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Problem 1 (2p) What would be your prediction for the ultimatum game when each of the players is a pure altruist i.e., he prefers that other player gets more and only if the other gets the same amount in two cases he prefers the case in which he gets more for himself. Other assumptions are standard, as specified in the first example in lecture notes. What do you predict is going to happen in this game? Problem 2 (4p) (a) What would be your prediction for the ultimatum game when player 1 is benevolent, player 2 is malevolent but player 1 wrongly believes that player 2 is benevolent (player's 2 belief is correct)? Assume that they both know their own type and each player's belief about the other player is common knowledge. (b) What would be your prediction for the ultimatum game when player 1 is benevolent, player 2 is malevolent but player 2 wrongly believes that player 1 is male bolent (player's 1 belief is correct)? Assume that they both know their own type and each player's belief about the other player is common knowledge. Problem 3 (2p) What would be your prediction for the ultimatum game under the following assumption: both players know that the other player is an egoist (as defined by Axiom 1 in lecture notes) but they don't know anything about the other player beyond that. For instance, they cannot assume Axiom 2 or Axiom 2' or anything else for that matter. Suppose, then, that they both will act to maximize the amount of money they can get for sure. All these assumptions are common knowledge. What is the maximal amount of money player 1 can be sure to get in this game

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