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Saudi Arabia and Russia simultaneously must decide their oil production for the next quarter. Both countries can either choose High or Low output. If both opt for High, Russia gets a payoff of 5 and Saudi Arabia 7. If Russia opts of Low and Saudi Arabia High, the payoffs are 2 for Russia and 11 for Saudi Arabia. If Russia chooses High and its Saudi rival Low, the payoffs are 8 for Russia and 3 for Saudi Arabia. Finally, if both opt for Low, the payoffs are 6 and 9 to Russia and Saudi Arabia, respectively. Which statement is FALSE?Group of answer choicesThis game is a version of the prisoners’ dilemma.Saudi Arabia has a dominant strategy to play H.The Nash equilibrium is (H, H); the dominant strategy equilibrium is (H, H)Russia has a dominant strategy to play H.The Nash equilibrium is (H, H); the dominant strategy equilibrium is (L, L)

Question

Saudi Arabia and Russia simultaneously must decide their oil production for the next quarter. Both countries can either choose High or Low output. If both opt for High, Russia gets a payoff of 5 and Saudi Arabia 7. If Russia opts of Low and Saudi Arabia High, the payoffs are 2 for Russia and 11 for Saudi Arabia. If Russia chooses High and its Saudi rival Low, the payoffs are 8 for Russia and 3 for Saudi Arabia. Finally, if both opt for Low, the payoffs are 6 and 9 to Russia and Saudi Arabia, respectively. Which statement is FALSE?Group of answer choicesThis game is a version of the prisoners’ dilemma.Saudi Arabia has a dominant strategy to play H.The Nash equilibrium is (H, H); the dominant strategy equilibrium is (H, H)Russia has a dominant strategy to play H.The Nash equilibrium is (H, H); the dominant strategy equilibrium is (L, L)

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Solution

To answer this question, we first need to understand the concepts of Nash equilibrium and dominant strategy in game theory.

  1. Nash Equilibrium: A Nash equilibrium is a set of strategies, one for each player, such that no player has incentive to unilaterally change her action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy.

  2. Dominant Strategy: A dominant strategy is the best strategy for a player to follow regardless of the strategies chosen by other players.

Now, let's analyze the game:

  • If both Russia and Saudi Arabia choose High (H), Russia gets 5 and Saudi Arabia gets 7.
  • If Russia chooses Low (L) and Saudi Arabia chooses High (H), Russia gets 2 and Saudi Arabia gets 11.
  • If Russia chooses High (H) and Saudi Arabia chooses Low (L), Russia gets 8 and Saudi Arabia gets 3.
  • If both choose Low (L), Russia gets 6 and Saudi Arabia gets 9.

From this, we can see that:

  • For Russia, the best response to Saudi Arabia choosing High (H) is to choose High (H) as well, and the best response to Saudi Arabia choosing Low (L) is also to choose High (H). Therefore, Russia has a dominant strategy to play High (H).
  • For Saudi Arabia, the best response to Russia choosing High (H) is to choose High (H), and the best response to Russia choosing Low (L) is to choose Low (L). Therefore, Saudi Arabia does not have a dominant strategy.

The Nash equilibrium is the combination of strategies where no player can improve their payoff by unilaterally deviating. Here, the Nash equilibrium is (H, H) because neither Russia nor Saudi Arabia can improve their payoff by choosing Low (L) when the other chooses High (H).

Therefore, the statement "Saudi Arabia has a dominant strategy to play H" is FALSE. Saudi Arabia does not have a dominant strategy in this game.

This problem has been solved

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