Please answer the following questions!!

Question 1. Consider the following strategic setting. There are three players, numbered 1, 2, and 3. Player 1 has two cards, labeled King and Ace. At the beginning of the game, player 1 deals one of the cards to player 2 and the other card to player 3; that is, player 1 either gives the Ace to player 3 and the King to player 2 (call this the action A) or the King to player 3 and the Ace to player 2 (action K). Player 2 observes the card dealt to him; player 3 does not get to see the card dealt to her. Player 2 then must decide between switching cards with player 3 (S) or not (N). Player 3 observes whether player 2 made the switch, but does not see her card. Finally, player 3 responds to the question \"Is your card the Ace?\" by saying either \"yes\" (Y) or \"no\" (N). If player 3 correctly states whether her card is the Ace, then she obtains a payoff of 1 and the other players get 0; otherwise, players 1 and 2 both get a payoff of 1 and player 3 obtains 0. (1) Represent this game in the extensive form using a game tree. (2) How many information sets are there for player 1? For player 2? For player 3? (3) Write down the strategy spaces for this game. (4) Give an example of a strategy prole for this game, and write down each player's payoff given the strategy prole you have chosen. Use the correct mathematical notation in your