Image transcription text 4. Consider the following variant of the card game discussed in class. Initially each player puts a dollar in the pot. Then

Image transcription text 4. Consider the following variant of the card game discussed in class. Initially each player
puts a dollar in the pot. Then each player is dealt a card; each player’s card is equally
likely to be High or Low, independent of the other player’s card. Each player sees only
her own card. Player 1 may see or raise. If she sees, then the players compare their cards.
The one with the higher card Wins the pot; if the cards are the same, then each player
takes back the dollar she had put in the pot. If player 1 raises, then she adds $2 to the pot,
and player 2 may pass or meet. If player 2 passes, then player 1 takes the money in the
pot. If player 2 meets, then she adds $2 to the pot and the players compare cards, the one
with the higher card winning the pot; if the cards are the same, then each player takes
back the $3 she had put in the pot. a. Model this card game as an extensive game. (Drawing a diagram is sufficient; you
can avoid the need for information sets to cross histories by putting the initial
move in the center of your diagram.) b. Find each player’s strategies in this game. c. Find the Nash equilibria of this game.