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- 3. Consider the following game with nature: 6, 8 X Y 4, 5, 0 X 4, 6 Y 2 (p) L (1-P) High Low L' H 1 M (1/2) (1/2) 2 M' (9) (1-q) X' 3, 3 Y 10,7 X' 3, 0 Y' 8, 4 Does this game have any separating perfect Bayesian equilibrium? Show your analysis and, if there is such an equilibrium, report it (only one is required).Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors rock 0. -3 1 1. раper scissors -1 -1 3 (a) Show that xT= (,) and yT= (5) together are not a Nash equilibrium 3'31 for this modified 3'3 game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.Aedri Quick 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 esc 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 tab Treats CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 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. %3D caps lo 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information hift 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…
- What is the Nash Equilibrium in a game?A. A situation where all players cooperate for maximum gainB. A situation where no player can improve their outcome by changing their strategy unilaterallyC. A situation where players always choose the same strategyD. A situation where players randomly select strategiesHi 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 above1. With nash equilibrium, do you always choose the optimal strategy? 2. Can a game have more than one nash equilibrium?
- rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.Tucker and Eddie are playing the following game. Tucker can choose A or B and Eddie can choose C or D. The first payoff is for Tucker, the second for Eddie. Eddie Tucker C D A 3, 2 4, 3 B 4, 5 3, 4 Identify the Nash equilibrium(s) in this game. What rational game theoretic advice would you offer Tucker and Eddie on how to play this game? If Tucker and Eddie follow your advice, what payoff should each expect? Show your work.9. In the game played in the class, "Guess 2/3 of the average", assume there are 3 students, each guesses a number between 0 and 100 (including 0 and 100) simultaneously. The winner will be the one whose number is closest to 2/3 of the average. Which of the following is a Nash Equilibrium for this game? A. Everyone guesses "0" B. Everyone guesses "100" C. One student guesses "0", one guesses "100" and one guesses "50" D. One student guesses "0", one guesses "0" and one guesses "100" E. None of the above
- rock paper scissors rock 0. -3 0. раper scissors -1 -1 3. 0. (a) Show that xT= (,) and yT= (,) together are not a Nash equilibrium 3' 3 3131 for this modified game.Game theory 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. Player 2 7. Player 1 ہے A B C D -3, -3 0, -11 -4, 3 -11, E 0 -7, -7 -12, 0 (a) Identify any dominated strategies in this game. If there are none, state this clearly. (b) Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly.Consider the following price game: Firm 1 Firm 2 High Low High 20, 20 12, 24 Low 24, 12 14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?