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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?
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- Pfizer and a competitor, Astra-Zeneca, are considering developing a new drug for a particular illness at the same time. The illness is relatively rare but the fixed cost of production is very high. In particular, the forecast demand for such a drug is insufficient to cover both firms’ costs. Analyse the interaction between the two firms using game theory. Present a payoff matrix to model the situation and analyse it for Nash equilibrium. What can either of these firms do to make their best, most- preferred outcome more likely?Two firms, X and Y, are planning to market their new products. Each firm can develop TV, Laptop. Market research indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix : MATRIX IS ATTACHED Find the Nash equilibria for this game, assuming that both firms make their decisions at the same time. (explain the decision step by step) If each firm is risk averse and uses a maximin strategy, what will be the resulting equilibrium? (explain the decision step by step) What will be the equilibrium if Firm X makes its selection first? If Firm Y goes first?A total of n ≥ 2 companies are considering entry into a new market. The cost of entry is 30. If only one company enters, then its gross profit is 200. If more than one company enters, then each entrant earns a gross profit of 40. The payoff to a company that enters is its gross profit minus its entry cost, while the payoff to a company that does not enter is 60. Find a symmetric Nash equilibrium in mixed strategies.
- Suppose that two companies – AlphaTech and BetaLabs – are competing for market share and must simultaneously decide whether to develop a new product. Both companies are reluctant to make a decision as it is only economical for one company to develop a new product. Each company earns nothing if they decide not to develop a new product. One company can earn $50 million by developing a new product only if their competitor does not. If both companies decide to develop a new product, they each lose $10 million. Complete the payoff matrix to represent this game. Based on your solution in part (a), determine the maximin solution.If you advertise and your rival advertises, you each will earn $4 million in profits. If neither of you advertises, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $1 million and the non-advertising firm will earn $5 million. If you and your rival plan to be in business for only one year, the Nash equilibrium is Group of answer choices for each firm to advertise. for neither firm to advertise. for your firm to advertise and the other not to advertise. none of the provided answers. 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.Consider two beer producers, POTUS Pilsner and Supreme Court Stout. If they advertise, they can both sell more beer and increase their revenue. However, the cost of advertising more than offsets the increased revenue so that each producer ends up with a lower profit than if they do not advertise. On the other hand, if only one advertises, that producer increases its market share and also its profit. Construct a payoff matrix using the following hypothetical information: If neither producer advertises, each earns a profit of $35 million per year. If both advertise, each earns a profit of $20 million per year. If one advertises and the other does not, the producer who advertises earns a profit of $50 million and the producer who does not advertise earns a profit of $9 million. If POTUS Pilsner wants to maximize profit, will it advertise? Briefly explain. If Supreme Court Stout wants to maximize profit, will it advertise? Briefly explain. Is there a dominant strategy for each…
- Suppose the five potential entrants are identical in that each faces the same entry cost of $300. Given the total number of companies in the market, the accompanying table reports a company’s net profit (or payoff) if it enters. As before, the payoff from staying out of the market is zero, and each company can choose either enter or do not enter. Find all Nash equilibria.Represent the following games in a normal form and find their Nash equilibria. b) Firm A decides whether to enter the market in which firm B already operates. Firm B knows about firm A’s considerations. If firm A enters the market, both firms decide at the same time whether to run an advertising campaign. In the opposite case, only firm B decides about running an advertising campaign. When both firms are in the market, each obtains profit of $3 mln if both pursue a campaign, or of $5 mln if both decide not to run a campaign. If only one firm runs a campaign, it obtains $6 mln, whereas the other firm gets $1 mln. If only firm B operates in the market, it obtains $4 mln when it advertises its product, or $3.5 mln if it does not. Firm A receives $0 if it does not enter the market.Economics Represent the following games in a normal form and find their Nash equilibria. b) Firm A decides whether to enter the market in which firm B already operates. Firm B knows about firm A’s considerations. If firm A enters the market, both firms decide at the same time whether to run an advertising campaign. In the opposite case, only firm B decides about running an advertising campaign. When both firms are in the market, each obtains profit of $3 mln if both pursue a campaign, or of $5 mln if both decide not to run a campaign. If only one firm runs a campaign, it obtains $6 mln, whereas the other firm gets $1 mln. If only firm B operates in the market, it obtains $4 mln when it advertises its product, or $3.5 mln if it does not. Firm A receives $0 if it does not enter the market.
- Refer to the normal-form game of price competition in the payoff matrix below Firm B Low Price High Price Firm A Low Price 0, 0 50, −10 High Price −10, 50 20, 20 Suppose the game is infinitely repeated, and the interest rate is 20 percent. Both firms agree to charge a high price, provided no player has charged a low price in the past. This collusive outcome will be implemented with a trigger strategy that states that if any firm cheats, then the agreement is no longer valid, and each firm may make independent decisions. Will the trigger strategy be effective in implementing the collusive agreement? Please explain and show all necessary calculations.We consider a game between two players, Alice and Bob. Alice chooses a number x (between -infinity and +infinity), and Bob chooses a number y (between -infinity and +infinity). Alice's payoff is given by the following function: 35 x + 87 x y - 95 x squared. (the last entry is "x squared".) Bob's payoff is given by the following function: 30 y + 42 x y + 75 y squared. (the last entry is "y squared".) Calculate Alice's strategy in the (unique) Nash equilibrium of this game.Two car producers, Firm A operates in Country A and Firm B operates in Country B, are considering producing a new 8-seater Multi-Purpose Vehicle (MPV)for the international market. The payoff matrix is as follows (payoff values are in millions of dollars). The above payoffs imply that the international market demand is large enough to support only one producer. If both firms produce, both will sustain a loss. (i) Explain and solve for the Nash equilibrium in this game. (ii) Suppose the government of Country A decides to subsidise Firm A with $25 million if it produces. Revise the payoff matrix to account for this subsidy. What is the new equilibrium outcome? Compare the two outcomes and discuss the effect of the subsidy.
