There are two players 1 and 2. There are two cards: "High" and "Low". Player

1 chooses at random one card (Prob. 1/2 to each card). He looks at the card but does not

show it to Player 2. Then Player 1 decides whether to pay player 2 $10 and to terminate

the game or to continue to play. If he continues then Player 2 decides whether to continue

to play or to pay Player 1 $10 and to terminate the game. If Player 2 also continues then

the card is shown to Player 2. If the card is Low, Player 1 pays 2 $50. If it is High, Player 2

pays $40 to player 1.

(1) Describe the game by a tree.

(2) Write it in a strategic form.

(3) Find the optimal strategies of the players.

1 chooses at random one card (Prob. 1/2 to each card). He looks at the card but does not

show it to Player 2. Then Player 1 decides whether to pay player 2 $10 and to terminate

the game or to continue to play. If he continues then Player 2 decides whether to continue

to play or to pay Player 1 $10 and to terminate the game. If Player 2 also continues then

the card is shown to Player 2. If the card is Low, Player 1 pays 2 $50. If it is High, Player 2

pays $40 to player 1.

(1) Describe the game by a tree.

(2) Write it in a strategic form.

(3) Find the optimal strategies of the players.

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