# Game Theory Worksheet assignment at an affordable cost

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Note that down is strictly dominated by up (when left, 2<3, and when right, 0<1) and therefore never used in a (mixed) Nash equilibrium. In the reduced game without down, denote the probability that player 1 plays up by p and the probability that player 2 plays left by q. The Nash equilibria in mixed strategies are determined by?

Consider the following team production game played by three players. Player 1 moves first and chooses between Effort and No Effort. If she chooses No Effort, the game is finished, and all players receive a payoff of 1 euro. If she chooses Effort, player 2 observes the choice of player 1 and chooses between Effort and No Effort. If in this case player 2 chooses No Effort, the game is finished, and players 2 and 3 receive 1 euro while player 1 receives 0 euro. If player 2 chooses Effort, player 3 observes the choices of players 1 and 2 and chooses between Effort and No Effort. If in this case player 3 chooses No Effort, the game is finished, player 3 receives 1 euro while players 1 and 2 receive 0 euro. If in this case player 3 chooses Effort, the game is finished, and all three players receive 2 euro. The players maximize their expected monetary outcome. a. 5 points Draw the extensive game tree that corresponds to the situation

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