If a game does not have an equilibrium in pure strategies, then it will not have an equilibrium in mixed strategies either. True False
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- Consider a firm run by an “incumbent” manager. Suppose the incumbent manager has the opportunity to invest in one of two different projects, Project 1 or Project 2. The incumbent manager has a higher ability in managing Project 1 rather than Project 2. Also, if theincumbent is fired by shareholders, she is replaced by an “alternative” manager whose ability to manage Project 1 is lower than the incumbent’s ability. Suppose the investment in a project is irreversible, and the shareholders’ choice of the incumbent manager salary (as well as their decision on whether to fire her) is taken afterthe investment is made. Also, assume the incumbent manager has a stake in the firm she runs, but she does not fully control it. Questions:(a) Suppose none of the projects gives the manager a direct utility. According to Shleifer and Vishny (1989), which of the two projects should the incumbent manager choose? What is the economic rationale behind this choice? Explain. (b) Suppose the incumbent…Using the following table, perform ALL FIVE of the techniques for Decision Making under Uncertainty: Maximax, Maximin, Hurwicz Realism (α = 0.7), LaPlace and Minimax Regret. Use the .50 for the probability of a Good Economy and .50 for the probability of a Poor Economy. You must show your work for obtaining the points. STATE OF NATURE DECISION ALTERNATIVE GOOD ECONOMY POOR ECONOMY Sotck market 80,000 -20,000 Bonds 30,000 20,000 CDs 23,000 23,0001. The Requirement 4 for a Perfect Bayesian Equilibrium states that “At information sets off the equilibrium path, beliefs are determined by Bayes’ rule and the players’ equilibrium strategies, where possible”. This requirement is vacuous in a signaling game because (a) A signaling game never has an information set off the equilibrium path. (b) A signaling game does not specify the receiver’s strategy off the equilibrium path. (c) A signaling game does not require beliefs to be specified off the equilibrium path. (d) None of the above.
- Two animals are fighting over some prey. Each can be passive or aggressive. Each prefers to be aggressive if its opponent is passive, and passive if its opponent is aggressive; given its own stance, it prefers the out- come when its opponent is passive to that in which its opponent is aggressive. Formulate this situation as a strategic game and find its Nash equilibria.Using the following table, perform ALL FIVE of the techniques for Decision Making under Uncertainty: Maximax, Maximin, Hurwicz Realism (α = 0.7), LaPlace and Minimax Regret. Use the .50 for the probability of a Good Economy and .50 for the probability of a Poor Economy. You must show your work. STATE OF NATURE DECISION ALTERNATIVE GOOD ECONOMY POOR ECONOMY Sotck market 80,000 -20,000 Bonds 30,000 20,000 CDs 23,000 23,000When choosing whether to make, lease, or buy, a manager must consider the profits to be made under each consideration. Group startsTrue or False
- Explain with example each of the following terms of the game theory : (i)strategy (ii)Pay off table (iii) value of the game and (iv) saddle point1. If today stock is trading for $60 a share. You are confident that the stock price will experience a change in the value of over 30% relative to the current price in either upward or downward direction over the course of next year. Today you decide to transact in either one or two stocks maturing in one year. The strike price of both options is $60 a share. The call option premium is $6 and put option premium is $5. Given this information and your belief, you should _______. a. buy 2 calls b. buy 1 call and sell 1 put c. sell 1 call and 1 sell put d. buy 1 call and buy 1 put e. sell 2 puts Please explainYou are planning to rent a car for a one-week vacation. You have the option of buying an insurance that costs $80 dollars for a week. If you do not purchase insurance, you would be personally liable for any damages. You anticipate that a minor collision will cost $2,000, whereas a major accident might cost $16,000 in repairs. Develop a payoff table for this situation. What decision should you make using each strategy? Aggressive (Optimistic) Conservative (Pessimistic) Opportunity Loss You have recently read in a magazine that that the probability of a major accident is 0.05% and that the probability of a minor collision is 0.18%. Construct a decision tree and identify the best expected value decision.
- Consider a 3-month European put option on a non-dividend-paying stock. The current stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, and the volatility is 30% per annum. What is the price of the put according to the Black-Scholes-Merton model?Suppose that you want to invest $10,000 in the stock market by buying shares in one of two companies: A and B. Shares in company A though risky, could yield a 50% return on investment during the next year. If the stock market if conditions are not favorable (bear market) the stock may lose 20% of it value. Company B provides safe investments with 15% return in a bull market and only 5% in a bear market Ali the applications you have consulted are predicting a 60% chance for a bull market and 40% for a bear market. Where you invest your money? Construct a decision tree.1) A television network earns an average of $1.6 million each season from a hit program and loses an averageof $400,000 each season on a program that turns out to be a flop, and of all programs picked up by thisnetwork in recent years, 25% turn out to be hits and 75% turn out to be flops. a) Construct a decision tree to help the television network identify the strategy that maximizes itsexpected profit in responding to a newly proposed television program. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. b) What should the network do? What is their expected profit? c) The network can conduct market research to determine whether a program will be a hit or a flop. Ifthe market research report is perfectly reliable, what is the most the network should be willing to payfor it? 2) A buyer for a large sporting goods store chain must place orders for professional footballs with the footballmanufacturer six months prior to the time…