Please correct answer and don't use hand rating 3. Consider a two-player Rock-Paper-Scissors game: rock beats scissors, scissors beat paper,paper beats rock (this is another zero-sum game). Find pure strategy and mixed strategy nashequilibrium. Suppose winning gives player payoff of 1 and losing results in -1 payoff, in caseof tie both get zero. Lets add one more strategy called Dynamite. Dynamite beats everything,but if both players choose it, they end up in the hospital, payoff -10,000 for both. Discuss howadding this new strategy affects the equilibrium outcomes of the game.

1. Original Rock-Paper-Scissors Game (Without Dynamite)In the original Rock-Paper-Scissors (RPS)…

Answered: 3. Consider a two-player…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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. 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 that
P1 gets $45 Up P2 gets $150 ... Up P1 gets $100 Down P2 gets $100 Up P1 gets $95 Down P2 gets $95 P1 gets $15 Down P2 gets $25 Player 1 Player 2 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? A (down, up) B NO EFFICIENT equilibrium exists C (up,down) D (down, down) E) (up,up)
The 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
4. Consider the two-player Rock-Paper-Scissors game. Each player can choose between three pure strategies: Rock, Paper, and Scissors. Strategy Rock beats Scissors, but loses to Paper. Strategy Paper beats Rock but loses to Scissors. Strategy Scissors beats Paper, but loses to Rock. When the game is a draw, the payoff for the players is '0'. The payoff of winning is ‘+1' and the payoff of losing is '-1'. Formulate this problem as a two-person, zero-sum game by constructing a payoff table.
Hi this is from a textbook. Thank you. Consider the following game in which Sally can play T or B and John chooses between L or R. Each player makes their choice simultaneously. If Sally chooses T and John chooses L, Sally gets a payoff of 5 and John has a payoff of 4. If Sally plays T and John R, Sally’s payoff is 8 and John gets 3. If Sally Chooses B and John L, the payoffs are 3 to Sally and 2 to John. Finally, if Sally chooses B and John R, the payoffs are 7 to Sally and 0 to John. Which statement is true? a) The Nash equilibrium is (B,R); this is a prisoners’ dilemma b) The Nash equilibrium is (T,R); this is a prisoners’ dilemma c) The Nash equilibrium is (T,R); this is not dominant strategy equilibrium d) The Nash equilibrium is (T,L); this is a dominant strategy equilibrium e) None of the above
5. Aaron and Betty play the following one-shot game. Aaron Up Middle Down Left 10,0 5,10 1,1 Betty Right 0,5 1,0 2,2 a. Does the game above have any (pure strategy) Nash equilibria? Find any equilibria or explain why an equilibrium doesn't exist. b. Suppose instead that Aaron moves first and Betty moves second. Represent this situation with a game tree and find the subgame perfect Nash equilibrium. Are Aaron and Betty better off playing a simultaneous game or a sequential game in which Aaron moves first? Explain. c.
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.
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.
2. Brad and Angelina have agreed to meet up for their first date. Neither of them can remember the exact location where they arranged to meet up and have forgotten their phones at home. Their payoff matrix can be described as follows: Brad The Hive Le Monde a) What is the Nash equilibrium in this game? Angelina The Hive 5; 5 0; 0 Le Monde 0; 0 5; 5
Keith and Blake play a simultaneous one-shot game given by the following table: Blake Left Right Keith Top Bottom 4.00, -5.00 0.00, -6.00 5.00, 0.00 -2.00, 7.00 As there is no unique pure strategy Nash equilibrium, assume that each player plays each of his choices half of the time. What is the average payoff for Keith? | What is the average payoff for Blake? (Round to two decimals if necessary.) (Round to two decimals if necessary.)
2. Two players play the following normal form game. 1\2 Left Middle Right Left Middle Right 4,2 3,3 2,1 3,3 5,5 6,2 1,2 2,6 3,3 Suppose that the game is repeated for two periods. What is the outcome from the subgame perfect Nash equilibrium of the whole game: ○ a) (Left, Left) is played in both periods. ◇ b) (Right, Right) is played in both periods. ◇ c) (Middle, Middle) is played in the first period, followed by (Left, Left) ◇ d) (Middle, Middle) is played in the first period, followed by (Right, Right)
3. Solving for dominant strategies and the Nash equilibrium Suppose Charles and Dina are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Charles chooses Right and Dina chooses Right, Charles will receive a payoff of 3 and Dina will receive a payoff of 8. Dina Left Right Left 3,7 2,6 Charles Right 4,5 3,8 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Charles chooses and Dina chooses

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