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- Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.1.9. What is a mixed strategy in a normal-form game? What is a mixed-strategy Nash equilibrium in a normal-form game?1. Two electricity firms compete in the same market and are deciding their level of advertising in order to increase customers and profits. The following matrix shows the profits (in millions) according to the strategy chosen: Firm 1 Strategies Low Advertising Aggressive Advertising Firm 2 Low Advertising 15, 15 20, -2 Aggressive Advertising -2, 20 5,5 a. Identify the one-shot Nash equilibrium. Comment. b. Suppose the players know this game will be repeated exactly 10 times. Can they achieve payoffs that are better than the one-shot Nash equilibrium? Explain. c. Suppose this game is infinitely repeated and the interest rate is 5%. Can the players achieve the collusive outcome? Explain.
- Short Answer Part 1 Consider this as a simultaneous-move (static) game: Player A Top Bottom Player B Left 5,1 0,4 Right 1,3 2,4 1.a) Write down the Best Response Correspondence for each of the two players. 1.b) Does any player have a dominant strategy in this game? Explain. 1.c) Find all Nash Equilibria in pure strategies of this game. 1.d) Is there any Nash Equilibria in mixed strategies? If so, find it.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?Suppose Proctor & Gamble (PG) and Johnson & Johnson (JNJ) are simultaneously considering new advertising campaigns. Each firm may choose a high, medium or low level of advertising. a. What are each firm’s best responses to its rival’s strategies? b. Does either firm have a dominant strategy? c. What is the Nash equilibrium in this game?
- 12) What is a Nash equilibrium? Why do we generally think that Nash equilibria will be likely outcomes of games?8. To advertise or not to advertise Suppose that Creamland and Dairy King are the only two firms that sell ice cream. The following payoff matrix shows the profit (in millions of dollars) each company will earn depending on whether or not it advertises: Creamland Dairy King Advertises Doesn't Advertise 9,9 Doesn't Advertise 3, 15 Advertises 15, 3 11, 11 For example, the upper-right cell shows that, if Creamland advertises and Dairy King doesn't advertise, Creamland will make a profit of $15 million, and Dairy King will make a profit of $3 million. Assume this is a simultaneous game and that Creamland and Dairy King are both profit-maximizing firms. If Creamland decides to advertise, it will earn a profit of $ not advertise. If Creamland decides not to advertise, it will earn a profit of $ does not advertise. million if Dairy King advertises and a profit of $ If Dairy King advertises, Creamland makes a higher profit if it chooses million if Dairy King advertises and a profit of $…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?
- 4. Suppose in 1977 Honda and Toyota each have to decide whether to build an automobile plant in the North American market. The payoff matrix below shows Honda's payoff on the left, and Toyota's on the right. Is there a Nash equilibrium? If so, where, and how do you know? Тoyota Build small Don't build anything plant Build small 16, 16 20, 15 Honda plant Don't build anything 15, 20 18, 18In Brandenburger and Nalebuff's article "Use game theory to shape strategy," coopetition is a game where ______Group of answer choices firms in an industry compete with each other indirectly, rather than directly. firms in an industry pursue win - win and win - lose strategies simultaneously. firms in an industry compete directly with firms in other industries. firms in an industry pursue pure win - win strategies.The following is a static game: Convert this game into dynamic form game. Find the Nash equilibrium and subgame perfect Nash equilibrium of this game. If you consider this game as dynamic then what kind of dynamic game is this.
