Question 2 30 marks Health guidelines stipulate that if you feel that you are showing any kind of cold- or flu-like symptoms, you should self-isolate for 10 days just in case you have caught COVID-19. Essentially, what this boils down to is that individuals have to wake up every morning and assess whether or not they have any potential COVID-19 symptoms, and based on this, they make the decision whether to self-isolate or not. If an individual chooses to self-isolate, they potentially help to stop the spread of COVID-19. Thus, each person in society gains a payoff of 100 per individual who chooses to self-isolate. However, for the person choosing to isolate, this exerts a toll on them (through things like added inconvenience in completing daily tasks, or additional costs to have groceries delivered to them], which decreases their payoff by 40. The payoff to an individual for not self-isolating is 65, and their choice to not isolate provides no benefit to other members of society. Assume, for simplicity, that these payoffs are cardinal/monetary in nature. (a) Imagine that this scenario were to play out between two people: Person A and Person B. Calculate the following payoffs: The payoff Person A receives if they self-isolate and Person B self-isolates. iI. The payoff Person A receives if they self-isolate and Person B does not self- isolate. The payoff Person A receives if they do not self-isolate and Person B does self- isolate IV. The payoff Person A receives if they do not self-isolate and Person B doesn't self-isolate either. [4] (b) Using your answers from (a), fill in the following game table to represent the interaction between Person A and Person B. Then solve for the Nash Equilibrium/Equilibria and Nash Equilibrium Outcome(s) of the game. (6] Person B Self-isolate Don't self-isolate Person A Self-isolate Don't self-isolate (c) What is the socially optimal cell of the game above? Briefly explain your answer. [2] (d) Does Person A have a dominant strategy in this game? If so, what is it? Justify your answer. [3] (e) What kind of game is this? Briefly explain your answer. (4] (f) Represent the game between Person A and Person B graphically, with Person A's payoffs on the horizontal axis and Person B's payoffs on the vertical axis. [5] (g) Using your diagram in (f), explain briefly how if a player's preferences were somewhat altruistic rather than purely selfish, then we could reach the socially optimal outcome of this game. Hint: Think about where the socially optimal cell lies in relation to a player's most preferred cell for each type of preferences. (6]
