Question

2) Here's another game: There are three players, numbered 1,2, and 3. At the beginning of the game, players1 and 2 simultaneously make decisions, each pulling out a Red or Blue marble. Neither player can see what the other player is choosing. After this choice, the players secretly reveal their marbles to each other without letting player 3 see. If both players choose Red, then the game ends and the payoff vector is(, 0, 0). If both players choose Blue, then the game ends and the payoff vector is (0, 1, 0) However, if one player chooses Red while the other player chooses Blue, player 3 must guess which player is holding a Red marble; that is, player 3 must choose between player 1 or player 2 If player 3 guesses correctly, then he and the player holding the Red marble each obtain a payoff of 2 and the player holding the blue marble gets 0. If player 3 guesses incorrectly then the game ends and the payoff vector is (0, 0,0) Represent this game fully in the extensive form. Furthermore, discuss whether or not onc player in this game has an advantage (in this case, do you think one player is more likely to get consistently better payouts)?

Answer 1