1.Draw the extensive form representation of this game. 2. Find a subgame perfect equilibrium (SPE) of this game. focus on pure-strategies only.
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1.Draw the extensive form representation of this game.
2. Find a subgame perfect equilibrium (SPE) of this game. focus on pure-strategies only.
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- 2 firms are engaged in Cournot competition; firm A faces the cost curveCA(yA)=40yAand firm Bfaces the cost curveCB(yB)=40yB. The inverse market demand curve isP(y)=100y, whereyrepresents market level of output. a)Define the Cournot game. b)In 1 or 2 sentences explain why a firm has no incentive to deviate from the Cournot Nash equilibrium(holding their opponent’s strategy constant). c)Find the Cournot Nash Equilibrium. d)Now suppose instead of playing their strategies at the same time, firm A moves first and then firm B moves second(sequentialgame).Does firm A earn higher profits in this game or the game in part c)?The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has a cost of production of C1= 15*Q1 and firm 2 has a cost of production of C2=20*Q2 a) Suppose that firm play a Stackelberg game. First firm 1 sets the quantity in t=1, then, knowing which quantityfirm 1 has set, firm 2 chooses the quantity in t=2. What are the Stackelberg quantities and prices? What arethe profits od firm 1 and 2? Compared to part a) which firm benefits and which firm loses?Suppose that Fizzo and Pop Hop are the only two firms that sell orange soda. The following payoff matrix shows the profit (in millions of dollars) each company will earn depending on whether or not it advertises: Рop Hop Advertise Doesn't Advertise Advertise 8, 8 15, 2 Fizzo Doesn't Advertise 2, 15 11, 11 For example, the upper right cell shows that if Fizzo advertises and Pop Hop doesn't advertise, Fizzo will make a profit of $15 million, and Pop Hop will make a profit of $2 million. Assume this is a simultaneous game and that Fizzo and Pop Hop are both profit-maximizing firms. If Fizzo decides to advertise, it will earn a profit of $ million if Pop Hop advertises and a profit of $ million if Pop Hop does not advertise. If Fizzo decides not to advertise, it will earn a profit of $ million if Pop Hop advertises and a profit of $ million if Pop Hop does not advertise. If Pop Hop advertises, Fizzo makes a higher profit if it chooses If Pop Hop doesn't advertise, Fizzo makes a higher…
- Two firms, X and Y, are involved in a price war. The demand equations for each firm are the following: Qx = 52 - 2Px + Py Qy = 52 - 2Py + Px Further, assume the cost of each unit of out is constant at $4. What is the Nash equilibrium of this game? (Use the best response functions in a graph to answer) There is no Nash equilibrium O $24 $20 $22Suppose that Flashfry and Warmbreeze are the only two firms in a hypothetical market that produce and sell air fryers. The following payoff matrix gives profit scenarios for each company (in millions of dollars), depending on whether it chooses to set a high or low price for fryers. Warmbreeze Pricing High Low Flashfry Pricing High 11, 11 2, 15 Low 15, 2 8, 8 For example, the lower-left cell shows that if Flashfry prices low and Warmbreeze prices high, Flashfry will earn a profit of $15 million, and Warmbreeze will earn a profit of $2 million. Assume this is a simultaneous game and that Flashfry and Warmbreeze are both profit-maximizing firms. If Flashfry prices high, Warmbreeze will make more profit if it chooses a price, and if Flashfry prices low, Warmbreeze will make more profit if it chooses a price. If Warmbreeze prices high, Flashfry will make more profit if it chooses a price, and if Warmbreeze prices low, Flashfry will make more profit if…Consider the following normal form representation of the standard competition between firm A and firm B. Each firm can choose either standard A or standard B. Their payoffs are given as follows: Firm B A В A Firm A В 1 1 3 1 (1) (10 points) What's Nash equilibrium (NE) in this game? If there are more than one, find them all. But there is no NE, state that there is no NE. (2) (10 points) If you find a NE (or multiple Nash equilibria), is it (or are they) Pareto efficient?
- 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?Exercise 6.7. Suppose two identical companies produce wood stoves and they are the only ones on the market. Its costs are given by: C1 (q1 )=200q1 and C2 (q2) = 200q2. And the inverse market demand curve is: P=2000-2Q, where Q =q1 + q2 Get the Cournot-Nash equilibrium. Calculate the profits of each company. Show graphically. Suppose that the two companies form a cartel to maximize joint profits. How many stoves will you produce? Calculate the profits of each company. Represent graphically. Managers now note that explicit agreements to collude are illegal. Each company must decide on its own whether to produce the amount of Cournot or that of the cartel.Two firms face decisions with two alternatives that can be modeled using Game Theory. For each of the situations described below, CIRCLE the ("Nash") equilibrium (or equilibria) for the "game" given the profit payouts (firm 1, firm 2) for the choices for the firms (or mark "None"). a. Sell One Medium-Size Item or Sell One Large Item and One Small Item Firm 1 Choices Firm 2 Choices Medium-Size Item Large and Small Items Medium-Size Item 31,27 25, 33 Large/Small Items 42,24 30,28 b. Use "9" Price Endings or Use "5" Price Endings Firm 2 Choices Use "9" Price Endings | Use "5" Price Endings Firm 1 Choices Use "9" Endings Use "5" Endings 45,28 42,30 c. Hire a Celebrity Endorser or Donate to Charity 27,25 25,28 Firm 2 Choices Firm 1 Choices Hire Celebrity Endorser Donate to Charity Celebrity Endorser 40, 29 30, 33 Donate to Charity 37,36 48, 32 d. Locate Downtown or Locate in Suburban Strip Mall Firm 2 Choices Firm 1 Choices Locate Downtown Locate in Strip Mall Locate Downtown 32,31 28, 34…
- Consider a Stackelberg duopoly:There are two firms in an industry with demand Q = 1 − Pd.The “leader” chooses a quantity qL to produce. The “follower” observes qL and chooses a quantity qF.Suppose now that the cost function is Ci(qi) = qi2 for i = L, F. (a) Find the subgame perfect equilibrium. (b) Compare the equilibrium you found with the Nash equilibrium if the game was simultaneous (i.e., Cournot competition). Is the Nash equilibrium of the Cournot game also a Nash equilibrium of the sequential game? Why or why not?Suppose that Fizzo and Pop Hop are the only two firms that sell orange soda. The following payoff matrix shows the profit (in millions of dollars) each company will earn depending on whether or not it advertises: Fizzo Advertise Doesn't Advertise Advertise 10, 10 2, 18 Pop Hop Doesn't Advertise For example, the upper right cell shows that if Fizzo advertises and Pop Hop doesn't advertise, Fizzo will make a profit of $18 million, and Pop Hop will make a profit of $2 million. Assume this is a simultaneous game and that Fizzo and Pop Hop are both profit-maximizing firms. 18, 2 11, 11 If Fizzo decides to advertise, it will earn a profit of $ advertise. If Fizzo decides not to advertise, it will earn a profit of $ advertise. If Pop Hop advertises, Fizzo makes a higher profit if it chooses If Pop Hop doesn't advertise, Fizzo makes a higher profit if it chooses Both firms will choose to advertise. million if Pop Hop advertises and a profit of $ O Fizzo will choose to advertise and Pop Hop…Imagine that firm X chooses their quantity first, then firm Y observes the quantity of firm X and chooses their own quantity. What is the subgame perfect Nash Equilibrium? Is there a first or second-mover advantage here? You don't need to draw the whole game tree but you should give some kind of explanation for how you came to this equilibrium. (You may assume that firm X can only choose quantities that are multiples of 200. This prevents you from having to deal with prices that are not on the schedule and makes firm Y's strategy easier to write. )
