1. What is a Nash equilibrium? And use your definition to identify and explain in full, all the Nash equilibrium strategy pairs and their payoffs in this game. 2. Suppose that Blue can publish its prices for the year before Red. Draw a diagram of the sequential game in extensive form showing and labelling clearly all three subgames. What is the outcome of the game if both players are rational and fully informed, and both reason using backward induction? 3. Would the outcome of the game change if Red published its prices first? Draw a suitable diagram showing all three subgames and explain your answer in full.
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- Consider the oil-drilling game depicted in Figure 5.4 in which payoffs are in millions of dollars. Suppose that this game is played repeatedly and the probability that the game will end in the next round is 10 percent and the discount rate is 25 percent. What is the present value of the stream of payoffs from not cooperating? GLOMAR Narrow Wide PETROX Narrow (52, 52) (20, 108) Wide (108, 20) (24, 24) Payoffs: (PETROX, GLOMAR) FIGURE 5.4 An amount between $85.7 and $85.8 million. An amount between $113.7 and $113.8 million. O An amount between $185.7 and $185.8 million. O An amount between $210.8 and $210.9 million.A manager is deciding whether to build a small or a large facility. Much depends on the future demand that thefacility must serve, and demand may be small or large. The manager knows with certainty the payoffs that willresult under each alternative, shown in the following payoff table. The payoffs (in $000) are the present values offuture revenues minus costs for each alternative in each event.What is the best choice if future demand will be low?You are one of five risk-neutral bidders participating in an independent private values auction. Each bidder perceives that bidders' valuations for the item are evenly distributed between $20,000 and $50,000. For each of the following auction t determine your optimal bidding strategy if you value the item at $35,000. a. First-price, sealed-bid auction. O Bid $20,00. O Bid $50,00. O Bid $35,00. O Bid $32,000 b. Dutch auction O Let the auctioneer continue to lower the price until it reaches $20,000, and then yell "Minel". O Let the auctioneer continue to lower the price until it reaches $35.000, and then yell "Mine!" O Let the auctioneer continue to lower the price until it reaches $32,000, and then yell "Mine!" O Let the auctioneer continue to lower the price until it reaches $50,000, and then yell "Mine!". C. ond-price, sealed-bid auction O Bid $50,00. O Bid $35.000 O Bid $32,00. b. Dutch auction. O Let the auctioneer continue to lower the price until it reaches $20,000, and then yell…
- Transcendent Technologies is deciding between developing a complicated thought- activated software, or a simple voice-activated software. Since the thought-activated software is complicated, it only has a 30% chance of actually going through to a successful launch, but would generate revenues of $50million if launched. The voice-activated software is simple and hence has a 80% chance of being launched but only generates a revenue of $10million. The complicated technology costs 10million, whereas the simple technology costs 2 million. What is the expected profit from developing the complicated software? $10 million $15 million $20 million $5 millionq52 If you advertise and your rival advertises, you each will earn 14 million in profits. If neither of you advertises, you will each earn 20 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn 10 million and the non-advertising firm will earn 16 million. If you and your rival plan to be in business for only one year, the Nash equilibrium is a. for each firm to advertise. b. for the other firm to advertise and your firm not to advertise. c. for your firm to advertise and the other not to advertise. d. for neither firm to advertise.Solve this game using iterated elimination of strictly dominated strategies. Write down your process as well as your final solution. a b d e А 31,-1 | 1,3 |1,0 |32,-2 1,1 B 62,-3 -3,-2 27,-3-3,43 -4,17 с 53,-1 | -1,0 194,-33,-3 |-1,2 D0,-35 -3,37 -4,41 0,-14 -2,15 E -23,-2 -3,86 0,-15 -3,55 -4,7o
- Please no written by hand solutions Suppose that the pricing strategies for FiberOne and of Starlink are shown in the table below. They have to decide whether to charge a high or low price for their internet service. The four pairs of payoff values show what each company expects to earn or lose in millions of dollars, depending on what the other company does. FiberOne’s Price Strategy Starlink’s Price Strategy High Price Low Price High Price Starlink+$200 FiberOne +$200 Starlink+$500 FiberOne - $100 Low Price Starlink-$100 FiberOne + 500 Starlink+$100 FiberOne +$100 If it’s expected that the incomes of people living in rural Nigeria is expected to increase, what will the equilibrium outcome be, ceteris paribus? a) a) Starlink will charge a low price; FiberOne will charge a high price. b) b) Starlink will charge a high price; FiberOne will charge a low price. c) c) Both Starlink and FiberOne will charge a low price. d) d) Both Starlink and FiberOne will charge a high price.First Player can invest $1.00 with Second Player. Second Player chooses whether tc cooperate and make the promised investment, or appropriate and keep First Player'a $1.00. Based on the payoff matrix shown below (first player payoffs on bottom left of cell, second player payoffa on upper right of cell), what will be First Player's payoff if contracis are not enforceable? Second Player Cooperate Appropriate Invest 1.5 1.0 First Player 1.5 -1.0 Don't Invest17-5. You are offered the following gamble based on coin flips. If the first head occurs on the first flip , you get $2 IF the first head occurs on the second flip you get $4, and so on, so that is the first head is on the Nth flip , you get $2N. The game ends only when a flip on the coin results in heads. What is the expected value of this gamble? When offered, most people say they would only pay less than $10 to play this game. What are two reasons why people are willing to pay so much less than the expected value?
- Pl and P2 play a simultaneous move game with payoffs given below. Suppose now that both players have private information. P1 knows the value of 01, but P2 does not. P2 knows the value of 02, but P1 does not. Р2 A В A 01,–1 1,0 P1 В 1,0 0, 02 Suppose 01 is equal to either 0 or –1, each with probability 1 Suppose 02 is equal to either –l or 1, each with probability 1/2. All of the above is common knowledge. Again, notice that even though 0; is random from Pj's perspective, Pi knows what O; is. Consider pure equilibria of the game. (By pure equilibrium, I mean that no type of any player mixes in the equilibrium, but this doesn't mean that each type of a player has to do the same thing.) How many pure equilibria does this game have? Numerical answerA firm plans to expand its product line and faces a dilemma whether to build a small or largefacility to produce new products. If it builds a small facility and demand is low, the NPV afterdeducting for building costs will be four hundred thousand pesos. If demand is high, the firm caneither maintain the small facility or expand it. Expansion would have an NPV of four hundredfifty pesos while maintaining the small facility would have an NPV of fifty thousand pesos. If alarge facility is built and demand is high, the estimated NPV would be eight hundred thousandpesos. If demand turns out to be low, the NPV would be a loss of ten thousand. The probabilitythat the demand is high is estimated to be sixty percent.a. Analyze using a decision tree.b. Compute for EVPI.c. Determine the range over which each alternative would be best in terms of the valuewhen demand is low.Panther Airlines (PA) is the only airline that flies several routes. They have a potential competitor, Leopard Airlines (LA) who are considering entering these markets. PA maintains some excesscapacityas an entry deterrent and is eurrently earning $1 Om profit. PA signals that if LA enters these markets, theywill drop their prices. PA's profits will fall to $2m and LA will make a loss of $5m. If PA drops its prices and LA does not enter the markets, PA will earn $3m in profit. If PA were to accommodatethe new entranl, they would each earn $5m profit. i. Draw up the payoffmatrix for this game.ii. Do PA and LA have dominant strategies? Explain your answer.iii. What is the Nash equilibrium? Explain your answer.