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 L R l's Payoff 1 2's Payoff 1
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- Consider the following game in normal form. Not cooperate Cooperate Not cooperate 20,20 50,0 Cooperate 0,50 40,40 What is Nash equilibrium? Is it efficient? Why? What needs to be complied with so that the players would like to cooperate? What happens when one of the players does not cooperate? Why? Define trigger strategy. Calculate the discount factor (δ) that would make both players decide to cooperate.1. Assume this game is played 2 times and there is no discounting. The whole payoff for two periods is the sum of payoffs of each period. Draw a tree of the game and solve it with subgame prefect Nash equilibrium. Explain clearly, handwritten is preferable.4. Boeing and Airbus, change in profits ($m) from the development of a super jumbo jet.AirbusDevelop Do not developBoeing Develop -50, -50 -30, 80Do not develop 80, -30 0, 0a) Identify the key assumption of Game theoryb) What important lesson does game theory reveal about coordination inan oligopoly market?c) In the game above, what is the Nash equilibrium?
- 3. Three politicians are voting on whether to allow themselves a salary increase of $ 3,500 per year. If they vote in favour of a raise, then they lose some public support, costing them each $ 1,500 per year. The salary increase passes if two or more politicians vote in favour of it. What is this game’s Nash equilibrium (or equilibria)? Explain. There is no need to draw a payoff matrix. (20%. 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 thatConsider Bernard \ Mary Left Center Right Top 0,5 1,0 2,2 Bottom 1,0 0,3 2,2 The first number in a cell denotes the payoff to Bernard and the second number denotes the payoff to MaryForexample: πB(B,L)=1and πM(T,L)=5. a Give all pure strategy Nash equilibria of this one-shot game, if any. Briefly explain.Let Bernard play Top with probability p and Bottom with probability 1 − p; let Mary play Left with probability qL , Center with probability qC and Right with probability qR = 1 − qL − qC . b Give all mixed strategy Nash equilibria of this game.
- Refer to the payoff matrix in question 8 at the end of this chapter. First, assume this is a one-time game. Explain how the $60/$57 outcome might be achieved through a credible threat. Next, assume this is a repeated game (rather than a one-time game) and that the interaction between the two firms occurs indefifi nitely. Why might collusion with a credible threat not be necessary to achieve the $60/$57 outcome?4. Correlated EquilibriaConstruct an example (not one from class or the reading) of a Normal form game with a correlated equilibrium that is not a Nash equilibrium.Game Theory. 1. Yuppie town has two food stores, LA Boulangerie, which sells bread, and La Fromagerie, whichsells cheese. It costs $1 to make a loaf of bread and $2 to make a pound of cheese. If LaBoulangerie's price is P 1 dollars per loaf of bread and La Fromagerie's price is P 2 dollars per pound ofcheese, their respective weekly sales, Q 1 thousand loaves of bread and Q 2 thousand pounds ofcheese, are given by the following equations: a) For each store, write its profits as a function of P 1 and P 2 , and find the Nash equilibriumprices in this game. b) Suppose that the two stores collude and set prices jointly to maximize the sum of theirprofits. Find the joint profit-maximizing prices for the stores.c) Provide an explanation for the differences between the Nash equilibrium prices and thosethat maximize joint profits.
- 1. Consider the following simultaneous move game Player 2 C D Player 1 A 4,3 4,-2 B 2,2 3,-1 C 3,0 4,0 C) Find the pure strategy Nash equilibria.Consider a sequential game between a shopkeeper and a haggling customer. The party who moves first chooses either a high price ($50) or low price ($20) and the second mover either agrees to the price or walks away from the deal and neither party gets anything. Ignore costs and assume the customer values the item at $60.If the shopkeeper goes first and quotes a low price, what is the best response of the customer? Question 33 options: a)Slam the storeowner's door on the way out b)Laugh at the storeowner c)Walk away from the deal d)Accept the low price happily Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.