Draw the extensive-form representation of the following three-card poker game. There are three cards in the deck: an Ace, a King, and a Queen. The deck is shuffled, one card is dealt to player 1, and one card is dealt to player 2. Assume the deck is perfectly shuffled so that the six different ways in which the cards may be dealt are equally likely.
Each player observes his own card but not the card dealt to the other player. Player 1 then decides whether to fold or bid. If he folds, then the game ends and the payoff vector is (-1, 1); that is, player 1 obtains -1 (he loses his ante), and player 2 obtains 1 (gaining player 1's ante). If player 1 bids, then player 2 must decide whether to fold or bid. If player 2 folds, then the game ends with payoff vector (1, -1). If player 2 decides to bid, then the players reveal their cards.
The player with the higher card wins, obtaining a payoff of 2; the player with the lower card loses, getting a payoff of -2. Note that when both players bid, the stakes are raised. By the way, the Ace is considered the highest card, whereas the Queen is the lowest card.