"If a normal form game has no pure strategy Nash equilibrium, then in any Nash equilibrium, at least one player is indifferent between both of her pure strategies given the equilibrium strategy of her opponent." Consider a 2 player game in which every player has two pure strategies. Is the following statement true or false? A. True B. False
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- 2. Consider the following game: u 1 r 6,0 0,6 d 3,2 6,0 Are there any Nash equilibria in pure strategies for this game? Find the mixed strategy Nash equilibrium.Consider the attached game depicted in Normal Form. Find one Nash equilibrium and verify that it is a Nash equilibrium. Note: 1. Remember to express the Nash equilibrium in the form of a strategy profile. 2. Use the definition of Nash equilibrium to verify that the strategy profile you find is really a Nash equilibrium.5. Consider a simultaneous game in which player A chooses one of two actions (Up or Down), and B chooses one of two actions (Left or Right). The game has the following payoff matrix, where the first payoff in each entry is for A and the second for B.(8 points) B Right Left 3,3 5,1 Down 2,2 4,4 a. Find the Nash equilibrium or equilibria. b. Which player, if any, has a dominant strategy? A Up
- Consider the following game : Stag Rabbit Stag 9, 9 0, 8 Rabbit 8, 0 7, 7 The first payoff is that of player 1 and the second that of player 2. a. ) Draw the extensive form of the simultaneous game. Find all the Nash equilibrium. p. Suppose player 1 moves first or we are in a sequential game now. Draw the extensive form in the sequential version. c. What is the subgame perfect Nash Equilibrium (SPNE) in the sequential version? d. ) Explain why it is an SPNE.. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do thatQuick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No The Ice Cream Guys $3.99 $4.99 Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 Treats The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would they agree upon, if any? a) Both…
- Consider the following simultaneous move game: Player 1 U M D Player 2 L 2,10 2,5 8,7 C 5,2 11,8 8,4 R 5,4 2,9 8,3 In the Nash equilibrium of this game, player 1 receives a payoff of ✓ and player 2 receives a payoff ofLet G be the following static game. Rose Colin A A (3,4) B (4,2) B (1,5) (0, 1) (a) Determine the pure Nash equilibria of G. (b) Rose A, B, Colin A, B is a mixed Nash equilibrium of H. (You do not have to verify this.) Determine the expected payoffs of both players given that they choose their strategies according to this Nash equilibrium. (c) Draw the payoff polygon of H. Indicate on your diagram the points corresponding to the Nash equilibria of H, and the points corresponding to Pareto optimal solu- tions of H.1\2 L 1,-1 | 5,0 | 0,0 0,5 4,4 0,0 0,0 3,3 M R C 0,0 В 1. Find all set of rationalizable strategies (Hint: We are allowed to eliminate a pure strategy, if it is strictly dominated by a mixed strategy). 2. Find all set of pure strategy Nash equilibria. 3. Is there a dominant strategy equilibrium for this game?
- 1) Put together an example of a 2x2 game (two players with each having two options) that has NO pure-strategyNash equilibria. (Hint: just try some values and then change them as you need to; as an example think aboutthe Rock, Scissors paper which has no pure strategy NE).2) Using your own words, explain how the concept of elimination of dominated strategies differs from theconcept of Nash equilibrium.3) Indicate whether the following statement is TRUE or FALSE and explain your answer: If one player is theleader in a game it means that s/he has the first move in the game. The key thing is that this move can beobserved by the follower before making his/her own decision, otherwise it would be a simultaneous movegame that cannot be solved by backwards induction.4) MULTIPLE CHOICE (identify the one best answer below and explain your reasoning for each option): Recallthe Game of chicken from the previous problem set. If James is the leader in the game then: (hint: you candraw the game tree…5. Consider the following Extended Form game where P1 stands for Player one and P2 stands for player two with A, B and A', B' being their respective strategies. A' (1,1) P2 B' (2,3) P1 A' B (4,5) P2 What is the set of Nash Equilibria? Clearly explain your answer. Full-screen Snip B' (6,7)Consider a Centipede game below. Player 1 moves first and he can choose either L or R. If player 1 chooses R; then Player 2 moves choosing either L or R and if he chooses R then Player 1 moves choosing either L or R and then finally player 2 moves. 1 R 2 R 1 R 2 R 9,9 L 2,0 0,4 6,2 4,8 a. Represent this game in a normal form b. Find all the Pure Strategy Nash equilibrium or equilibria c. Find all the Sub-game Perfect Nash Equilibrium of this game