Problem 1: Antonia and Bob cannot decide where to go to dinner. Antonia proposes the following procedure: she will write on a piece of paper either the number 2 or the number 4 or the number 6, while Bob will write on his piece of paper either the number 1 or 3 or 5. They will write their numbers secretly and independently. They then will show each other what they wrote and choose a restaurant according to the following rule: if the sum of the two numbers is 5 or less, they will go to a Mexican restaurant (M), if the sum is 7 they will go to an Italian restaurant (1) and if the number is 9 or more they will go to a Japanese restaurant (J). 1) Formulate problem as game-frame and assign for each cell choice (M, I, or J). 2) Assume that preference for Antonio for restaurants is as follows descending (M,I,J) => (3,2,1) And for Bob (1, M, J) => (3,2,1). Represent from the table you built at first step, payoff of players at each cell. Problem 2: Two students work in team project Player 2 Lazy Work Hard Lazy Player 1 1, 1 3,0 Work Hard 0,3 2, 2 A) Define I, Si for each player i, S, and n for each strategy profile. B) Is there any strictly dominated strategy? Problem 3: Player 2 X Y A 5,2 4.2 Player1 3,1 3,2 5,1 2,1 4,3 5,4