Please Answer a. and b.

1. [30 points] During the COVID-19 pandemic, public health experts advised (and some governments required) people to wear face masks when in public places. Suppose there are just two people, and assume that both are entirely self-regarding (they care only about their own comfort and health). They both find it somewhat uncomfortable to wear a mask. They believe that masks are more effective in preventing the mask wearer from infecting others than in protecting the wearer themselves. They each would define their preferences as follows: "No-one wearing a mask is the least preferred outcome for me, so if the other person is not wearing a mask, then I prefer to wear a mask. But, if the other person is wearing a mask, then I prefer not to wear a mask. If I am wearing a mask, then I would rather have the other person wear a mask as well." a. Assume that they simultaneously choose between the strategies, Wear (the mask) and Don't, without knowing the strategy chosen by the other player. i. [7] Write down a payoff matrix representing the strategic interaction between these two people. Use {1, 2, 3, 4} as the payoff numbers. ii. [5] Find the Nash Equilibrium. iii. [3] What kind of game is this? (Consider the main classes of games discussed in class: Prisoners' Dilemma, Invisible Hand Game, Assurance Game, Disagreement Game) b. Now suppose the moves are sequential, in that one player, say Player 1, moves first, chooses between Wear and Don't, then Player 2 observes the choice of Player 1 and decides on her strategy accordingly. The preferences are as defined above. i. [6] Write down the game tree that represents this sequential move game. ii. [6] Find the Backward Induction equilibrium. State the equilibrium in terms of the players' strategies. iii. [3] Is there a first-mover advantage, second-mover advantage or neither? Explain. 1. [30 points] During the COVID-19 pandemic, public health experts advised (and some governments required) people to wear face masks when in public places. Suppose there are just two people, and assume that both are entirely self-regarding (they care only about their own comfort and health). They both find it somewhat uncomfortable to wear a mask. They believe that masks are more effective in preventing the mask wearer from infecting others than in protecting the wearer themselves. They each would define their preferences as follows: "No-one wearing a mask is the least preferred outcome for me, so if the other person is not wearing a mask, then I prefer to wear a mask. But, if the other person is wearing a mask, then I prefer not to wear a mask. If I am wearing a mask, then I would rather have the other person wear a mask as well." a. Assume that they simultaneously choose between the strategies, Wear (the mask) and Don't, without knowing the strategy chosen by the other player. i. [7] Write down a payoff matrix representing the strategic interaction between these two people. Use {1, 2, 3, 4} as the payoff numbers. ii. [5] Find the Nash Equilibrium. iii. [3] What kind of game is this? (Consider the main classes of games discussed in class: Prisoners' Dilemma, Invisible Hand Game, Assurance Game, Disagreement Game) b. Now suppose the moves are sequential, in that one player, say Player 1, moves first, chooses between Wear and Don't, then Player 2 observes the choice of Player 1 and decides on her strategy accordingly. The preferences are as defined above. i. [6] Write down the game tree that represents this sequential move game. ii. [6] Find the Backward Induction equilibrium. State the equilibrium in terms of the players' strategies. iii. [3] Is there a first-mover advantage, second-mover advantage or neither? Explain