3 matchsticks can be removed by the players, but the question clearly mentions that 1, 2, 3 or 4 matchsticks can be removed. Read the questions carefully in future. Answering the question referring to the 21 Flags game (week 1 tutorial) is not correct. Although both games are similar, allowed actions are not the same; you need to explain your knowledge to the particular setting of the question. (a) (6 marks) - A big majority of the students have done this correct. (b) (7 marks) - Students were required to write down the action for each round (i.e. an action for each decision point). - If optimally played there are two rounds remaining, so students were supposed to mention how many matchsticks should Barney leave Fred facing at each round. (c) (12 marks) - Students were required to write down the action for each round. - In some cases, only the action of first round is mentioned the rest of the game has not been discussed. - Please note that in a sequential game, a strategy describes the optimal action at each decision point, and therefore each round of the game needs to be discussed when asked about the optimal strategy. The strategy here is to mention how many match-sticks Fred should leave Barney facing at the end of each round. - Students have not read the question carefully. In the question it was written that Fred is the player who starts the game. This information was important while answering part (c).

Question 2 (40 marks) -

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Students have not mentioned that the first order conditions are the best response functions (i.e. 𝐵𝑅1 (𝑞2 ) for the best reponse function of Firm 1 against any quantities 𝑞2 of Firm 2, and similarly 𝐵𝑅2 (𝑞1 ) for Firm 2). Note that profit of firm 𝑖(= 1, 2); 𝜋𝑖 = 𝑇𝑅𝑖 − 𝑇𝐶𝑖 , where 𝑇𝑅𝑖 = 𝑝𝑞𝑖 and 𝑇𝐶𝑖 = 𝑀𝐶𝑖 𝑞𝑖 . Students have written 𝑇𝑅𝑖 = 𝑝𝑄, where 𝑄 = 𝑞1 + 𝑞2 . Please note that in the question we have different marginal costs for the two firms, i.e. 𝑀𝐶1 = 𝑐 and 𝑀𝐶2 = 𝑐 + 1. Students have made mistakes when solving the two best response functions simultaneously.

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Econ228 (2016-17): SSG -

Some students used directly the conditions MR=MC without even mentioning the maximisation problem of the firm. A few students confused the procedure to solve the Stackelberg duopoly (sequential game) with Cournot duopoly (simultaneous game).

Question 3 (35 marks) (a) (10 marks) - Majority have got this one correct. - Some students were confused on the strategies of Player 2. Notice that, for defining her strategies, actions from the set of information 2.1 (P and Q) must be combined with an action from the set of information 2.2 (A and B). (b) (25 marks) - Convert the subgame 2.2 to a normal form game. Please note that in this subgame only Players 2 and 3 are involved. Students need to be careful while writing down the payoffs of players 2 and 3 in the normal form table and make sure that in each cell row player’s payoffs come first, followed by the payoff of the column player. - Write the solutions (PSNE) of the normal form game. - Also it is important to explain briefly the steps of backward induction, rather than just deleting the dominated actions. - Equilibrium strategy profile and equilibrium path were to be written as final answers. - Please note that there are two equilibrium strategy profiles for this game and both were to be mentioned.

Summary statistics Avg. 1st 2(i) 2(ii) 3 Fail

65.75887 118 45 20 62 37

2...