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Question: 1 a represent the following strategic situation in a normal...

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1.

A.

Represent the following strategic situation in a NORMAL FORM game. Janet is a contestant on a popular game show, and her task is to guess behind which door Liz, another contestant, is standing. With Janet out of the room, Liz chooses a door behind which to stand—either door A or door B. The host, Monty, observes this choice. Janet, not having observed Liz’s choice, then enters the room. Monty says to Janet either “Red” or “Green” (which sounds silly, of course, but it is a silly game show). After hearing Monty’s statement, Janet picks a door (she says either “A” or “B”). If she picks the correct door, then she wins $100. If she picks the wrong door, then she wins nothing. Liz wins $100 if Janet picks the wrong door and nothing if she picks the correct door. (Thus, Liz would like to hide from Janet, and Janet would like to find Liz.) Monty likes the letter A. If Janet selects door A, then this selection makes Monty happy to the tune of 10 units of utility. If she selects door B, then Monty receives 0 utility units.

B.

The following game is routinely played by youngsters—and adults as well—throughout the world. Two players simultaneously throw their right arms up and down to the count of “one, two, three.” (Nothing strategic happens as they do this.) On the count of three, each player quickly forms his or her hand into the shape of either a rock, a piece of paper, or a pair of scissors. Abbreviate these shapes as R, P, and S, respectively. The players make this choice at the same time. If the players pick the same shape, then the game ends in a tie. Otherwise, one of the players wins and the other loses. The winner is determined by the following rule: rock beats scissors, scissors beats paper, and paper beats rock. Each player obtains a payoff of 1 if he or she wins, −1 if he or she loses, and 0 if he or she ties. Represent this game in NORMAL FORM. Also discuss the relevance of the order of play (which of the players has the move at the initial node) in the extensive form.

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