Consider a game in which two players simultaneously pick an integer from 1 through 10. Let s1 denote choice of player 1, and let s2 denote the choice of player 2. If s1 # 82 then player 1's payoff is: 81 + 82 2 and player 2's payoff is 81+ 82 10 – If s1 = 82 then each player gets 5. How many pure strategy Nash equilibria does the game have (you will get full points if you are within 2 of the correct answer)?

Refer to Table Left-Right-ZigZag. How many pure strategy Nash equilibria does this game have? Table: Left-Right-ZigZag Player 1 Drive left Driver right Zigzag 1) 1 2) 2 3) 3 4) 4 5) None of the above. Drive left (1,1) (-1,-1) (0,0) Player 2 Driver right (-1,-1) (1,1) (0,0) Zigzag (0,0) (0,0) (0,0)

The count is three balls and two strikes, and the bases are empty. The batter wants to maximize the probability of getting a hit or a walk, while the pitcher wants to minimize this probability. The pitcher has to decide whether to throw a fast ball or a curve ball, while the batter has to decide whether to prepare for a fast ball or a curve ball. The strategic form of this game is shown here. Find all Nash equilibria in mixed strategies.

Consider the following two player game. In each cell the first number refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Suppose the two players move simultaneously (at the same time). Which one of the following statements is CORRECT? Player #1 Player #2 Top Bottom Left 7.7 4.0 Right 0,4 4,4 O There are three equilibria in this game: two pure strategy equilibria at [Top, Left] and [Bottom, Right) and al third equilibrium in mixed strategies. In the mixed strategy equilibrium of this game. Player 1 should play Top with probability 2/5 and Bottom with probability 3/5; Player 2 should play Left with probability 2/5 and Right with probability 3/5. O There are three equilibria in this game; two pure strategy equilibria at (Top. Left) and (Bottom, Right) and a third equilibrium in mixed strategies. In the mixed strategy equilibrium of this game, both players should randomize over the strategies with probability and %. O There is a unique dominant…

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Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly.

1.a) If the three executives of a fraudulent organization report nothing to the authorities, each gets a payoff of 100. If at least one of them blows the whistle, then those who reported the fraud get 28, while those who didn’t get -100. Suppose they play a symmetric mixed-strategy Nash equilibrium where each is silent (does not report fraud) with probability p. What is p?A, 0.1B, 0.28C, 0.5D, 0.8 b) In a two-player game, with strategies and (some known and some unknown) payoffs as shown below, suppose a mixed-strategy equilibrium exists where 1 plays C with probability 3/4, and Player 2 randomizes over X, Y, and Z with equal probabilities.   What are the pure-strategy equilibria of this game?      A, (A, Y) and (B, X)B, (A, Z) and (C, Y)C, (B, X) and (C, X)D, (C, X) and (C, Y)

Hello, please help me to solve this Game Theory question. Thanks in advance! Hobby hunter Jack decides what to do the next weekend. He can either stay at home and watch movies (Movies), or call his friend Katherine to go hunting (Hunt). If he stays in, both Jack and Katherine get a payoff of 2. If he decides to hunt, he knows the situation with his friend will resemble a classic stag hunt game with simultaneous moves: Hunting a stag is better than hunting a rabbit, but it only works if they cooperate. The hunting subgame is captured as:     Katherine       Stag Rabbit Jack Stag 3 , 3 0 , 1   Rabbit 1 , 0 1 , 1 Draw the entire game as an extensive form (game tree), capturing both Jack’s initial decision (M or H) and the subsequent hunting game. Make sure to correctly label all players, actions, and information sets.