3. Consider the following game where Energia and Airtricity offer dual-fuel energy products and can set...

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3. Consider the following game where Energia and Airtricity offer dual-fuel energy products and can set their annual prices High (H) or Low (L). The payoffs are as follows, with the first payoff in each cell being Energia's: Airtricity Energia |L H L 200, 160 100, 320 H 400, 80 280, 220 (a) What is the Nash equilibrium outcome in a one-shot simultaneous-move game? (b) Suppose the game is repeated twelve times. What is the subgame perfect Nash equilibrium outcome of this repeated game? Explain your answer. Suppose now that the game is repeated infinitely and both companies discount their future payoffs by a common annual discount factor of 8, where 0 < 8 <1 and is common knowledge. (c) If Energia and Airtricity begin by 'co-operating' and choosing the high price (H) in the first stage, under what circumstances are both companies playing a 'tit-for-tat' strategy a subgame perfect Nash equilibrium, assuming that both playing a tit-for-tat strategy is common knowledge? Compare your answer to that in (a) and explain any difference. (d) Again assuming that both companies begin by co-operating in the first stage, under what circumstances are both players playing a 'trigger' strategy a subgame perfect Nash equilibrium, assuming that both players playing such a strategy is common knowledge? Compare your answer to that in (c) and explain any difference. 3. Consider the following game where Energia and Airtricity offer dual-fuel energy products and can set their annual prices High (H) or Low (L). The payoffs are as follows, with the first payoff in each cell being Energia's: Airtricity Energia |L H L 200, 160 100, 320 H 400, 80 280, 220 (a) What is the Nash equilibrium outcome in a one-shot simultaneous-move game? (b) Suppose the game is repeated twelve times. What is the subgame perfect Nash equilibrium outcome of this repeated game? Explain your answer. Suppose now that the game is repeated infinitely and both companies discount their future payoffs by a common annual discount factor of 8, where 0 < 8 <1 and is common knowledge. (c) If Energia and Airtricity begin by 'co-operating' and choosing the high price (H) in the first stage, under what circumstances are both companies playing a 'tit-for-tat' strategy a subgame perfect Nash equilibrium, assuming that both playing a tit-for-tat strategy is common knowledge? Compare your answer to that in (a) and explain any difference. (d) Again assuming that both companies begin by co-operating in the first stage, under what circumstances are both players playing a 'trigger' strategy a subgame perfect Nash equilibrium, assuming that both players playing such a strategy is common knowledge? Compare your answer to that in (c) and explain any difference.

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a In a oneshot simultaneousmove game we can determine the Nash equilibrium by finding the strategy profile where no player has an incentive to unilate... View the full answer