Game Theory and Strategic Decision Making Write precise answers (do not exceed word limits, however, answers without proper explanations will be penalised). 1. 2+3+5+3=15 Amar and Vasin are roommates. Each of them prefers a clean room to a dirty room, but neither likes to clean the room. If both clean the room, they each get a payoff of 5. If one cleans and the other doesn't clean the room, the person who does the cleaning has a utility of 0, and the person who doesn't clean the room has a utility of 8. If neither cleans the room, the room stays a mess and each has a utility of 1. (a) Write down the payoff matrix (b) Is there any strictly dominating strategy for any player? Explain. (50 words) (c) Solve for the Nash equilibrium. (100 words) (d) Comment. (100 words) 2. 5+10=15 Suppose Amar and Vasin are dividing 10 chocolates between themselves. At the first period, Amar offers the split. If Vasin accepts the split, then they share the chocolates according to Amar's offer. If Vasin does not agree to Amar's offer, in the next period, he gets to offer the split. However, only 9 chocolates will be there in the second period at the time when Vasin makes the offer. Assume that chocolates cannot be broken. Also, assume that if Vasin(Amar) is indifferent between two offers, he will accept the one that is most preferred by Amar(Vasin). (a) Write down the extensive form game. (b) Solve for the subgame perfect equilibrium. (200 words)