SITUATION: TEAM-PROJECT GAME Stanford is sort of a big, incredibly smart high school, the high school that we never had. We’ve got the jocks, the nerds, the sorority girls, the frat boys, the indie kids, the preps, the `whatever’ college kids. . . . —TAM VO IN THE STANFORD DAILY Consider a college class with […]
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SITUATION: THE PROXY BID PARADOX AT eBAY Have you ever bid for an item at eBay? Since an auction typically take days, eBay was smart enough to provide a mechanism that doesn’t require a bidder to hang out online 24/7; instead, you can enter a proxy bid, which works as fol- lows: As long as
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How much should you bid? How much should you bid? Since bidding 5—which is in excess of what the piece is worth to you—is strictly dominated by bidding 4, then, clearly, you don’t want to bid that much. Also, you probably don’t want to bid 4—which is your valuation of the item—since that is weakly
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Bidding at an Auction Bidding at an Auction It’s been 20 years since you’ve graduated from college, and you’ve just sold your Internet company for a cool $50 million. With all this cash on hand, you decide to indulge your passion for modern art. An auction house is selling an Andy Warhol piece that you’ve
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Weak Dominance Not to be absolutely certain is, I think, one of the essential things in rationality. —BERTRAND RUSSELL Returning to the world of Italian opera yet again, suppose we now assume that Scarpia, upon being stabbed by Tosca, does not care whether Cavaradossi is killed. The resulting payoff matrix is shown in FIGURE 3.6.
Solving a Game when Players Are Rational 63 TABLE 3.2 SPENDING 15 IS A DOMINANT STRATEGY FOR PM RJR PM Payoff PM Payoff PM Payoff Strategy from 15 from 10 from 5 Spend 5 60 > 57 > 45 Spend 10 45 > 40 > 28 Spend 15 35 > 30 > 20 FIGURE 3.5
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ELIMINATING THE IMPOSSIBLE: SOLVING A GAME WHEN RATIONALITY IS COMMON KNOWLEDGE *In response to complaints about grammar from language mavens, Winston responded with a new slogan: “What do you want, good grammar or good taste?” 3.2 Solving a Game when Players Are Rational 61 cigarettes sold. Some studies by economists show that advertising doesn’t have
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SITUATION: BANNING CIGARETTE ADVERTISING ON TELEVISION Winston tastes good like a cigarette should!* If you grew up in the 1960s, you would know that popular jingle from tele- vision commercials for Winston cigarettes. In fact, it was so common that many people (like me!) remember it even though it hasn’t been broadcast for more than
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RENT IN THE HOUSING MARKET No. of Black Rent Paid by a Black Rent Paid by a White Families Family Family Total Rent 0 — 100 800 1 110 105 845 2 115 110 890 3 120 100 860 4 110 90 800 5 100 75 725 6 90 75 690 7 85 70 665
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Does the game have to be factually accurate? If our objective in formulating and then solving a game is to understand be- havior, then what matters is not what is factually or objectively true, but rather what is perceived by the players. Their behavior will be driven by their pref- erences and what they believe,
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