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有关博弈的一些题目，求助高手解答！万分感谢！
1)
Consider two firms that compete in quantities, q1 and q2. Each has unit cost c. The inverse demand function is p(Q) where Q is total output. Using the firm’s Nash strategy (first order condition), drive the general expression for the relationship between the firm’s equilibrium price-cost margin and its market share in this Cournot game. Does this relationship have any “casual” interpretation?
2)
Discuss the factors that determine whether a competitive (Nash in prices) market will generate too much, or too little, product diversity relative to the socially efficient level. Define clearly what you mean by socially efficient. (You may use some formalization from the circle model, but do not re-drive the whole model).
3)
Discuss what is meant by ‘ownership’ in a world of incomplete contracts. Explain how incentives to invest are affected by the choice of which party gets ‘ownership’ in this sense [hint: how is the bargaining outcome affected by who has ‘residual control rights’?]
4)
Using either the Dixit-Spence framework or the circular model of product location, explain why credible commitment is at the heart of entry deterrence and how much commitment can be achieved.
5)
Consider two firms that produce a homogeneous product and compete in prices for an infinite number of periods. Discuss what the theory of repeated games tells us about the various possible non-cooperative equilibrium outcomes that can arise in this setting, and graphically represent those outcomes. Does this result have any useful policy implications?
6)
(i) Describe formally the Ghemwhat model of capacity of expansion for an anticipated increase in market demand. Briefly discuss how the equilibrium of the game is affected by uncertainty about market demand.
(ii) Discuss what you think this model teaches us about how antitrust policy should treat cases where firms with market power ‘build ahead of demand.’ Illustrate or compare your conclusions with the positions taken by the courts regarding DuPont in the titanium dioxide marker and/ or Alcoa in the aluminium market.
7)
Two firms are considering entry into a new market (there are no current firms). The market demand function is Q=1-p. if only one firm enters, it prices as a monopolist at the second stage. If two enter, they compete in quantities. Unit cost is zero. The sunk cost of entry is s，where 1/4≥s≥1/9.
(i) Compute the pure strategy Nash equilibrium in this entry game.
(ii) Compute the mixed strategy equilibrium for the entry game. Explain how this result depends on the level of sunk cost.
(iii) Now assume that s=1/9. Compute the probability that both firms enter the market, and the probability that neither firm enters the market. Comparing this result with your answer in part (i), briefly comment on how the predicted outcome of the entry game depends on whether potential entrants have private information.
8)
(i) Formally describe the double marginalization and moral hazard problems in vertically-related markets, including their welfare implications. For each case, be careful to identify the assumptions about the market structure both upstream and downstream, and what information the upstream firm is assumed to have.
(ii) Identify what instruments, or combination of instruments, are required to address each of these problems. Comment briefly on the risk-sharing implications of the proposed solutions.
(iii) Comment briefly on how your conclusions would change if the upstream or downstream market were competitive?
9)
Customers are uniformly distributed on a line (not a circle) of length one. Each consumer buys one unit of a product (homogeneous except for location). In addition to the money price, there is linear transport costs of t per unit distance traveled. There are two firms, with asymmetric unit costs. Firm 1 is located at the left-hand end of the line and has unit cost c1. Firm 2 is located at the right-hand end of the line and unit cost c2>c1. Firm compete in prices.
(i) Compute the Nash prices for each firm, and the associated equilibrium market shares.
(ii) Suppose that the internet is introduced and has the effect of reducing the unit transport cost. Using your result in (i), analyze how this reduction in t affects the marker shares of the firm 1 (the low cost firm) and firm 2 (the high cost firm). Provide the economic intuition behind this result.
10)
A monopolist operates in a market with demand Q=a-p, where a>0 represents the market size. Unit cost is zero. There is a potential entrant with unit cost of zero and sun cost of entry s<a2/9. If he enters, the two firms compete simultaneously in capacities (i.e. quantities).
(i) Suppose the second firm enters. Compute the quantities and profits for both firms in Nash equilibrium.
(ii) Compute the quantity the incumbent has to set in order to deter the entry of the second firm. Comment briefly on the credibility of this strategy.
(iii) What is the condition under which the incumbent prefers to accommodate rather than deter entry? Explain how this depends on the level of the sunk cost, and provide the economic intuition.
11)
Consider a situation in which two firms simultaneously compete in prices in a differentiated product industry. Demand each year is described by the following differentiated product demand system
q1=1-p1+p2
q2=1-p2+p1
Where firms have constant marginal costs, c1 and c2 respectively and fixed costs are zero. You can assume throughout that both firms are active.
a) Assume that firms choose their prices to maximize profits. Find the best response functions for each firm, the Nash equilibrium in prices and the profits made in equilibrium by each firm.
b) a large foreign firm is considering simultaneously offering licenses to a new technology it has developed to both firms. Suppose that the technology would reduce any firm’s marginal cost to c. write down the normal form of the 2x2 game between the two domestic firms where they each decide whether to license the offered technology or not.
c) Suppose that c1 =1and c2=2 and c=0.what is the Nash equilibrium of the game? What is the maximum amount each firm would be willing to pay in equilibrium for the license? What are equilibrium prices and quantities before the new technology is licensed and what are they afterwards?
d) Next, suppose the foreign firm considers granting one of the companies an exclusive license for the new technology with a view to forcing an outcome to the licensing game you developed in part c that is not the Nash equilibrium outcome of the game. Which outcome would the foreign firm like to enforce through licensing? What are the prices and quantities of each firm at these prices?
e) Suppose the owner of the new technology is a charitable foundation that aims to maximize consumer surplus. Briefly describe to which firm it would give the technology, and why.
[此贴子已经被作者于2006-4-7 18:46:14编辑过]
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