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. represent this game in the extensive for