Consider the following game. There are two players, 1 and 2. Player 1 moves first, and names...

Question:

Consider the following game.

There are two players, 1 and 2. Player 1 moves first, and names either Heads (H) or Tails (T) or Middle (M). If he chooses Heads or Tails, the game ends with probability 0.5. If it ends and player 1 has said Heads, payoffs are (3,2). If it ends and player 1 has said Tails, payoffs are (4,3). If the game does not end, player 2 gets to make a choice, after which the game ends. If player 1 has chosen Heads, player 2 can choose either Up, yielding payoff (9,6), Down, yielding payoff (3,1), or InsideOut yielding payoffs (1,5). Player 2 cannot tell the difference between player 1 choosing Tails or Middle. In either case, his alternatives are to choose Up or Backwards. If player 1 has chosen Tails, Up yields (1,1) and Backwards yields (2,6). If player 1 has chosen Middle, Up yields (1,1) and Backwards yields (6,2).

a. Draw the extensive form of this game.

Extensive Form

In Game Theory, the extensive form is a way to depict a sequential game in which players take turns to make decisions. It takes the form of decision tree with each node representing the decision maker and each branch representing the choice. The payoff are shown at the end of the branch. While simultaneous games are represented in a game matrix, game tree is the typical approach to present the game in which decisions are made at different points in time.

Answer and Explanation:

See attached for the extensive form of the game:


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