The above figure shows the reaction functions for two pizza shops in a small isola town. The Stackelberg leader will produce A) 100 pizzas. B) 50 pizzas. OC) 25 pizzas. D) 66.7 pizzas.
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- Player 1 Cooperate (C) Defect (D) Cooperate (C) 3,3 8,0 Player 2 Defect (D) 0,8 1,1 In general, a combination of strategies is a Nash equilibrium if ... Every player is choosing a best response against the other players' strategies. Every player has a positive payoff. The players maximize the sum of their payoffs. The players choose identical strategies. If the game is repeated, which cooperative actions could benefit both players? O Both players choose C. Player 1 chooses C, Player 2 chooses D. O Player 1 chooses D, Player 2 chooses C. Both players choose D.(a) Stan and Ollie are two students who share a flat. Both of them prefer to live in a clean flat. However, neither is too fond of housecleaning. Each of them receives a payoff of 12 if they both clean the flat. If neither person cleans the flat, they receive a payoff of 6 each. If one person cleans the flat but the other person does not, then the payoff for the person who does the cleaning is 5 and the payoff for the person who doesn't do any cleaning is 15. (i) Write down the payoff matrix of this game. Derive the dominant strategy equilibrium. Is this also a Nash equilibrium? (ii) Expiain your reasoning. Consider a game with N players. Each player chooses Black or White. If a player (b) chooses Black, she gets 100 if everyone else also chooses Black, and she gets 0 if any of the other players does not choose Black. If a player chooses White, she always gets 50. Show that everyone choosing Black and everyone choosing White are both Nash equilibria of this game.Profits for two competing firms depend on the decisions to advertise or not to advertise as follows: If neither firm advertises, each makes a weekly profit of $100. If one firm advertises while the other does not, the firm that advertises makes $120 while the firm that doesn’t advertise makes $60. If both firms advertise, each firm makes $80. (a) What is the Nash equilibrium? Is this outcome efficient, from the perspective of the two firms? (b) How does the outcome of the game change if the parties can make a binding agreement in advance about advertising practices? (c) How does the game change if it is repeated over the course of many weeks (but the firms cannot make a binding agreement about how much advertising they will do)?
- 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.which is the nash equilibrium? small pig does press large pig does press (20, 130), small pig doesn't press large pig does press (140, 10), small pig does press large pig doesn't press (-5, 150), small pig does not press large pig doesn't press (0,0).10. Game theory
- UI. In American football, the offense can either run the ball or pass the ball, whereas the defense can either anticipate (and prepare for) a run or anticipate (and prepare for) a pass. Assume that the expected payoffs (in yards) for the two teams on any given down are as follows: (a) (b) (c) (d) OFFENSE Run Pass Anticipate Run 1,-1 DEFENSE 9,-9 Anticipate Pass 5,-5 3, -3 Show that this game has no pure-strategy Nash equilibrium. Find the unique mixed-strategy Nash equilibrium of this game. Explain why the mixture used by the offense is different from the mixture used by the defense. How many yards is the offense expected to gain per down in equilibrium?34. Which one would have the greatest effectし(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?
- There are two firms, each having the option of polluting during production or cleaning up its production process such that it doesn't pollute. Of course, polluting is cheaper than not polluting. The payoffs for each of the choice combinations are shown in the decision matrix below. Firm B Pollute Don't Pollute $75,000 $25.000 $75,000 $10,000 $10,000 $25,000 $25.000 What kind of commitment strategy could keep these firms from polluting? Instructions: In order to receive full credit, you must make a selection for each option. For correct answer(s), click the option once to place a check mark. For incorrect answer(s), click the option twice to empty the box. The environmental protection agency conducts a study on the dangers of pollution ? The government recommends that the companies not pollute. 7 The government makes pollution illegal and charges a company a $10,000 fine if it is caught polluting. 7 The companies agree not to pollute. The government makes pollution illegal and charges a…Starbucks and Krispy Kreme are trying to decide whether or not to open a shop in the new Mall of Africa. They both prefer if the other firm opens a shop because they can draw bigger crowds but neither wants to be the only American-branded coffee shop in the Mall. The payoff matrix for this dilemma is below. Krispy Kreme Open Don't Open Starbucks Open (i) (ii) 5,5 2,6 Don't open (iii) (iii) 6,2 3,3 MCQ question 4 Find the Nash Equilibrium (Starbucks, Krispy Kreme) for the payoff matrix when the game is played simultaneously. A. (5:5) only. B. (6,2) only. C. (2,6) only. D. (3,3) only E. There is no stable Nash Equilibrium. MCQ question 5 Suppose that Starbucks goes first in choosing to open or not to open. What is the outcome for this game? A. (5:5) only. B. (6,2) only. C. (2,6) only. D. (3,3) only E. There is no stable Nash Equilibrium.2. There are two ice-cream stores, each of whom chooses a position from ten spots along the beach: spot 1, 2, 3, ...10. The ten spots are lined up and separated 100 meters from each other. 1 2 3 4 5 6 7 8 9 10 The consumers are equally distributed across these ten spots. Consumers buy from the store whose spot is closest to theirs. If the two stores are equidistant from a given spot, the consumers at that position split their consumption equally. The aim of the ice-cream stores is to maximize their share of the total ice-cream consumption. a. Is there any dominated strategy? If so, spell out explicitly how one strategy is dominated by another strategy. b. Is there any iterated dominance equilibrium?
