Consider a Cournot competition game. The market demand function is: p= 4 – q1 – q2, - - where p is price and q is firm i's output level. Suppose that the firm's marginal cost of production is: C1 = 1, c2 = 0, respectively. A) Find the Nash equilibrium of the above game.
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- Two firms operating in the same market must decide between charging a high price or a low price. The Payoffs are as below. Firm A's profit is listed before the comma, B's profit after the comma. Firm B Firm A Low Price High Price Low Price 16, 17 7, 28 High Price 28, 7 22, 22 If each firm tries to choose a price that is optimal, regardless of the other firm's price, what is the Nash equilibrium? Does either firm have a dominant strategy?Imagine that there are two snowboard manufacturers (FatSki and WideBoard) in the market. Each firm can either produce ten or twenty snowboards per day. The table below (see attached) shows the profit per snowboard for each firm that will result given the joint production decisions of these two firms. Draw the game payoff matrix for this situation. Does either player have a dominant strategy? If so, what is it? What is the Nash equilibrium solution and how many boards should each player produce each day? Since FatSki and WideBoard must play this game repeatedly (i.e. make production decisions every day), what strategy would you advise them to play in order to maximize their payoff over the long term?We can see from the payoff matrix that there are no pure strategy Nash equilibrium in this game because at least one firm would always have an incentive to change its behavior. From Nash's theorem, we know there must be at least one Nash equilibrium so there must be a mixed strategy Nash equilibrium for this game. Find the mixed strategy Nash equilibrium by first deleting all dominated strategies in the game What's the expected payoff to Firm 2 in the equilibrium?
- I have constructed a Bertrand game (competition in prices) and presented you with the reaction functions of each firm. p1 = 12.5 + p2/4 p2 = 5/2 + p1/2 a) Use excel to draw the reaction functions. b) Solve for the Nash equilibriumO Cell A O Cell C O Cell E O Cell I None of the aboveThe market demand function is Q=10,000-1,000p. Each firm has a marginal cost of m=$0.28. Firm 1, the leader, acts before Firm 2, the follower. Solve for the Stackelberg-Nash equilibrium quantities, prices, and profits. Compare your solution to the Cournot-Nash equilibrium. The Stackelberg-Nash equilibrium quantities are: q1=___________ units and q2=____________units The Stackelberg-Nash equilibrium price is: p=$_____________ Profits for the firms are profit1=$_______________ and profit2=$_______________ The Cournot-Nash equilibrium quantities are: q1=______________units and q2=______________units The Cournot-Nash equilibrium price is: p=$______________ Profits for the firms are profit1=$_____________ and profit2=$_______________
- QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P₁, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2 (P1, P2) 140 - 2p2 + P1 Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)Consider two firms choosing quantities sequentially in a duopoly setting (i.e. the Stackelberg game). The two firms have identical products. Each firm has no fixed costs, and faces marginal costs equal to 5 plus the quantity it produces (i.e. MC = 5 + q). Market demand is given by Q = 46 - P, where Q is market quantity and P is market price. In equilibrium, how much will the firm that moves first produce?I have constructed a Bertrand game (competition in prices) and presented you with the reaction functions of each firm. P2 P1 = 12.5 + 4 P1 P2 == Use excel to draw the reaction functions. Solve for the Nash equilibrium + n IN
- Two firms A and B produce a product jointly. The total value to the two firms from the joint venture is given by V = √iA + √iB where iA and iB are the firms’ respective investment levels. After the investment levels have been chosen, the firms divide V equally. a) Find the Nash equilibrium investment levels, and the payoffs for each firm. b) Suppose that A and B merge. Find the optimal investment levels and the payoffs for the merged firm. Do the firms benefit from the merger? Why?Problem 5.1. The inverse market demand for printer paper is given by P = 400 – 2Q. There are two firms who compete to produce this paper, each with a marginal cost of production equal to c = 40 over a large range of output (ie, assume constant marginal cost). The two firms compete in quantities, in other words they each simultaneously choose a quantity to produce (Cournot competition). Derive the Cournot-Nash equilibrium of this game. Please write final answers in the boxes, showing work in blank areas. (a) The reaction function for each firm. 91 (92): 92 (91) (b) Optimal output q for each firm. 92 = р = = π1 = (c) Market price (from demand curve). (d) Firm profits. 92 = π2 =Consider a market with two firms, Hewlett-Packard (HP) and Dell, that sell printers. Both companies must choose whether to charge a high price ($400) or a low price ($350) for their printers. These price strategies with corresponding profits are depicted in the bavoli matris to the right. HP's profits are in red and Dell's are in blue. Suppose HP and Dell are initially at the game's Nash equilibrium. Then, HP and Dell advertise that they will match any lower price of their competitors. For example, if HP charges $350, then Dell will match that price and also charge $350. What effect will matching prices have on profits (relative to the Nash equilibrium without price matching)? Assuming HP and Dell can coordinate to maximize profits, HP's profit will change by $ and Dell's profit will change by (Enter either positive or negative numeric responses using integers.) Price $400 Dell Price $350 HP Price = $400 Price $350 $80 $90 $80 $20 $20 $50 $90 $50 G