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In 1962, the US discovered that the Soviet Union had placed offensive nuclear missiles in Cuba, just off the American shore. President Kennedy ordered a blockade of Russian ships headed to Cuba, which pushed the two countries toward nuclear war. Soviet premier Khrushchev agreed to back down if the US removed its own missiles from Turkey, a short distance from Russia.
Taking an opponent to the brink of disaster is now called “brinkmanship.” People sometimes threaten to go on strike, get a divorce, or shut down an important service; these are acts of brinkmanship.
In Cuba, both the Americans and Soviets had several options. Each could, for example, do nothing, attack the other side’s military—the US bombing the missile sites, the Russians sailing into the naval blockade—or even launch a nuclear attack against the other country. The happy middle point that resolves the crisis was hard to discern.
Brinkmanship is a variety of a strategic move, “a threat, but of a special kind” (207). It must warn of a believable risk, not an implausible certainty, of massive retaliation. The threat can use the “small steps” tactic that escalates the confrontation a little at a time, as needed. This replaces a “sharp precipice” with a “slippery slope.” Brinkmanship “deliberately hides the precipice by creating a situation that is slightly out of control” (211).
The Cuban crisis wasn’t just two world leaders staring each other down; it involved many players, some of whom were hard to control. US Secretary of Defense McNamara, for instance, couldn’t get his Navy chief to explain how the boarding of ships at the blockade would be managed, something that might go badly. Yet this uncertainty adds credibility to the threat of annihilation. It also increases the risk faced by the threatener. Brinkmanship can get dicey all around.
It also can lead to disaster: The Chinese government faced student protesters in Tiananmen Square and called their bluff, bringing in military force to quell the demonstrations with disastrous consequences. The Romanian Communist government similarly suppressed demonstrations with violence, and “in the end President Nicolae Ceausescu was executed for crimes against his people” (217).
The nuclear threat is so huge that it becomes worthless in small skirmishes. The Soviets, for example, might start a small disturbance along the border, make inroads, and push gently farther into NATO territory until they’ve gained hundreds of miles. Effective use of nuclear brinkmanship in such a scenario involves arranging decisions so there’s always a small chance of unintentionally sliding down the slippery slope into a sudden nuclear exchange; that way, the opponent never can be sure the next small aggression won’t result in mutual annihilation.
“Case Study #8: Brinkmanship in the Atlantic” (220) describes US Naval policy in the North Atlantic during the 1980s, when American ships would, during a conventional conflict, sink all Soviet subs they could find. This would risk striking a sub carrying nuclear weapons, forcing the Russians to consider retaliating with a nuclear attack. This policy keeps both sides from getting into conventional conflicts, which has prevented war for decades, but some experts argue that the risk of total annihilation is too great to use such a threat.
If the nuclear risk of a given battle strategy goes up, the country using it will simply go slower along that route, and the opponent will become more likely to offer concessions. All strategies adjust to account for changes in risk; thus, nuclear brinkmanship can never be risk-free. The real solution lies in changing, not the rules of war but the entire game itself—scaling down the need for conflict and increasing cooperation and shared values between nuclear nations.
Philosopher Adam Smith in 1776 theorized that a person works for selfish reasons, yet “By pursuing his own interest, he frequently promotes that of society more effectually than when he really intends to promote it” (223). This is the theory of the “invisible hand” that guides commercial activity toward the betterment of society.
The authors believe this principle works only when goods and services have prices. It doesn’t work when, for example, a firm goes to the expense of training a new worker and that worker leaves to work for another company, or when a manufacturing company pollutes the air. Those things aren’t for sale and therefore aren’t priced.
Individuals tend to make choices based on what’s best for them, but in some group settings their choices collectively result in a bad outcome for everyone. US Ivy League colleges during the 1950s all greatly improved their athletic training and recruiting, but league members didn’t improve their average win-loss records. This was costly to no end, so the teams agreed to limit spring training to a single day. Fumbles increased, but the games were just as exciting.
Students graded on a curve can agree to limit studying; their grades turn out roughly the same, but they save a great deal of effort. In this case, though, such an agreement causes a negative social benefit because the students end up poorly educated.
The trip from Berkeley to San Francisco can be made by car across the Bay Bridge or by BART train. The train trip always takes about 40 minutes; the drive, depending on traffic, takes between 20 and 70 minutes. As the number of drivers increases, travel times increase; on a graph, this shows as a line that rises until it crosses the 40-minute constant line of the BART train. At that point, travel times for drivers and train riders are the same, and the number of drivers and riders settle into an equilibrium point.
If the number of drivers is restricted, traffic clears up and drive times get shorter, so that, even though more commuters take the 40-minute train, average per-person travel time improves. If the restriction is lifted, commuters notice the reduced drive time and revert back to driving until bridge crowding increases and travel time reverts to 40 minutes for all. Because there’s no pricing for the option to drive, a selfish choice doesn’t improve social benefit.
One way to solve this is to set a price for car commutes by adjusting bridge tolls until drivers begin to revert to train travel and the traffic mix settles on a new and better equilibrium. Everyone’s selfish commuting preferences are shifted by the pricing system until drive times converge on a more optimal number.
Sometimes an established equilibrium point becomes hard to change even when a better equilibrium point develops. Early typewriters were prone to jamming, so the layout of keys was adjusted to slow down typing. This system, called QWERTY for its six upper-left keys, became obsolete when the faster “DSK,” or “Dvorak,” keyboard arrangement was invented, but typists didn’t want to learn an entirely new keyboard layout. About 98% of typists use QWERTY; if that number dropped below 72%, new typists would learn DSK in droves, after which QWERTY would become extinct. The 98% QWERTY usage rate is very persistent, however, and unlikely to change.
The gasoline car engine, though inferior, became the standard over electric and steam engines because of a series of historical flukes early in automotive history. Heavy-water and gas-cooled nuclear reactors are safer, and heavy-water 25% cheaper, than the more common light-water reactors, but, early in the Cold War, the US Navy needed atomic power for its submarines, and light-water systems were more compact and ahead in development, and they quickly became the standard.
Another area where people coordinate to a poor standard involves driving. It’s generally safer to flow along with traffic even if everyone breaks the speed limit. Hiding within such a group of cars also makes it harder for police to pull you over. If, on the other hand, everyone abides by the speed limit, then speeding becomes more unsafe, and speeding cars become obvious to law enforcement. Thus, the smart move is always to drive with the pack. Police can slow speeding traffic with a short period of tough enforcement, after which the new speed becomes self-sustaining.
Despite increasing racial tolerance in society, both Black people and white people feel uncomfortable in neighborhoods where they’re distinct minorities. In a diverse neighborhood, any shift in the percentage of new residents in one direction or the other causes the mix to slide in that direction until the neighborhood becomes fully segregated. Thus, notwithstanding the desirability of diverse communities, they tend to end up at the extremes.
Chicago’s Oak Park suburb solves this by banning “For Sale” yard signs and by guaranteeing house resale prices. With moves less public, and with fewer financial concerns, Black and white residents will be less likely to panic, and they’ll tend to move in or out for reasons other than race.
An example of private decisions that scuttle a group effort involves the US Congress’ 1989 effort to vote itself a 50% pay raise. Each member’s constituents protested, and each member voted against it while thinking the other members would vote for it. The vote failed.
In an election campaign, an incumbent merely needs to take a political position between the challenger’s and the midpoint of the voters’ opinions; this wins a majority of the votes. The challenger’s best chance is to take the midpoint view, which forces the incumbent also to move to the center. The result is no real choice for the voters. A third-party entrant will migrate toward the middle candidate’s views, forcing that candidate to “jump to the outside and acquire a whole new and larger base of voters” and break up the equilibrium point (250).
Investors tend to pick stocks not because they prefer them but because they believe other investors will prefer them, thus selecting investments for popularity rather than quality.
In “Case Study #9: A Prescription for Allocating Dentists” (254), dentists make more money in urban than rural areas; this means there aren't enough dentists to service oral health needs in the countryside. As more dentists enter city practice, competition drives down their earnings, to the point where it’s more lucrative to move to the countryside. The question is whether an incentive should be added to attract more dentists to rural work.
When a new dentist enters the city, she drives down the earnings of all other dentists. Prices come down, which benefits consumers. Thus, the government doesn’t have an interest in restricting urban dentistry. At the same time, dental societies, wishing to maximize their members’ urban incomes, have an incentive to set up a fund that helps dentists relocate to the country.
A citizen’s vote only counts if it’s a tiebreaker. Otherwise, it has no effect. Voting is vital to a functioning democracy; thus, societies appeal to patriotism or pass laws requiring people to vote.
In a two-person race, voters should always vote their preference, in case theirs is the tie-breaking vote. Centrist candidates, meanwhile, will align themselves, not with the average voter, but with the median voter, on either side of whom are an equal number of voters; this “does not depend on the intensity of the voters’ preferences, only their preferred direction” (266). Meanwhile, in primary elections, voting for an extreme candidate may pull your preferred, more moderate candidate a bit more in your direction.
Changes in the sequence of voting can cause opposite outcomes. If three judges hear a murder case and two want to convict but two are against the death penalty, the fate of the defendant depends on the order in which the judges consider guilt or innocence, the severity of the crime, and mandatory sentencing. If determining guilt or innocence comes first, the defendant will be found innocent (the anti-death-penalty judges prevent a death sentence); if the crime’s severity is predetermined as worthy of life in prison, the defendant will be found guilty; if the death penalty is mandatory, the defendant will be found innocent.
Any time a voter has a set number of votes to allot among several candidates—for example, during US presidential primaries or during the voting for Baseball’s Hall of Fame—voters no longer vote solely for their favorites but switch votes from preferred candidates likely to lose toward lesser candidates more likely to win. A workaround is “approval voting,” in which voters check off as many candidates as they like.
In the Baseball Hall of Fame, approval voting still would be subject to voter preferences about the number of players admitted. If, for example, many players from one position are on the ballot, voters might not vote for their favorite at that position who’s already likely to get in, or they might vote for a lesser candidate who played another position. If there’s a quota—say, two candidates admitted per year—and everyone assumes the one terrific candidate will be voted in, they’ll spend their votes on other candidates they also like, and this may result in the best candidate not getting in at all.
Smaller charities may “vote” by spending most of their budget on their second-favorite causes, betting that larger charities and the government will pay for the bigger causes. On the other hand, England’s Marshall Fund waits for the Rhodes Scholarship to announce its winners, whereupon Marshall selects from the remaining candidates so as to increase the total number of acceptances.
“Case Study #10: All or Nothing” (284) asks whether the US president should have a line-item veto on bills passed by Congress, a power possessed by more than 40 of the 50 state governors. Currently, the president must sign or reject an entire bill with its many add-ons intact, but a line-item veto would clean out much of the wasteful cruft that adheres to bills, thereby saving money.
A study shows that states with line-item vetoes don’t reduce their deficits. As well, a president with a line-item veto might have less, rather than more, power because a Congress controlled by the other party would be reluctant to present any bills to the president for signature, lest he remove their pet projects from the bill.
A resort hotel prepares to open for the 101-day summer season by bargaining with the employees’ union over the estimated daily profits of $1,000. If bargaining drags through to the last day of the season, there’ll be nothing left to split except the last $1,000. Instead, the two sides, looking forward and reasoning backward, realize that the best arrangement is to split the profits, start immediately to work, and each side gets the maximum possible amount, $50,500.
If the union can make $300 on the outside, management must concede this to them at the outset, and the remainder of profit, $700, gets split: the union ends up with $650 and management gets $350. If management can use scab labor, even if they make only $500 profit per day, they start with a $500 advantage. The remaining $500 profit from a full day of union participation gets split, so the union gets $250 and management gets $750. If both conditions pertain, the union starts with $300, management starts with $500, and the remaining $200 gets split; the union ends up with $400 and management receives $600.
The moral is that “the better a party can do by itself in the absence of an agreement, the higher will be its share of the pie” (290). Each side then looks for ways to improve its pre-work advantage. The union might threaten more vigorous picketing, reducing management’s profit to $300 and the union’s outside earnings to $200. The two groups split the remaining $500 from a full $1,000 day, so that management gets $550 while the union improves its fortunes to $450.
Generally, both sides in a labor negotiation will begin early and reach agreement well beforehand, lest misunderstandings or other problems delay the process past the deadline. If, however, the two sides don’t have a good idea about how long the other side can hold out during a strike, this may lead them to test those waters by engaging in brinkmanship, with the possibility of a work stoppage hanging in the balance.
Another issue that can roil the waters is whether to bargain about one item at a time—perhaps healthcare first, then money, then other perks—or whether to bundle all issues together into one simultaneous negotiation—for example, two nations discussing trade and defense pacts together.
The chapter’s Case Study, “#11: ’Tis Better to Give than to Receive?” (296), presents a change in the chapter’s opening example, so that hotel management makes all offers and the employees’ union simply accepts or rejects. The question is whether this approach generates a 50/50 split, as in the earlier example, or some other arrangement.
Management is in a powerful bargaining position: It can simply add one dollar to its offer each day. Looking forward and reasoning backward, the union realizes it will end up accepting roughly one-third of the profit. Fifty-fifty splits, though common, aren’t always the end result; the case study’s example, though exaggerated, shows that the rules of the negotiation can give one side an advantage.
Chapter 11 contains an appendix, “Patience Is Its Own Reward” (300), which discusses bargaining over an open-ended contract during a steel strike. Delays cause loyal customers to leave for other manufacturers; longer delays increase the risk of a plant closure. Job actions also cost both sides money and its interest value in investments, so that, given a long enough strike, lost income begins to multiply.
If a week’s delay makes a lost dollar worth $1.01 to the union but $1.02 to management, the owners are more impatient to settle, and the one-penny difference leads to a contract that gives the union a two-to-one split, or two-thirds of the profits.
In negotiations between the US and other countries, American bargainers tend to be impatient—Congress likes quick action, and the media pressures the administration for results—and other nations, more patient, tend to get the better part of the deal.
Market economies operate on the profit motive, which rewards efficiency and popular products while punishing inefficiency and inferior goods. Employees don’t all have identical goals, however, and managers must design incentives that motivate every worker. These motives vary from job to job and from department to department. Partnerships between companies also must adjust their contracts so that each side is fully engaged in doing its best.
Higher pay garners inspired workers, but their efforts must produce more profit than their extra cost. However, products often fail for reasons other than effort, and it’s hard to tell if the better-qualified hire is doing inspired or routine work.
One solution is to offer a reward for a product that succeeds in the marketplace. Writers of computer programs who make $50,000 might be inspired to work harder if they earn $20,000 bonuses. If the odds of an application’s success are 20%, then the company offers a $100,000 bonus on success, and the programmer reasons that take-home pay will average $20,000 extra on a given project. Some approaches involve much higher reward against no pay for failure, but most involve a mix of guaranteed pay and reward pay.
These types of incentives remove much of the costs of monitoring, since employees will want to get the work done to maximize the chances of getting bonuses.
Partnerships are more complicated. When two firms work on a joint project, each may be tempted to shirk their duties or threaten to walk away unless the agreement is rewritten in their favor. Several devices can reduce this risk.
First, each side must agree to put up a sum toward product development that they lose if they quit. Second, a large penalty must accrue for breaching the pact. The contract should stipulate that if initial studies prove the project will lose money, the partnership can be dissolved.
If the project goes ahead, partners should be paid their expenses and then a share of profits that’s based on their proportion of the expenses. This, though, tempts each side to exaggerate its costs, usually by assigning an overly large portion of its general overhead to the project or by overpaying managers. Such a strategy, especially if adopted by both sides, can lead to cancellation of a project that otherwise would have been profitable. A contract must motivate both sides to be truthful about their costs, and that, if one side quits, it will pay the other’s expenses.
Auctions are a common way for companies to reduce costs from contractors. Each applicant makes a secret bid, and the contract goes to the lowest bidder. The best strategy is for every firm to bid slightly above their costs, which makes the bid worthwhile if it wins but not so high that it will be undercut by other bidders. Some auctions, though, award the contract to the lowest bidder and pay it the next-lowest bid price; this is called a Vickrey auction. This system further reduces the temptation to inflate bids and lowers the cost to the auctioneer.
This auction also works in reverse, when buyers vie with secret bids to pay for an auctioned item: The highest bid wins but pays the second-highest bid price. In open auctions, this system is the norm: When the second-highest bidder drops out, the remaining bidder effectively pays the last bidder’s price.
“Case Study #12: The Risk of Winning” (324) presents the problem of uncertainty in a Vickrey auction: Bidders for the right to buy a valuable item don’t know how much they’ll pay, since the winner is assigned the price of the next-lower bid. This suggests bidders might lower their bids to reduce the uncertainty, which always is a problem in financial situations.
In fact, the uncertainty “is only over the degree of good news” (325), and the correct strategy is to bid one’s best estimate of the item’s actual value. In all cases, the winner will pay less than that price.
This chapter contains 23 extra Case Studies intended for practice and to point out interesting asides in game theory. Below are three of the cases.
“2. The Last Shall Be First” (328): The US government wants all late teens to register for the draft, but it can punish only one of them for failure to do so. The challenge is for the US to achieve full compliance.
“The government announces that it will go after evaders in alphabetical order” (328). This forces all Aarons to comply because they’ll be inspected first. All Abrams will then have to comply because they’re next in line; this logic extends all the way through the alphabet to the Zweibels. This system also works if inspections start at the low end of birthdays or Social Security numbers. In real life, it’d end as soon as one careless teen gets caught, so the Zweibels can relax.
“13. The King Lear Problem” (351). (King Lear distributed his estate while alive and lost the affections of his children.) A wealthy couple wants attention from their three grown offspring. They set up their will so that any child who doesn’t visit once and call twice per week gets disinherited, but at least one child will receive an inheritance. The kids respond by forming a cartel and reduce all their visits below the minimum. The parents must find a way to outplay the children.
The solution is to give the entire estate to whichever below-quota child visits the most. Thus, any child who defects from the cartel gets everything. The cartel collapses and the children visit and call as ordered.
“17. Brinkmanship and the Jury” (358). The jury in the 1988 “Preppy Murder” trial was hopelessly deadlocked, their votes swinging wildly between acquittal and conviction. Neither side could predict the outcome, and a hung jury was very bad for both sides, since it would force them both to undergo the expense and stress of starting all over again. The judge needs a solution.
The judge’s best play is to use the threat of a hung jury to force the two sides to negotiate a settlement. This is a form of brinkmanship that warns the parties they’ll otherwise slide down the slippery slope to financial disaster.
In Part 3, the authors take a closer look at several important game types and how to manage them, including negotiating, voting, bargaining, and coordinating.
The talks between Kennedy’s team and Khrushchev’s during the Cuban Missile Crisis have ever after been described as an American victory. In fact, Khrushchev won an important concession—he got US missiles removed from a country near the Soviet border. Khrushchev thus sacrificed the public-relations battle but won the strategic one. The entire experience, though, was so scary to both sides that neither ever tried such a move again.
Thereafter, the two nations took to fighting “proxy wars,” or battles involving third countries using local militaries to avoid direct confrontations. The Vietnam War was one such example: The Soviets supported Communist North Vietnam with supplies and advice but otherwise kept to the shadows; the US backed the anti-Communist South. In Afghanistan it was the US’s turn to supply the resistance fighters, who battled Soviet occupation forces. More recently, the US and Russia found themselves part of a multi-sided civil war in Syria and had to step carefully to avoid bumping into each other.
The San Francisco commuting example shows how individuals reach a consensus by doing what’s best for each commuter, but it doesn’t consider some people’s need for a car once they’re in the city, nor the benefits of a private vehicle that include making phone calls, chatting with carpoolers, grabbing a bite of food, and so forth. In that respect, the example is oversimplified, but it ignores such variables to make a general point.
As for consensus tools, like QWERTY keyboards and gas engines, sometimes an inferior solution gets so much of a head start that it becomes the standard, and better alternatives must fight a steep uphill battle for acceptance. Examples of such “platform monopolies” include those enjoyed by Microsoft computing software, the Facebook social network, or the Amazon online sales emporium. Once these become standard, everyone wants to use them because everyone else is using them. Alternatives must scrape to survive apart from the mainstream.
The authors suggest that bad outcomes in group decisions can be regulated by governments that incentivize a wider selection process that allows for better solutions to appear. This, though, opens the door to bureaucrats “picking winners,” which itself can push decisions in the wrong direction. The main problem is that it’s hard to know ahead of time which standard will be best in the future.
In a sense, the market already has solved the problem: It’s found that, though people chose an inferior standard, that standard is good enough because it’s too costly to change it for something better. More tinkering won’t give a better result. The standard actually does have a price—the cost to change it—and thus resources already have been allocated correctly.
Chapter 11 mentions that the US tends to be impatient for quick results during negotiations with other nations. Many years ago, a story circulated about an American negotiator sent to East Asia by his company, where he had two weeks to craft a deal with a local firm. The firm wined and dined the American for nearly the entire two weeks while postponing actual talks. Not until he was in the limo driving to the airport for the flight back to the US did local negotiators bring up the contract. Needless to say, the American got the short end of the deal.
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