good service, do you think people are always self- ish in the narrowest sense? (LO4) e a small firm k sedans. The 3. Blackadder and Baldrick are rational, self-interested criminals imprisoned in separate cells in a dark medie- val dungeon. They face the prisoner's dilemma dis- played in the matrix. ching pen- ach of you ther heads ne in your Assume that Blackadder is willing to pay $1,000 for each year by which he can reduce his sentence below 20 years. A corrupt jailer tells Blackadder that before he decides whether to confess or deny the crime, she ou simul- er. If the p side of can tell him Baldrick's decision. How much is this infor- mation worth to Blackadder? (LO2) pennies. to keep are each atrix for Blackadder Deny Confess ? If so, O for Baldrick 5 years for each Confess 20 years for Blackadder uarters If she offered Harry's Baldrick 20 years for Baldrick 1 year for each Deny game O for Blackadder unt of strate- each
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- Two individuals each receive fifty dollars to play the following game. Independently of each other, they decide how much money to put in a common pot. They keep the rest for themselves. As for the money in the pot, it is increased by 80% and then distributed equally among the two individuals. For instance, suppose that the first individual puts $10 in the pot while the second individual puts $20. Increasing the total pot of $30 by 80% gives $54 to share equally between the two individuals. So the first individual’s payoff in this case is $(40 + 27) = $67, while the second individual’s payoff is $(30 + 27) = $57. (a) Compute the Nash equilibrium. (b) Is the Nash equilibrium Pareto efficient? ExplainJill and Jack both have two pails that can be used to carry water down from a hill. Each makes only one trip down the hill, and each pail of water can be sold for $4. Carrying the pails of water down requires considerable effort. Both Jill and Jack would be willing to pay $2 each to avoid carrying one pail down the hill, and an additional $3 to avoid carrying a second pail down the hill.a. If Jack and Jill each must decide whether to carry one or two pails of water down from the top of the hill, how many pails will each child choose to carry? ___ pail(s)b. Jill and Jack’s parents are worried that the two children don’t cooperate enough with one another. Suppose they make Jill and Jack share equally their revenues from selling the water. Given that both are self-interested, construct the payoff matrix for the decisions Jill and Jack face regarding the number of pails of water each should carry. Carry 1 pail Jack Carry 2 pails…Daniel and Kevin are two hardworking builders for solo, independently-owned companies. They can produce Chairs and Tables. As a result, they each have PPFs (Possibilities Production Frontiers) that illustrate their production. Daniel's PPF is shown by the equation: Qc = 12 - 3Qt. Likewise, Kevin's PPF is shown by the equation: Qt = 12 - 3Qc. Since they trust each other and are honest in their terms, Daniel and Kevin trade with each other and only each other; they do not take their goods to markets, and they do not interact with outside sellers/buyers. Since they want to make sure that they provide for their families in the most fair way possible, they set up and agree upon a few terms of trade. The terms are as follows: FIRST, the terms of trade are 1 Chair in exchange for 1 Table. SECOND, each of them specializes according to their own comparative advantage. THIRD, since Kevin needs a few extra things, he CONSUMES 3 units of the goods that he produces. With that said, I have a few…
- Three players (Allen, Mark, Alice) must divide a cake among them. The cake is divided into three slices.The table below shows the value of each slice in the eyes of each of the players. S1 S2 S3 Allen $7.00 $6.00 $5.00 Mark $4.00 $4.00 $4.00 Alice $5.00 $4.00 $6.00 Which of the slices does Allen deem fair? Group of answer choices S1 and S2 S1 and S3 S2 and S3 S1, S2, and S3 S1 onlyProve that in the variation on the centipede game given in figure 14.5(b) the unique sequential equilibrium described is, in fact, the unique Nash equilibrium. (Hint: Take some presumed Nash equilibrium and suppose information set 2n+ 1 [for player 2] is the first unreached information set. Derive an immediate contradiction. Then suppose that node (2n) t is the first unreached information set and derive a contradiction that is one degree removed from immediate.)Consider the strategic voting game discussed at the endof this chapter, where we saw that the strategy profile (Bustamante, Schwarzenegger,Schwarzenegger) is a Nash equilibrium of the game. Show that (Bustamante, Schwarzeneg-ger, Schwarzenegger) is, in fact , the only rationalizable strategy profile. Do this by firstconsidering the dominated strategies of player L. (Basically, the question is asking youto find the outcome of the iterative elimination of strictly dominated strategies)
- Newfoundland’s fishing industry has recently declined sharply due to overfish- ing, even though fishing companies were supposedly bound by a quota agree- ment. If all fishermen had abided by the agreement, yields could have been maintained at high levels. LO4 Model this situation as a prisoner’s dilemma in which the players are Company A and Company B and the strategies are to keep the quota and break the quota. Include appropriate payoffs in the matrix. Explain why overfishing is inevitable in the absence of effective enforcement of the quota agreement. Provide another environmental example of a prisoner’s dilemma. In many potential prisoner’s dilemmas, a way out of the dilemma for a would-be cooperator is to make reliable character judgments about the trustworthiness of potential partners. Explain why this solution is not avail- able in many situations involving degradation of the environment.Assume the following game situation: If Player A plays UP and Player B plays LEFT then Player A gets $1 and Player B gets $3. If Player A plays UP and Player B plays RIGHT then Player A gets $2 and Player B gets $5. If Player A plays DOWN and Player B plays LEFET then Player A gets $4 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 Equilibrium for Player B? O. (LEFT, RIGHT) = (1/8, 3/8) O. (LEFT, RIGHT) = (1/4, 3/4) O. (LEFT, RIGHT) = (1/2, 1/2) O. (LEFT, RIGHT) = (3/8, 1/8)Q17. What the information sets in the above game denote? Player 2 does not observe the action of player 1, so he does not know in which decision node he/she is playing at. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and b, or one between c and d. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played one between a and c, or one between b and d. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and d, or one between b and c.
- Q17. What the information sets in the above game denote? Player 2 does not observe the action of player 1, so he does not know in which decision node he/she is playing at. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and b, or one between c and d. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played one between a and c, or one between b and d. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and d, or one between b and c. Q18. If we want to describe the above game with a strategic form representation, what would the strategy sets for the three players? Player 1={a, b, c, d} ; Player 2={x, y} Player 1={a, b, c, d} ; Player 2={xx, xy, yx, yy}Type out the correct answer ASAP with proper explanation of it In the Ultimatum Game, player 1 is given some money (e.g. $10; this is public knowledge), and may give some or all of this to player 2. In turn, player 2 may accept player 1’s offer, in which case the game is over; or player 2 may reject player 1’s offer, in which case neither player gets any money, and the game is over. a. If you are player 2 and strictly rational, explain why you would accept any positive offer from player 1. b. In reality, many players reject offers from player 1 that are significantly below 50%. WhyPlayer 1 and Player 2 are trying to agree on how to split a pie of size 1 in a two-stage bargaining game. If no agreement is reached after the two stages are complete, the pie is split for them according to a pre-arranged agreement that gives Player 1 and Player 2 one-quarter and three quarters of the pie, respectively. In the first stage, Player 1 makes an offer (x1, x2), where x1 + x2 = 1. Player 2 can either accept this offer (at which point the game ends and the pie is split according to Player 1’s offer), or can make a counter-offer. When Player 2 makes a counter offer, Player 1 can either accept (in which case the pie is split according to Player 2’s offer) or can reject, in which case the pie is split according to the pre-arranged agreement. Both players have a discount factor d – getting dx in the first stage (after Player 1’s proposal) is as good as getting x in the second stage (after Player 2’s proposal). a) In the last stage of the game, Player 1 will accept any offer…