(3) Intransitive dice. A die has six sides, each labeled with a number. Consider three dice...

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(3) Intransitive dice. A die has six sides, each labeled with a number. Consider three dice that are labeled as follows (a) 2, 2, 4, 4, 9, 9. (b) 1, 1, 6, 6, 8, 8. (c) 3, 3, 5, 5, 7, 7. Players 1 and 2 play the following extensive form game with perfect infor- mation. First, player 1 picks one of these three dice. Then player 2 picks one of the two that are left over. The utility of a player is the probability, when the two picked dice are rolled, that their die shows the higher number. (a) 10 points. Find a subgame perfect equilibrium of this game. (b) 9 points. Who has the higher utility? Is there a subgame perfect equi- librium in which the other player has higher utility? (c) 1 point. Read this: https://en.wikipedia.org/wiki/Intransitive_dice#Warren Buffett. (3) Intransitive dice. A die has six sides, each labeled with a number. Consider three dice that are labeled as follows (a) 2, 2, 4, 4, 9, 9. (b) 1, 1, 6, 6, 8, 8. (c) 3, 3, 5, 5, 7, 7. Players 1 and 2 play the following extensive form game with perfect infor- mation. First, player 1 picks one of these three dice. Then player 2 picks one of the two that are left over. The utility of a player is the probability, when the two picked dice are rolled, that their die shows the higher number. (a) 10 points. Find a subgame perfect equilibrium of this game. (b) 9 points. Who has the higher utility? Is there a subgame perfect equi- librium in which the other player has higher utility? (c) 1 point. Read this: https://en.wikipedia.org/wiki/Intransitive_dice#Warren Buffett.