n a game, you are given a chance to own 20,000 in $100 banknote denomination. What you need to do is to offer your opponent some amount of money which he is willing to accept, and you have two chances to offer her the amount. If she refuses both of your offers, both of you will leave the game with $0. Assuming that your opponent is rational and she has rejected your first offe what will be your second offer to her?
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- Consider the following compound lottery, described in words: "The probability that the price of copper increases tomorrow is objectively determined to be 0.5. If it increases, then tomorrow I will flip a coin to determine a monetary payout that you will receive: if the flip is Heads, you win $100, while if it is Tails, you win $50. If it does not increase, then I will roll a 10-sided die (assume each side is equally likely to be rolled). If the die roll is a 4 or lower, you will win $100. If it is a 5, then you will win $200, and if it is a 6 or greater, you will win $50." Fill in the blanks below for the reduced lottery that corresponds to this compound lottery (write in decimals). R= ( , $50; , $100; , $200)Theo and Addy are deciding what toys to pick out at the toy store. Depending on what toys they pick, they can play different games together, but they can’t coordinate their choices. They can’t talk to one another at all until after that make their choice. Below is their payout matrix which shows their utility for each choice. All the bold figures are for Theo and all the non bold figures are for Addy. Addy Strategies Theo Strategies Toy Gas Pump Jump Rope Toy food 20 10 10 3 Ball 7 3 9 4 a) If Theo chooses Toy Food, what would be the possible outcomes for Addy? What would be best for Addy? b) If Addy chose a Toy Gas Pump, what are the possible outcomes for Theo? What would be best for Theo? c) Does Addy have a dominant strategy? If yes, what is her strategy? If not how can you tell? d) Does Theo have a dominant strategy? If yes, what is her strategy? If not how…Suppose it is a well-known fact that among ten-year old Ford F-150s, half the trucks are good and half of them are lemons. Suppose that it is also known to all parties that a good truck is worth $8,000 to current owners and $10,000 to potential buyers. A bad truck, on the other hand, is only worth $1,000 to current owners and $2,000 to potential buyers. Throughout, assume that buyers are risk-neutral. 4) Suppose that after much haggling, the current owner is willing to let her truck go for $6,000. What is the most likely implication? a) The truck is a lemon. b) The buyer is an excellent negotiator. c) It's a mutually beneficial transaction.
- Sophia is a contestant on a game show and has selected the prize that lies behind door number 3.The show’s host tells her that there is a 50% chance that there is a $15,000 diamond ring behindthe door and a 50% chance that there is a goat behind the door (which is worth nothing to Sophia,who is allergic to goats). Before the door is opened, someone in the audience shouts, “I will giveyou the option of selling me what is behind the door for $8,000 if you will pay me $4,500 for thisoption.” [Assume that the game show allows this offer.]a. If Sophia cares only about the expected dollar values of various outcomes, will she buythis option?b. Explain why Sophia’s degree of risk aversion might affect her willingness to buy thisoptionSuppose you are playing a game in which you and one other person each picks a number between 1 and 100, with the person closest to some randomly selected number between 1 and 100 winning the jackpot. (Ask your instructor to fund the jackpot.) Your opponent picks first. What number do you expect her to choose? Why? What number would you then pick? Why are the two numbers so close? How might this example relate to why Home Depot and Lowes, Walgreens and Rite-Aid, McDonald’s and Burger King, and other major pairs of rivals locate so close to each other in many well-defined geographical markets that are large enough for both firms to be profitable?Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. The game consists of tossing a coin. The player gets a payoff of 2^n where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses yields TTTH, you get a payoff of 2^4 this payoff occurs with probability (1/2^4). Compute the expected value of playing this game. Next, assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game? Finally, what is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function (found in Data, What-If Analysis) in Excel.
- Consider the following game. There are two payers, Player 1 and Player 2. Player 1 chooses a row (10, 20, or 30), and Player 2 chooses a column (10/20/30). Payoffs are in the cells of the table, with those on the left going to Player 1 and those on the right going to player 2. Suppose that Player 1 chooses his strategy (10, 20 or 30), first, and subsequently, and after observing Player 1’s choice, Player 2 chooses his own strategy (of 10, 20 or 30). Which of the following statements is true regarding this modified game? I. It is a simultaneous move game, because the timing of moves is irrelevant in classifying games.II. It is a sequential move game, because Player 2 observes Player 1’s choice before he chooses his own strategy.III. This modification gives Player 1 a ‘first mover advantage’. A) I and IIB) II and IIIC) I and IIID) I onlyE) II onlyAssume the following game situation: If Player A plays UP and Player B plays LEFT then Player A gets $2 and Player B gets $4. If Player A plays UP and Player B plays RIGHT then Player A gets $3 and Player B gets $6. If Player A plays DOWN and Player B plays LEFT then Player A gets $5 and Player B gets $2. If Player A plays DOWN and Player B plays RIGHT then Player A gets $1 and Player B gets $1. What is the mixed strategy expected payout for Player B? 1 40/15 39/15 11/2We learned that we can use choice between a gamble over someone's best and worst outcomes and getting an outcome of interest (like getting pizza) for certain as a way to assign numeric values to utility (on a scale of 0 to 1). Using this method, if you are indifferent between the following: A gamble that has a 0.3 chance of your best possible outcome (and no lower chance), and a 0.7 chance of your worst possible outcome. Getting pizza for certain. it means that your utility for getting pizza is:
- The following table contains the possible actions and payoffs of players 1 and 2. Player 2 Cooperate Not Cooperate Player Cooperate 15 , 15 -20 , 20 1 Not Cooperate 20 , -10 10 , 10 This game is infinitely repeated, and in each period both players must choose their actions simultaneously. If both players follow a tit-for-tat strategy, then they can Cooperate in equilibrium if the interest rate r is . At an interest rate of r=0.5, . If instead of playing an infinite number of times, the players play the game only 10 times, then in the first period player 1 receives a payoff ofIt is the week before the Yule Ball Dance, and Victor and Ron are each contemplating whether to ask Hermione. As portrayed above, Victor moves first by deciding whether or not to approach Hermione. (Keep in mind that asking a girl to a dance is more frightening than a rogue bludger). If he gets up the gumption to invite her, then Hermione decides whether or not to accept the invitation and go with Victor. After Victor (and possibly Hermione) have acted, Ron decides whether to conquer his case of nerves (perhaps Harry can trick him by making him think he’s drunk Felix Felicis) and finally tell Hermione how he feels about her (and also invite her to the dance). However, note that his information set is such that he doesn’t know what has happened between Victor and Hermione. Ron doesn’t know whether Victor asked Hermione and, if Victor did, whether Hermione accepted. If Ron does invite Hermione and she is not going with Victor— either because Victor didn’t ask, or he did and she…Victoria founded a start-up several years ago, together with her Macedonian friends. At first, she was fairly poor and therefore very afraid of taking risks. Any negative shock could send the company into bankruptcy. Nowadays her business is thriving, stretching across several markets from Europe to Asia. Victoria no longer worries about taking monetary risks. In fact she enjoys a good gamble over horse races from time to time. How would you draw Victoria's utility function in a way that describes her changing taste for risk as her wealth increased? Please draw a graph and comment. Please do fast ASAP fast