BP and ExxonMobil are engaged in negotiations regarding a new exploration. Simultaneously BP can choose to play Tough (T) or soft (S), while ExxonMobil can opt for Intransigent (I) or Acquiesce (A). The payoffs are as follows. If the choices are T and I, the payoffs are 3 to each firm. If the choices are S and I the payoffs are (1, 4) for BP and ExxonMobil, respectively. If the actions of the firms are T and A, the payoffs are (4, 1), and if the actions are S and A, then the payoffs are (5, 5). Which of the following is a Nash equilibrium? (CHOOSE ALL CORRECT ANSWER)Group of answer choices(S, I)(T, I)(T, A)(S, A)
Question
BP and ExxonMobil are engaged in negotiations regarding a new exploration. Simultaneously BP can choose to play Tough (T) or soft (S), while ExxonMobil can opt for Intransigent (I) or Acquiesce (A). The payoffs are as follows. If the choices are T and I, the payoffs are 3 to each firm. If the choices are S and I the payoffs are (1, 4) for BP and ExxonMobil, respectively. If the actions of the firms are T and A, the payoffs are (4, 1), and if the actions are S and A, then the payoffs are (5, 5). Which of the following is a Nash equilibrium? (CHOOSE ALL CORRECT ANSWER)Group of answer choices(S, I)(T, I)(T, A)(S, A)
Solution
A Nash equilibrium is a concept in game theory where the optimal outcome of a game is one where no player has an incentive to deviate from their chosen strategy after considering an opponent's choice.
Let's analyze each of the options:
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(S, I): If BP plays Soft and ExxonMobil plays Intransigent, the payoffs are (1, 4). However, BP could increase its payoff to 4 by switching to Tough, so this is not a Nash equilibrium.
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(T, I): If BP plays Tough and ExxonMobil plays Intransigent, the payoffs are (3, 3). Neither company can increase its payoff by unilaterally changing its strategy, so this is a Nash equilibrium.
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(T, A): If BP plays Tough and ExxonMobil plays Acquiesce, the payoffs are (4, 1). However, ExxonMobil could increase its payoff to 4 by switching to Intransigent, so this is not a Nash equilibrium.
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(S, A): If BP plays Soft and ExxonMobil plays Acquiesce, the payoffs are (5, 5). Neither company can increase its payoff by unilaterally changing its strategy, so this is a Nash equilibrium.
So, the Nash equilibriums are (T, I) and (S, A).
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