2. Find the Nash equilibrium of the game below: Low Price Medium Price High Price Firm B a. Low Price 4,4 6,3 8,2 Firm A Medium Price High Price 3,6 5,5 4,3 2,8 3,4 3,3
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- Assume a simultaneous-move game. Firm B Low Price High Price Firm A Low Price 10,10 100,2 High Price 2,100 90, 90 What is the Nash equilibrium of the game?H7. Find all pure strategy Nash equilibria and for each one, state whether or not it is subgame perfect.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.
- 1. Consider the pricing game between firm 1 (row) and firm 2 (column) belowwhere each number represents the profits made by each firm.:Table 1: Pricing gameLow HighLow 288,288 360,216High 216,360 324,324 a) Point out the Nash equilibrium. Is this a unique Nash equilibrium?c) What type of commitment can firm 1 make to improve its pay-off?Can it be classified as a threat or promise? (Assume that the commitmentis credible.)d) How would you represent the game as a game tree with the option tocommit?2. Consider the signalling / production game with the order of play given below.Assuming that the signal is informative (i.e. education is sufficiently costly),how would you change the order of the game to make sure that poolingequilibriums are ruled out? Verbally motivate your answer.• Nature chooses ability of the workers a ∈ (H, L), ability is observed byworkers but not employers.• The worker choose an education level s ∈ (0, 1).• The employer offer contracts w(s).• The worker accepts or…1. Find all subgame perfect nash equilibrium 2. Find a nash equilibrium that is not SPNE, and explain why it is not an SPNE.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.
- Assume that Acme and Gamma are the two main rivals in the market for hair dryers. Each firm is considering prices of $50 or $60, with the following possible profit outcomes: Gamma Price = 50 Price = 60 Price = 50 40, 45 45, 42 Acme Price = 60 24, 55 30, 48 A) Assume the firms choose prices simultaneously. Does the game have a solution? Explain. B) Is the solution you have identified a Nash Equilibrium? Explain why or why not.1. Assume this game is played 2 times and there is no discounting. The whole payoff for two periods is the sum of payoffs of each period. Draw a tree of the game and solve it with subgame prefect Nash equilibrium. Explain clearly, handwritten is preferable.Give typing answer with explanation and conclusion Suppose two firms produce identical good. The inverse demand curve for the good is: P = 240-Q, where Q is the total quantity produced by the two firms. Each firm has a constant marginal cost 20 of producing the good and fixed cost = 100. Find the Cournot Nash equilibrium of this game. What quantity will each firm produce? what will be the market price? What would be the profits of each firm?
- 3. There are 2 firms that are considering entering a new market. The payoff for each firm that enters is 100/ n where n is the number of firms that enter. The cost of entering is 62. Find all the pure strategy Nash equilibria. Find the mixed strategy equilibrium.4. Boeing and Airbus, change in profits ($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?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.