Suppose that the proposer in the ultimatum game may not propose fractional amounts, and therefore must propose $0, $1, $2, ...... or $10 (see figure below). As always, the responder must Accept (A) or Reject (R). $0 $1 $2 33 $3 $4 $5 $6 $7 $8 $9 $10 A R ($6,54) ($0,$0) (a) Suppose, first, that this game is played by two egoists, for whom u(x,y)=x. What is the Nash equilibrium? (b) Suppose, second, that this game is played by two altruists, for whom u(x, y) = 2/3√x + 1/3√y. Find the new Nash Equilibrium.
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- -bid U2. Suppose that three risk-neutral bidders are interested in purchasing a Princess Beanie Baby. The bidders (numbered 1 through 3) have valua- tions of $12, $14, and $16, respectively. The bidders will compete in auc- tions as described in parts (a) through (d); in each case, bids can be made in $1 increments at any value from $5 to $25. (a) Which bidder wins an open-outcry English auction? What are the final price paid and the profit to the winning bidder? (b) Which bidder wins a second-price, sealed-bid auction? What are the final price paid and the profit to the winning bidder? Contrast your answer here with that for part (a). What is the cause of the difference in profits in these two cases? 190 HO (c) In a sealed-bid, first-price auction, all the bidders will bid a positive amount (at least $1) less than their true valuations. What is the likely outcome in this auction? Contrast your answer with those for parts (a) and (b). Does the seller of the Princess Beanie Baby have…3. Suppose that the utility functions u(x, y) and v(x, y) are related by v(x, y) = f(u(x, y)). In each case below, check if f is a positive monotonic transformation' of u. (a) f(u) = 3.141592u (b) f(u) = 5000 – 23u (c) f(u) = ! %3D (d) f(u) = -u-16. Are the following utility functions consistent with the axioms of the expected utility theorem? Everything is in monetary terms. (a) u(x) = = -x. (b) u(x) = x² for a E (-10, 10]. (c) u(x) = 5. %3D
- 1. Suppose that you are in charge of purchasing for a U.S. corporation that is planning to acquire a large number of new computers. The company's computer specialist has identified two models, one Japanese-made and one U.S.-made, that meet the necessary specifications. Since the two models are essentially equivalent, the company will buy the one with the lower price. Suppose the U.S.-made computer costs $2,400, and a similar Japanese-made computer costs 242,000 yen. If the nominal exchange rate is 110 yen per dollar, which computer is a better buy? (Hint: calculate the real exchange rate for computers)6) You have been assigned to create a new TV game show, and you have an interesting idea that you call, “I WANT TO BE A MILLIONAIRE.” The basics are: 1) two contestants; 2) the show begins with each contestant being given $1 million (!); and then 3) they begin playing a game that can increase or decrease that $1 million. You worry that the initial outlay of $2 million will stun your producers, so you decide to prepare them with a simpler version of your game that you call: “I WANT $3.” There are four steps in this simpler game: There are two contestants/opponents (who do not know each other and cannot communicate with each other during the game). Each player is given $3 at the start of the game. Independently and simultaneously, each player must choose whether they want to add $0, $1, $2 or $3 to their initial stake of $3. Doing so reduces their opponent’s award by $0, $2, $4, or $6, respectively. Each player knows that their payoff at the end of the game is based on their initial…A gambling game requires people to place bets on either "Big" or "Small" or "Seven" designating the result of two dice throws. Big represents a sum of 8 to 12, while small is from 2 to 6. The special space "seven" is reserved for, of course, 7. Betting on "Big" provides a 1:1 betting win ratio amount. (Ex: Any bet amount of X, will net the winner another amount X, and still get his bet amount X back. ) Betting on "Small" also provides a 1:1 betting win ratio. The space "Seven" gives a 1:5 win ratio amount: Betting 100 money units on "Seven" and having a result of 7 nets the bettor 500 money units, and still have his 100 money units returned to him. If your bet does not appear, then the player loses his/her bet. What is the net Expected value of the strategy of betting 100 money units on "Big" ? Give your answer to two decimal places.
- Suppose that there are three beachfront parcels of land available for sale in Astoria, and six people who would each like to purchase one parcel. Assume that the parcels are essentially identical and that the selling price of each is $745,000. The following table states each person's willingness and ability to purchase a parcel. Willingness and Ability to Purchase (Dollars) Alyssa 720,000 Brian 690,000 Crystal 680,000 Nick 900,000 Rosa 810,000 Tim 770,000 Which of these people will buy one of the three beachfront parcels? Check all that apply. Alyssa Brian Crystal Nick Rosa Tim Assume that the three beachfront parcels are sold to the people you indicated in the previous section. Suppose that a few days after the last of those beachfront parcels is sold, another essentially identical beachfront parcel becomes available for sale at a price of $732,500. This fourth parcel _____________be sold…6) You have been assigned to create a new TV game show, and you have an interesting idea that you call, “I WANT TO BE A MILLIONAIRE.” The basics are: 1) two contestants; 2) the show begins with each contestant being given $1 million (!), and then 3) they begin playing a game that can increase or decrease that $1 million. You worry that the initial outlay of $2 million will stun your producers, so you decide to prepare them with a simpler version of your game that you call: “I WANT $3.” There are four steps in this simpler game: I. There are two contestants/opponents (who do not know each other and cannot communicate with each other during the game). II. Each player is given $3 at the start of the game. III. Independently and simultaneously, each player must choose whether they want to add $0, $1, $2 or $3 to their initial stake of $3. Doing so reduces their opponent’s award by $0, $2, $4, or $6, respectively. IV. Each player knows that their payoff at the end of the game is based on…6) You have been assigned to create a new TV game show, and you have an interesting idea that you call, “I WANT TO BE A MILLIONAIRE.” The basics are: 1) two contestants; 2) the show begins with each contestant being given $1 million (!), and then 3) they begin playing a game that can increase or decrease that $1 million. You worry that the initial outlay of $2 million will stun your producers, so you decide to prepare them with a simpler version of your game that you call: “I WANT $3.” There are four steps in this simpler game: I. There are two contestants/opponents (who do not know each other and cannot communicate with each other during the game). II. Each player is given $3 at the start of the game. III. Independently and simultaneously, each player must choose whether they want to add $0, $1, $2 or $3 to their initial stake of $3. Doing so reduces their opponent’s award by $0, $2, $4, or $6, respectively. IV. Each player knows that their payoff at the end of the game is based on…
- Suppose that there are three beachfront parcels of land available for sale in Astoria and six people who would each like to purchase one parcel. Assume that the parcels are essentially identical and that the minimum selling price of each is $570,000. The following table states each person's willingness and ability to purchase a parcel. Person Willingness and Ability to Purchase (Dollars) Ana 630,000 Charles 590,000 Dina 550,000 Gilberto 510,000 Juanita 500,000 Yakov 700,000 Which of these people will buy one of the three beachfront parcels? Check all that apply. Ana Charles Dina Gilberto Juanita Yakov Assume that the three beachfront parcels are sold to the people that you indicated in the previous section. Suppose that a few days after the last of those beachfront parcels is sold, another essentially identical beachfront parcel becomes available for sale at a minimum price of $560,000. This fourth parcel ____ (will,…QUESTION 8 S1, S2, S3 and S4 are UIUC students who just graduated. They each have a poster of Dolly Parton that they are willing to sell. B1, 82, B3 and B4 are new students at UIUC and want to buy Dolly Parton postern for their rooms. The tables below give the minimum selling prices and maximum buying prices for each student. Minimum Selling Prices Maximum Buying Pricen X+$9 S1 $10 B1 S2 $11 B2 X+$14 S3 $20 B3 X+$16 S4 $25 B4 X+$26 If X is negative $5 (.e., Xu-$5), what is the market-clearing price? Note: Do not include the dollar sign,Q2 The market equilibrium price and quantity of a good may be found by solving the simultaneous equations: Q + 3P = 48 (1) Q – 2P = 30 (2) (a) Explain which of these equations represents the supply curve and which represents the demand curve. (b) If the demand curve were to be drawn with Q on the horizontal axis and P on the vertical axis, state the values of the slope and vertical intercept. (c) Determine the equilibrium price and quantity algebraically.