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behavioral economics

A Course In Behavioral Economics 3rd Edition Erik Angner - Solutions

Subgame-perfect equilibrium A subgame-perfect equilibrium is a strategy profile that constitutes a Nash equilibrium in each subgame.
Credible versus non-credible threats Consider a game with two stages. In the first stage, Player I plays U or D. If Player I plays D, both players get a payoff of 2. If Player I plays U, it is Player II’s turn. In the second stage, Player II plays L or R; if Player II plays L, Player I gets 5 and
Trembling-hand perfection Find (a) all Nash equilibria in pure strategies in Table 10.12 and (b) identify which of them are trembling-hand perfect.Substituting the concept of trembling-hand-perfect equilibrium for the concept of Nash equilibrium would eliminate some problematic implications of the
Battle of the sexes, cont. Are the two pure-strategy equilibria in the battle of the sexes (Table 10.8) trembling-hand perfect? Trembling-hand-perfect equilibrium is a refinement of Nash equilibrium. This means that every trembling-hand-perfect equilibrium is a Nash equilibrium, but not every Nash
Trembling-hand-perfect equilibrium A tremblinghand-perfect equilibrium is a Nash equilibrium that remains a best response for each player even when others have some minuscule probability of trembling, that is, accidentally playing an out-ofequilibrium strategy
Trembling-hand perfection Let us return to Table 10.9(c). As you know, (U, L) is a Nash equilibrium. (D, L) is not an equilibrium, since Player I can improve his payoff by playing U instead of D, and neither is (U, R). But consider (D, R). If Player II plays R, Player I can do no better than
The stag hunt This game is due to Jean-Jacques Rousseau, the eighteenth-century French philosopher. Rousseau describes a scenario in which two individuals go hunting. The two can hunt hare or deer but not both. Anyone can catch a hare by himself, but the only way to bag a deer is for both hunters
Chess Chess is a finite game. We know this because every player has a finite number of moves to choose from at any point in the game and because every game ends after a finite number of moves. Because it is a finite game, Nash’s theorem establishes that it has an equilibrium. This suggests that
Nash’s theorem Every finite game – that is, every game in which all players have a finite number of pure strategies – has a Nash equilibrium.Given this theorem, the search for Nash equilibria is not futile. As long as the number of pure strategies available to each player is finite – and
Rock-paper-scissors (a) Draw the payoff matrix for the game rock-paper-scissors. Suppose that a win gives you 1 utile, a tie 0, and a loss −1. (b) What is the unique Nash equilibrium in this game? We already know that not all games have Nash equilibria in pure strategies. But now that we have
Pure vs. mixed equilibria Find all Nash equilibria (in pure and mixed strategies) in the games depicted in Table 10.9. Although a mixed-strategy equilibrium may at first blush seem like an artificial construct of mainly academic interest, mixed strategies are important and common in a wide variety
Mixed-strategy equilibrium Find the mixed-strategy Nash equilibria in Tables 10.4(a) and (b) In the mixed-strategy equilibrium in (a), notice that Player I is more likely to play D than U and that Player II is more likely to play R than L. This might seem strange, since you would perhaps expect the
Battle of the sexes, cont. In order to find the mixedstrategy equilibrium in the battle of the sexes (Table 10.8), let us assume that Player I plays U with probability p and D with probability (1 – p) and that Player II plays L with probability q and R with probability (1 – q). Consider Player
Coffee shops, cont. Suppose that you still have to go to one of the two coffee shops in Example 10.3 and that your ex has to also. You do not want to run into your ex, but your ex wants to run into you. What kind of game would you be playing against each other? If a player gets a utility of 1
The Leviathan The seventeenth-century political philosopher Thomas Hobbes offered a justification of political authority by imagining what life would be like without it. In one of the most famous lines in the history of Western philosophy, Hobbes described this “state of nature” as follows:
Prisoners’ dilemma Two criminals are arrested on suspicion of two separate crimes. The prosecutor has sufficient evidence to convict the two on the minor charge, but not on the major one. If the two criminals cooperate (C) with each other and stay mum, they will be convicted on the minor charge
Nash equilibrium in pure strategies Find all Nash equilibria in the games in Table 10.4, where Player I chooses between Up (U), Middle (M), and Down (D) and Player II chooses between Left (L), Middle (M), and Right (R).Notice that in Exercise 10.5(a), there are two Nash equilibria in pure
Battle of the sexes A husband and wife must decide whether to have dinner at the steak house or at the crab shack. All things equal, both would rather dine together than alone, but the man (Player I) prefers the steak house and the woman (Player II) prefers the crab shack. The man gets 2 units of
Coffee shops You and your study partner are planning to meet at noon at one of two coffee shops, Lucy’s Coffee and Crestwood Coffee. Unfortunately, you failed to specify which one, and you have no way of getting in touch with each other before noon. If you manage to meet, you get a utility of 1;
Nash equilibrium A Nash equilibrium is a strategy profile such that each strategy in the profile is a best response to the other strategies in the profile.
The makeup exam One year there were two students taking Chemistry. They both did so well on quizzes, midterms, and labs that they decided to leave town and go partying the weekend before the exam. They mightily enjoyed themselves. However, much like a scene in The Hangover: Part IV, they overslept
Drawing on your own experience, make up stories like those in Exercise 9.28 to illustrate the various ideas that you have read about in this chapter.
Match each of the vignettes below with one of the following phenomena: hyperbolic discounting, preference over profiles, choosing not to choose, and misprediction / miswanting. If in doubt, pick the best fit. (a) Allie goes to bed at night fully intending to get up at 5 am and study hard before
In much of the modern world, people are supposed to decide themselves whom to marry. The decision is often (expected to be) made when young, in love, and/or sexually aroused. (a) Give at least two reasons to think that people’s happiness predictions under the circumstances might be off. (b) How
Weights and shackles Seneca offered the following advice: [Reflect] that prisoners at first find the weights and shackles on their legs hard to bear, but subsequently, once they have determined to endure them rather than chafe against them, necessity teaches them to bear them bravely, habit to bear
From the underground The book Notes from the Underground, by Russian novelist Fyodor Dostoyevsky, is often described as the first existentialist novel. Here’s a sample:Now I ask you: what can be expected of man since he is a being endowed with strange qualities? Shower upon him every earthly
Orpheus and Eurydice Superstar singer–songwriter Orpheus messed up. Long story, but tl;dr he had to go get his main squeeze, Eurydice, back from the underworld. Things went well at first, but the king of the underworld, Hades, told Orpheus absolutely, positively not to look back, and what did he
Addiction Suppose that life has three periods: youth, middle age, and old age. In every period you decide whether to do drugs (“hit”) or not (“refrain”). The utility of hitting depends on whether you are addicted (“hooked”) or not. If you are not hooked, the utility from hitting is 10
Retirement savings When young, many people fully intend to save for retirement. However, when they start making money after college, they are often tempted to spend it immediately. Assume that Ximena and Yves have the choice between the following two options: (a) saving for retirement at time 1 (u1
Happiest professions Table 9.3 shows the result of a survey about the happiness of people in various professions: the middle column lists the five happiest professions, and the right-hand column the five unhappiest. You might think that you would be happiest if you were a lawyer or a doctor or
Buffet lines Perhaps you too have the following experience when picking up dinner from a buffet, where you can serve yourself exactly what kind of food you want. At the end of the meal, people find there is food on their plate they have no interest in eating. This is puzzling: if people were able
Sidgwick What kind of misprediction is described in the following passage, by the nineteenth-century moral philosopher Henry Sidgwick? In estimating for practical purposes the value of different pleasures open to us, we commonly trust most to our prospective imagination: we project ourselves into
Fasting Some religious traditions encourage fasting as a way to identify with less fortunate fellow human beings. The underlying insight is consistent with projection bias: it is only when we ourselves are hungry that we can begin to appreciate what it is like to actually starve. Projection bias
College Many adults will tell you that their college years were the best years of their lives. This is puzzling since actual college students are not, on the average, fantastically happy. Use the concept of the peak–end rule to explain why people remember their college years so fondly. There are
The peak–end rule, cont. This exercise refers to Figure 9.6. Would a person who follows the peak–end rule choose the episode represented by the solid line or the episode represented by the dashed line?
The peak–end rule Suppose you add a pleasant tail to an already pleasant episode. If people assess the episode as a whole in accordance with the peak–end rule, will this make people think of the episode as a whole as more or less pleasant?
Hunter S. Thompson The following passage, attributed to American writer Hunter S. Thompson, illustrates the power of stories: Life should not be a journey to the grave with the intention of arriving safely in a pretty and well-preserved body, but rather to skid in broadside in a cloud of smoke,
Economics professors Rumor has it that even economics professors frequently elect to receive their annual salary in twelve rather than nine installments, even though they would maximize their discounted utility by asking to be paid in nine. Obviously, they have the option of saving some of their
Cleaning the house It is Sunday morning (t = 0), and you are determined to accomplish two things today: cleaning the apartment and going to the movies. You can either clean during the morning (at t = 0) and go to the movies during the afternoon (at t = 1), or go to the movies during the morning (at
Johnny Depp 2 This exercise refers to Example 9.10. Suppose instead that you can only watch one of the four movies. Will you watch a the mediocre, b the good, c the great, or d the fantastic movie? (a) Show that an exponential discounter will watch d the fantastic movie. (b) Show that a naive
Johnny Depp 1 Your local cinema theater offers a mediocre movie this week (u0 = 3), a good movie next week (u1 = 5), a great movie in two weeks (u2 = 8), and a fantastic Johnny Depp movie in three weeks (u3 = 13). Unfortunately, you must skip one of the four. For all questions below, suppose that
Wicksteed’s blanket The theologian and economist Philip Wicksteed offers the following observation: “[We] lie awake (or what we call awake next morning) half the night consciously suffering from cold, when even without getting out of bed we could reach a blanket or a rug which would secure
Suppose that you discount the future hyperbolically. Assume that both β and δ are strictly greater than zero but strictly smaller than one. At t = 0, you are given the choice between the following three options: a (2 utiles at t = 0), b (5 utiles at t = 1), and c (10 utiles at t = 2). As a matter
Suppose that you discount the future hyperbolically. Assume that both β and δ are strictly greater than zero but strictly smaller than one. At t = 0, you are given the choice between the following three options: a (1 utile at t = 0), b (2 utiles at t = 1), and c (3 utiles at t = 2). As a matter
Suppose that you discount the future hyperbolically, that is, in accordance with the beta–delta function, and that from the point of view of Thursday you are indifferent between options a (1 utile on Thursday) and b (3 utiles on Friday). (a) If β = 1/2, what is δ? (b) If δ = 4/9, what is β?
Cancer screening Most colon cancers develop from polyps. Because early screening can detect polyps before they become cancerous and colon cancer in its early stages, many doctors advise patients over a certain age to have a colonoscopy. Unfortunately, colonoscopies are experienced as embarrassing
Impulsivity and impatience Suppose you are offered the choice between option a (8 utiles on Thursday) and b (12 utiles on Friday). (a) Assume that β = 1 and that δ = 5/6. From the point of view of Thursday, which one would you choose? From the point of view of Wednesday, which one would you
Dieting today and tomorrow Suppose that you are on a diet, but have to decide whether to have a slice of red-velvet cake at a party some random Saturday. Eating the cake would give you a utility of 4. If you have the cake, however, you will have to exercise for hours on Sunday, which would give you
The beta–delta function Suppose that you are facing a utility stream of 1 utile at t = 0, 3 utiles at t = 1, and 9 utiles at t = 2. For each of the following parameter values, apply the beta–delta function to determine the discounted utility of the stream. (a) β = 1/3 and δ = 1. (b) β = 1
The beta–delta function According to the beta–delta function, the utility U0 (u) of utility stream u = 〈u0 , u1 , u2 , …〉 from the point of view of t = 0 is U 0 (u) = u0 + βδu1 + βδ 2u2 + βδ 3u3 + … = u0 + ∞ ∑ i=1 βδ iui
Time discounting and interest rates Whether you should spend or save will depend not just on your time preference, but on the interest you can get when putting your money in a savings account. Suppose you have the option of spending $w now or saving it until next year. If you save it, the bank will
The afterlife Some people believe in an afterlife where wrongs are righted and good behavior rewarded. What sort of time preference should we expect such believers to reveal in their behavior?
Heaven can wait Researchers have explored the possibility that a religious upbringing helps shape discount rates. A 2013 study starts off with the following stylized facts: (1) Calvinism discourages immediate consumption but encourages long-term accumulation, whereas Catholicism frowns equally upon
Credit scores A study in the journal Psychological Science by two economists from the Federal Reserve Bank in Boston found a connection between people’s discount factor δ and their credit score. A credit score is a number representing a person’s creditworthiness: the higher the score the
Suppose instead that the utility function is u(x) = x 2 . What would Table 8.4(b) look like, and what would δ be?Exercise 8.24 Youth sports In a 2014 interview, basketball star Kobe Bryant discussed the importance of making sports fun for young people. “It’s hard to tell a kid that you need to
Suppose you are indifferent between dollar streams a and b in Table 8.4(a). Your utility function is u (x) = √x. What is your δ? Given the utility function, Table 8.4(a) can be converted into a matrix of utilities as in Table 8.4(b). We can compute δ by setting up the following equation: 3 +
As a financial advisor, you offer your clients the possibility to invest in an asset that generates a utility stream of 1 utile this year (t = 0), 0 utiles next year (t = 1), and 1 utile the year after that (t = 2). For each of the following clients, determine their δ: (a) Client P is indifferent
For each of the three decision problems in Table 8.3, compute δ on the assumption that a person is indifferent between a and b at time zero.
This exercise refers to the utility streams in Table 8.2. For each of the following people, compute δ. (a) At t = 0, Ahmed is indifferent between utility streams a andb. (b) At t = 0, Bella is indifferent between utility streams b andc. (c) At t = 0, Cathy is indifferent between utility streams a
Use Figure 8.3 to answer the following questions: (a) If δ < 1/3, what would the curve look like? (b) What if δ > 1/3?
A stitch in time “A stitch in time saves nine,” people say when they want you to do something now rather than later. But not everyone will be swayed by that sort of concern. Suppose that you can choose between one stitch at time zero and nine stitches at time one, and that each stitch gives you
Indifference Suppose that Alexandra, at time zero, is indifferent between utility streams a (2 utiles at t = 0) and b (6 utiles at t = 1). What is her discount factor δ? Given that Alexandra is indifferent between a and b at time zero, we know that U0 (a) = U0 (b), which implies that 2 = 6δ which
The impartial spectator Adam Smith’s Theory of Moral Sentiments made a big deal of the differences between an “impartial spectator” and our actual selves. An impartial spectator, Smith wrote, “does not feel the solicitations of our present appetites. To him the pleasure which we are to
Discount factors For each of the following, identify whether the person’s δ is likely to be high (as in close to one) or low (as in close to zero): (a) A person who raids his trust fund to purchase a convertible. (b) A person who enrolls in an MD/PhD program. (c) A person who religiously applies
The ant and the grasshopper According to the fable, the grasshopper chirped and played all summer while the ant was collecting food. When winter came, the ant had plenty of food but the grasshopper died from hunger. What can you surmise about their deltas? Economists believe discount factors can be
Exponential discounting, cont. Suppose instead that δ = 0.1. (a) Compute the utility of each of the four utility streams from the point of view of t = 0. (b) What would you choose if given the choice between all four? (c) What if you had to choose betweena, b, and c? As these calculations show,
Exponential discounting Suppose that δ = 0.9, and that each utility stream is evaluated from t = 0. If so, U0 (a) = u0 = 1, U0 (b) = δu1 = 0.9 * 3 = 2.7, U0 (c) = δ 2u2 = 0.92 * 4 = 3.24, and U0 (d) = u0 + δu1 + δ 2u2 = 1 + 2.7 + 3.24 = 6.94. Hence, if given the choice between all four
The delta function According to the delta function, the utility Uu) of utility stream u = (uo, u, u,...) from the point of view of t=0 is U (u) up+du +22 +8 us +.... = 40+ i=1
Payday loans, cont. Imagine that you borrow $61 from a payday loan establishment. After one week, it wants the principal plus 10 percent interest back. But you will not have that kind of money; so, instead, you go to another establishment and borrow the money you owe the first one. You do this for
Savings Suppose that you put $100 into a savings account today and that your bank promises a 5 percent annual interest rate. (a) What will your bank’s liability be after 1 year? (b) After 10 years? (c) After 50 years? Finally, let us return to the payday loan establishments.
Compound interest Imagine, again, that you use a credit card to borrow $100 and that the monthly interest rate is 18 percent. In contrast to the previous example, however, you do not make monthly interest payments. Instead, every month your interest is added to the principal. What is the total
Simple interest Imagine that you use a credit card to borrow $100, and that every month the credit-card company will charge you an interest rate of 18 percent of the principal. Every month, you pay only interest, but you pay it off in full. At the end of the year, you also repay the $100 principal.
Payday loans Payday loan establishments offer short-term loans to be repaid on the borrower’s next payday. Fees fluctuate, but such an establishment may offer you $400 on the 15th of the month, provided you repay $480 two weeks later. Over the course of the two weeks, what is the interest rate
Implicit interest Suppose that somebody offers to lend you $105 on condition that you pay them back $115 one year later. What is the interest rate (r) implicit in this offer? We know that P = $105 and L = $115. (8.5) implies that R = L/P = $115/$105 = 1.095. By (8.4), r = R − 1 = 1.095 − 1 =
Cost of credit, cont. What would it cost to borrow $ 1000 for one year using one of the other credit cards in Table 8.1? What if you need $100 or $10,000? Fees and APRs fluctuate; never make decisions about credit cards without looking up the latest figures. At the end of the year, the lender will
Cost of credit Suppose you need to invest $1000 in a new car for one year. If you charge it to the Silver Axxess Visa Card, what is the total cost of the credit, taking into account the fact that you would be charged both interest and an annual fee? Given that the annual percentage rate (APR) r =
Drawing on your own experience, make up stories like those in Exercise 7.38 to illustrate the various ideas that you have read about in this chapter.Exercie .8.1 Interest Suppose you borrow $100 for a year at an annual interest rate of 9 percent. At the end of the process, how much interest will
Match each of the vignettes below with one of the following phenomena: ambiguity aversion, cancellation, certainty ef ect, competence hypothesis, silver lining, and mental accounting. If in doubt, pick the best fit. (a) Abraham is seriously depressed after his girlfriend of several years leaves him
Life coaching Life coaches are people whose job it is to help you deal with challenges in your personal and professional life. (a) If you spend too much money, life coaches will sometimes suggest that you cut up your credit cards and pay cash for everything. Use the language of integration and
Zero expected value Prospect theory is consistent with the result that people frequently reject gambles with an expected value of zero. Suppose you are facing a gamble G with a 1/2 probability of winning $10 and a 1/2 probability of losing $10. According to prospect theory, would you prefer the
Savings decisions You are lucky enough to have a million dollars in the bank. You have decided that there are only three serious investment options: putting it in your mattress, investing in stocks, and investing in bonds. Your utility function over total wealth is u (x) = √x. There is no
Show graphically that the expected value of the high-stakes gamble is lower than the utility of the status quo in Figure 7.7. The theorem is quite general. For example, it does not assume any particular functional form. The calibration theorem is a problem for expected-utility theory as a
Lotteries as rewards Behavioral economists have found that using lotteries can be an effective way to incentivize behavioral change. Thus, a person may be more likely to fill in a survey or take a pill if offered a lottery ticket with a 1/1000 probability of winning $1000 than if offered a cash
Russian roulette Suppose that you are forced to play Russian roulette, but that you have the option to pay to remove one bullet from the loaded gun before pulling the trigger. Would you pay more to reduce the number of bullets in the cylinder from four to three or from one to zero? According to
Freakonomics The book Freakonomics discusses the economics of crack-cocaine. Contrary to what many people think, the vast majority of crack dealers make little money – frequently less than the federally mandated minimum wage. They stay in the job, according to the Freakonomics authors, because of
Value Given a decision problem as in Table 6.4 on page 132, the value (or weighted value) V(A) of an act A, is given by V(A) = [Pr (S)]*v (C) + * [Pr (S2)]*v (C) + ... + [Pr (Sn)]*v (Cin) Pr (S,)]v (C)
Known knowns In a 2002 press briefing, American Defense Secretary Donald H. Rumsfeld said: “[As] we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown
Nevada’s boom and bust Las Vegas entrepreneur Andrew Donner does not gamble at the casinos. Instead, he invests in real estate in the city’s downtown. Interviewed on Marketplace, Donner said: “Well, you know casinos, you somewhat know the odds, and I think there’s something beautiful about
Tennis You have been invited to bet on one of three tennis games. In game 1, two extraordinarily good tennis players are up against each other. In game 2, two extraordinarily poor tennis players are up against each other. In game 3, one very good and one very bad player are up against each other,
The coins Suppose that you have the opportunity to bet on the outcome of a coin toss. If the coin comes up heads, you win; if it comes up tails, you lose. Suppose also that you are ambiguity averse. Would you rather bet on a fair coin (with equal probabilities of coming up heads and tails) or on a
Ellsberg problem Suppose that Dan shows you an urn with a total of 90 balls in it. There are three kinds of ball: red, black, and yellow. You know (from a trustworthy authority) that 30 are red, but you do not know how many of the remaining 60 are black and how many are yellow: there could be
Certainty effect, cont. Show that it is a violation of expected-utility theory to choose (A) over (B) and (D) over (C) in Example 7.23. Notice that (C) and (D) can be obtained from (A) and (B) by dividing the probabilities by four. Does the certainty effect appear in the real world? It might. In a
Certainty effect Which of the following options do you prefer: (A) a sure win of $30; (B) an 80 percent chance to win $45? Which of the following options do you prefer: (C) a 25 percent chance to win $30; (D) a 20 percent chance to win $45? In this study, 78 percent of respondents favored A over B,
Sure-thing principle, cont. Suppose that you face the options in Table 7.2(c) and that you must choose first between (la) and (1b), and second between (2a) and (2b). What choice pattern is ruled out by the sure-thing principle? As a normative principle, the sure-thing principle has its appeal, but
Sure-thing principle (a) Suppose that you face the options in Table 7.2(a). Which state of the world does the sure-thing principle tell you to ignore? (b) Suppose that you face the options in Table 7.2(b). What does the sure-thing principle tell you about this decision problem?
Allais problem Suppose that you face the following options, and that you must choose first between (la) and (1b), and second between (2a) and (2b). What would you choose? (la) $1 million for sure (1b) An 89% chance of $1 million & a 10% chance of $5 million (2a) An 11% chance of $1 million (2b) A
Silver linings For this question, suppose your value function is v (x) = √x/2 for gains and v (x) = −2√|x| for losses. Last night, you lost $9 in a bet. There was a silver lining, though: on your way home, you found $2 lying on the sidewalk. (a) If you integrate the loss and the gain, what is
The pain of paying taxes The previous paragraph suggests that how you feel about paying your taxes will depend on whether you integrate that cost with the money you made or not. (a) If you are a politician known for favoring high taxes, should you encourage voters to integrate or segregate? How
Online booksellers If you look this book up at a large online retailer, you may see a little advertisement saying something like: “This book is frequently bought with Kahneman’s Thinking, Fast and Slow. Buy both for twice the price!” Presumably the message contains no new information: you
Evaluation of losses Yesterday, you had a terrible day: you got a $144 speeding ticket on your way to the opera, and then had to pay $25 for a ticket you thought would be free. Suppose your value function remains that of Exercise 7.12. (a) If you integrate the two losses, what is the total

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