2. Now consider a two player game that is symmetric (as well as zero-sum and simultaneous-move): Rock-Paper-Scissors. Do your best to write out the game of "RPS" using a game matrix. Then show that there are no pure-strategy equilibria.
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- Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.1. Consider the following two player 2x2, normal form game: (Payoffs are starting from northwest and moving clockwise are (10,5), (2,30), (5,5), and (40,10). Player 1 strategies are A and B, Player 2 strategies are C and D. Identify all Nash equilibria in pure strategies. a) 2. Using the normal form game, represent a two-player Rock-Paper-Scissors-Game where Player 1's losses and gains are triple that of Player 2.3. Write a normal form representation of the game shown in the figure below and derive all pure strategy Nash equilibria. P1 L R P2 P2 L R R l's Payoff 1 2's Payoff 2
- K In a game, there are two players: Player 1 and Player 2. They have two strategies to select from, A and B. Where the first payoff and the second payoff in every cell is for Player 1 and Player 2 respectively. Which of the following is an example of a game without a dominant strategy? (Check all that apply.) A. C. Player 1 Player 1 A B A B A 3,-3 1, 1 A 2,1 0,0 Player 2 Player 2 B 3, -3 5, -5 B 0,0 1,2 B. D. Player 1 Player 1 A B A B A 1,-1 -1, 1 Player 2 Player 2 A 3.5, -1.5 2.7, -1 B -1, 1 1,-1 B -5, 3 0,0 If the dominant strategy for Player 1 is selecting strategy A and the dominant strategy for Player 2 is strategy B, then A B is an example of a c From ame C Murat Çok Di id Kushn y My Handa) Draw an extensive form game with 4 outcomes (2 moves for player 1 followed by 2 moves for 2 after each of 1's moves) and no pure strategy Nash equilibrium. b) Write the strategic form to verify your answer to (a) c) Draw an extensive form 2-player game, in which both players always move, that has exactly 4 outcomes, 1 subgame perfect Nash equilibrium and no non-subgame perfect Nash equilibrium and no dominant strategies. d) Write the strategic form and use it to verify your answer to (b)In a game theory payoff matrix. Your company (A) and a major competitor (B) havetwo potential strategies: to advertise or to not advertise during the Super Bowl. The payoffs in each cell represent the change in firm profits from advertising. How would you create payoffs in each cell such that the Nash equilibrium is that both firms advertise despite having a higher profit if neither firm advertised
- Please look at the payoff matrix below which shows the benefits that would accrue to each player in a 2-player.non-sequential, non-repeated game. a) Identify the collusive (cooperative) equilibrium. b) Identify the secure strategy (maximin) equilibrium c) Identify the maximax equilibrium d) Identify the Nash equilibrium Apple Inc. Strategy 1 Strategy 2 Strategy 3 20 40 60 60 1000 200 Strategy A 70 50 90 Banana Inc. 400 70 300 Strategy B 40 80 100 90 150 80 Strategy C2. 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.2. Consider the following game. Two criminals are thinking about pulling off a bank robbery. The take from the bank would be $20,000 each, but the job requires two people (one to rob the bank and one to drive the getaway car. Each criminal could instead rob a liquor store. The take from robing a liquor store is only $1000 but can be done with one person acting alone. Write the payoff matrix of this game Player A Bank job Liqour store Player B Bank job Liquor store a. What are the Nash equilibria in this game? b. Explain why there can be multiple equilibria in this game. c. How the game will be played if mixed strategies are allowed? Discuss.
- The following payoff matrix represents a simultaneous-move game between two players: Kay and Jack. Each player has two choices: Black or White. The first number in each cell is the payoff to Kay, and the second number is the payoff to Jack. Jay Black White 50, 30, Black 50 30 Кay 45, 40, White 30 50 Refer to the scenario above. Which is true? a. This game has a dominant strategy equilibrium. b. This game has two dominant strategy equilibria. c. This game has two Nash equilibria. d. This game has one Nash equilibrium.. 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 thatThe following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff of