The following three problems are about the mini-ultimatum game in which the proposer receives 1000 yen as endowment and Y yen as a possible offer amount. Here, let XXX be the last three digits of your student ID, and Y=XXX yen. However, in case your XXX is 000 or 001, then let Y=521. Answer the problems, assuming that each player is a selfish economic man for the analysis based on game theory (Do not consider mixed strategies as this course only treats pure strategies).

A) Consider a mini-ultimatum game in which the proposer can offer either 1 yen or Y yen to the responder. Assume that each player shows his own strategy at the beginning of the game, and the responder makes a commitment to his own strategy even if the mood changes. Write a payoff table for this game and find all the Nash equilibria. Explain why each of these strategy pairs is a Nash equilibrium, while the others are not.

B) Suppose that the mini-ultimatum game in the previous problem is played as a sequential game. Draw a game tree, illustrating that offering 1 cent is a subgame perfect equilibrium and that offering Y yen is not subgame perfect equilibrium. Write the payoffs of the proposer and the responder as two numbers in parentheses in the game tree diagram.

C) Consider another mini-ultimatum game in which the proposer can offer can either 0 yen , 1 yen, or Y yen to the responder. Draw two game trees, illustrating that there are two subgame perfect equilibria, and that there is no other subgame perfect equilibrium. Draw one tree for a subgame perfect equilibrium and show the best response in each node by making the appropriate branch a bold line. Write the payoffs of the proposer and the responder as two numbers in parentheses in each of the game tree diagrams.

The following three problems are about the mini-ultimatum game in which the proposer receives 1000 yen as endowment and Y yen as a possible offer amount. Here, let XXX be the last three digits of your student ID, and Y=XXX yen. However, in case your XXX is 000 or 001 , then let Y=521. Answer the problems, assuming that each player is a selfish economic man for the analysis based on game theory (Do not consider mixed strategies as this course only treats pure strategies). A) Consider a mini-ultimatum game in which the proposer can offer either 1 yen or Y yen to the responder. Assume that each player shows his own strategy at the beginning of the game, and the responder makes a commitment to his own strategy even if the mood changes. Write a payoff table for this game and find all the Nash equilibria. Explain why each of these strategy pairs is a Nash equilibrium, while the others are not. B) Suppose that the mini-ultimatum game in the previous problem is played as a sequential game. Draw a game tree, illustrating that offering 1 cent is a subgame perfect equilibrium and that offering Y yen is not subgame perfect equilibrium. Write the payoffs of the proposer and the responder as two numbers in parentheses in the game tree diagram. C) Consider another mini-ultimatum game in which the proposer can offer can either 0 yen, 1 yen, or Y yen to the responder. Draw two game trees, illustrating that there are two subgame perfect equilibria, and that there is no other subgame perfect equilibrium. Draw one tree for a subgame perfect equilibrium and show the best response in each node by making the appropriate branch a bold line. Write the payoffs of the proposer and the responder as two numbers in parentheses in each of the game tree diagrams. The following three problems are about the mini-ultimatum game in which the proposer receives 1000 yen as endowment and Y yen as a possible offer amount. Here, let XXX be the last three digits of your student ID, and Y=XXX yen. However, in case your XXX is 000 or 001 , then let Y=521. Answer the problems, assuming that each player is a selfish economic man for the analysis based on game theory (Do not consider mixed strategies as this course only treats pure strategies). A) Consider a mini-ultimatum game in which the proposer can offer either 1 yen or Y yen to the responder. Assume that each player shows his own strategy at the beginning of the game, and the responder makes a commitment to his own strategy even if the mood changes. Write a payoff table for this game and find all the Nash equilibria. Explain why each of these strategy pairs is a Nash equilibrium, while the others are not. B) Suppose that the mini-ultimatum game in the previous problem is played as a sequential game. Draw a game tree, illustrating that offering 1 cent is a subgame perfect equilibrium and that offering Y yen is not subgame perfect equilibrium. Write the payoffs of the proposer and the responder as two numbers in parentheses in the game tree diagram. C) Consider another mini-ultimatum game in which the proposer can offer can either 0 yen, 1 yen, or Y yen to the responder. Draw two game trees, illustrating that there are two subgame perfect equilibria, and that there is no other subgame perfect equilibrium. Draw one tree for a subgame perfect equilibrium and show the best response in each node by making the appropriate branch a bold line. Write the payoffs of the proposer and the responder as two numbers in parentheses in each of the game tree diagrams