Following the meeting at the United Nations, South Africa must decide whether they want to impose economic sanctions on Russia. If South Africa chooses to impose economic sanctions on Russia, then Russia could retaliate by sanctioning South Africa back or by waging war on South Africa. If South Africa does not impose economic sanctions on Russia, they have two alternate options: either they can engage with President Putin and try to intercede on Ukraines behalf to bring about peace, or they can do nothing. If South Africa intercedes on Ukraines behalf, then Russia can either choose to engage with the discussions or be dismissive. If South Africa does nothing, then everything stays as it is and Russia will not react. This situation is summarised in the game tree below

Question 3 10 marks Following the meeting at the United Nations, South Africa must decide whether they want to impose economic sanctions on Russia. If South Africa chooses to impose economic sanctions on Russia, then Russia could retaliate by sanctioning South Africa back or by waging war on South Africa. If South Africa does not impose economic sanctions on Russia, they have two alternate options: either they can engage with President Putin and try to intercede on Ukraine's behalf to bring about peace, or they can do nothing. If South Africa intercedes on Ukraine's behalf, then Russia can either choose to engage with the discussions or be dismissive. If South Africa does nothing, then everything stays as it is and Russia will not react. This situation is summarised in the game tree below. South Africa Do nothing Sanctions Intercede Russia (1,3) Sanctions War Engage Dismiss (0,0) (X,Y) (5,4) (3,5) If Russia goes to war, there is some uncertainty about how this will play out for each country. Russia could choose to either make use of nuclear warfare, or they can choose to make use of cyber warfare to attack South Africa's IT infrastructure. Assume that if Russia chooses to make use of nuclear warfare, South Africa would receive a payoff of -5000, while Russia would receive a payoff of -1000. However, if Russia opts to use cyber warfare, then South Africa will receive a payoff of-2 and Russia will receive a payoff of 2. Assume that the probability of Russia using nuclear warfare is 0.001. Russia (a) Using the information above, calculate the values for X and Y-ie. the expected payoffs for South Africa and Russia if Russia chooses to go to war after South Africa has imposed sanctions. [4] (b) Using your answers in (a), and showing your working, determine what South Africa will choose to do in the subgame perfect Nash equilibrium of this game. [6] Question 3 10 marks Following the meeting at the United Nations, South Africa must decide whether they want to impose economic sanctions on Russia. If South Africa chooses to impose economic sanctions on Russia, then Russia could retaliate by sanctioning South Africa back or by waging war on South Africa. If South Africa does not impose economic sanctions on Russia, they have two alternate options: either they can engage with President Putin and try to intercede on Ukraine's behalf to bring about peace, or they can do nothing. If South Africa intercedes on Ukraine's behalf, then Russia can either choose to engage with the discussions or be dismissive. If South Africa does nothing, then everything stays as it is and Russia will not react. This situation is summarised in the game tree below. South Africa Do nothing Sanctions Intercede Russia (1,3) Sanctions War Engage Dismiss (0,0) (X,Y) (5,4) (3,5) If Russia goes to war, there is some uncertainty about how this will play out for each country. Russia could choose to either make use of nuclear warfare, or they can choose to make use of cyber warfare to attack South Africa's IT infrastructure. Assume that if Russia chooses to make use of nuclear warfare, South Africa would receive a payoff of -5000, while Russia would receive a payoff of -1000. However, if Russia opts to use cyber warfare, then South Africa will receive a payoff of-2 and Russia will receive a payoff of 2. Assume that the probability of Russia using nuclear warfare is 0.001. Russia (a) Using the information above, calculate the values for X and Y-ie. the expected payoffs for South Africa and Russia if Russia chooses to go to war after South Africa has imposed sanctions. [4] (b) Using your answers in (a), and showing your working, determine what South Africa will choose to do in the subgame perfect Nash equilibrium of this game. [6]