Economics经济学代写-ECON2070代写-ECON代写
Economics经济学代写

Economics经济学代写-ECON2070代写-ECON代写

ECON2070

PRACTICE ON BAYESIAN GAMES

Economics经济学代写 There are two firms in a market with two segments. Firm 1 (player 1) is the established firm in the high end market.

This is an optional exercise for you to get some practice on solving for Bayesian Games. There is no need to turn this in.

Question 1  Economics经济学代写

There are two firms in a market with two segments. Firm 1 (player 1) is the established firm in the high end market. Firm 2 (player 2) has been selling to the low end market for a long time. Recently, Firm 1 is deciding whether to run a big promotion (action B) or a small promotion (action S). Meanwhile, Firm 2 is deciding whether to launch into the high end market (action H) or stay in the low end market (action L). Neither firm knows each other choice when they make their own decision. The outcome,however, also depends on whether Firm 1 has a strong financial backing or not. Firm 1 knows whether it is strong or weak. Firm 2 only knows that 1 is strong with probability 1/3 and is weak with probability 2/3. The payoffs are given as follows:

(a)(LevelA) Write down the ex-ante normal form associated with this Bayesian

(b)(Level B) Solve for the unique Bayesian-Nash equilibrium. (There is no need to prove)

(c)(Level A) Suppose it is commonly known that Firm 1 is strong, what will be the Nash equilibrium of the correspondinggame?

(d)(LevelA) Suppose it is commonly known that Firm 1 is weak, what will be the Nash equilibrium of the corresponding game?  Economics经济学代写

(e)(LevelB) A legal firm makes a suggestion to Firm 2: it can obtain secret papers about Firm 1’s financial strengths and publish them (so that Firm 1’s financial strengths

will be commonly known). How much would Firm 2 be willing to pay for the legal firm to do this?

Economics经济学代写
Economics经济学代写

Question 2  Economics经济学代写

Two rival firms — Firm 1 (player 1) and Firm 2 (player 2) are deciding simultaneously on the location to launch their latest products. Each of them can choose to launch their product in either the Red State (action R) or the Blue State (action B). The Blue State government may be having a new initiative of boosting the economy in the Red State, which will change the payoffs to the firms. Firm 1 only knows that there is a probability of 1/4 that the initiative will be carried out. Firm 2, on the other hand, has insider information and knows exactly whether there will be an initiative. The payoffs are given as follows:

(a)(LevelA) Write down the ex-ante normal form associated with this Bayesian game.

(b)(Level A) Is there any dominated strategy? For each dominated strategy that you have identified, write down a strategy that dominates it.

(c)(Level B) Solve for all Bayesian-Nash equilibria of this game. (Hint: There are)

Question 3  Economics经济学代写

(This is an example of the possibility of trade under adverse selection.)

(Level B) Consider the following market for used cars. There are many sellers of usedcars. Each seller has exactly one used car to sell and is characterized by the quality of the used car he wishes to sell. The quality of a used car is indexed by θ, which is uniformly distributed between 0 and 1.

If a seller sells his car of quality θ for price p, hisutility is us(p, θ). If he does not sell his car, his utility is 0. Buyers of used cars receive utility θ  p if they buy a car of quality θ at price p and receive utility 0 if they do not purchasea car. There is asymmetric information regarding the quality of used cars. Sellers know the quality of the car they are selling, but buyers do not know its quality. Assume that there are not enough cars to supply to all potential buyers.

You may take the following formulae as given:

If x is a random variable distributed uniformly between a and b, and c is a number such that a c  b, then the expectation of x conditional on it being smaller than c is

(a)First suppose us(p, θ) = p θ.

(i)Supposethe price of a used car is p. Which sellers will sell?

(ii)Usingyour answer to part (i), find the expectation of quality of used cars con- ditional on them being sold at price p.   Economics经济学代写

(iii)Find the equilibrium market price of used cars. Which cars are traded in the equilibrium?(Hint: You may use the fact that, in any equilibrium of this mar- ket, the market price of used cars p must be equal to the conditional expectation you found in part (ii).)

(iv)The surplus from trading a car with qualityθ is defined by

θ p + us(p, θ).

An equilibrium outcome is (Pareto) efficient if all transactions that generate a positive surplus are conducted. Given your answer to (iii), is the equilibrium outcome efficient?

(b)Now suppose us(p, θ) = p θ3. Repeated parts (i) to (iv) above.

 

更多代写:Geography代考北美  多邻国代考  Economy(eco)经济代写  Essay代写安全吗  Finance金融论文代写  本科毕业论文查重

合作平台:essay代写 论文代写 写手招聘 英国留学生代写 

Economics经济学代写
Economics经济学代写

发表回复