Price Wars and the Prisoner’s Dilemma

cost could decrease without changing the firm’s optimal price. (Small shifts in demand that retain the kink at P* would also leave the firm’s optimal price unchanged.) In short, each firm’s price remains constant over a range of changing market conditions. The result is stable industry-wide prices.

The kinked demand curve model presumes that the firm determines its price behavior based on a prediction about its rivals’ reactions to potential price changes. This is one way to inject strategic considerations into the firm’s decisions. Paradoxically, the willingness of firms to respond aggressively to price cuts is the very thing that sustains stable prices. Price cuts will not be attempted if they are expected to beget other cuts. Unfortunately, the kinked demand curve model is incomplete. It does not explain why the kink occurs at the price P*. Nor does it justify the price-cutting behavior of rivals. (Price cutting may not be in the best interests of these firms. For instance, a rival may prefer to hold to its price and sacrifice market share rather than cut price and slash profit margins.) A complete model needs to incorporate a richer treatment of strategic behavior.

CHECK STATION 2

An oligopolist’s demand curve is P 30 Q for Q smaller than 10 and P 36

1.6Q for Q greater than or equal to 10. Its marginal cost is 7. Graph this kinked demand curve and the associated MR curve. What is the firm’s optimal output? What if MC falls to 5?

Stable prices constitute one oligopoly outcome, but not the only one. In many markets, oligopolists engage in vigorous price competition. To this topic we now turn.

A surprising number of product lines are dominated by two firms, so-called duopolists. Some immediate examples are Pepsi versus Coke, Nike versus Reebok (running shoes), Procter & Gamble versus Kimberly-Clark (disposable diapers), and Disney-MGM versus Universal (movie theme parks). When the competing goods or services are close substitutes, price is a key competitive weapon and usually the most important determinant of relative market shares and profits.

A PRICE WAR As a concrete example, consider a pair of duopolists engaged in price competition. To keep things simple, suppose that each duopolist can produce output at a cost of $4 per unit: AC MC $4. Furthermore, each firm has only two pricing options: charge a high price of $8 or charge a low price of $6. If both firms set high prices, each can expect to sell 2.5 million units annually. If both set low prices, each firm’s sales increase to 3.5 million

units. (The market-wide price reduction spurs total sales.) Finally, if one firm sets a high price and the other a low price, the former sells 1.25 million units, the latter 6 million units.

Table 9.2 presents a payoff table summarizing the profit implications of the firms’ different pricing strategies. Firm 1’s two possible prices are listed in the first and second rows. Firm 2’s options head the two columns. The upperleft cell shows that if both firms charge high prices, each will earn a profit of $10 million. (It is customary to list firm 1’s payoff or profit first and firm 2’s payoff second.) Each firm’s profit is computed as: (P AC)Q (8 4)(2.5) $10 million. The other entries are computed in analogous fashion. (Check these.) Notice that firm profits are lower when both charge lower prices. (The price reduction increases the firms’ total sales, but not by enough to compensate for lower margins. Demand is relatively inelastic.) Notice also that if one firm undercuts the other’s price, it wins significant market share and, most important, profit at the expense of the other.

Each firm must determine its pricing decision privately and independently of the other. Naturally, each seeks to maximize its profit. What pricing policy should each firm adopt? The answer is that each should set a low price. Indeed, this is each firm’s more profitable alternative, regardless of what action its rival takes. To see this, let’s look at the payoffs in Table 9.2 from firm 1’s point of view. To find its best strategy, firm 1 asks a pair of “what if” questions about its rival. What if firm 2 were to charge a high price? Then, clearly, firm 1 does best by setting a low price, that is, undercutting. (A profit of 12 is superior to a profit of 10.) Alternatively, if firm 2 sets a low price, firm 1’s profit-maximizing response is to set a low price, that is, to match. (Here, 7 is better than 5.) Because the firms face symmetric payoffs, exactly the same logic applies to firm 2. In short, self-interest dictates that each firm set a low price; this is the better strategy for each, regardless of the action the other takes.

The upshot of both sides charging low prices is profits of 7 for each—lower than the profits (10 each) if they both charged high prices. Both would prefer the larger profits enjoyed under a high-price regime. Yet the play of self-interested

Firm 1 Firm 2 High Price Low Price

High Price 10,10 5,12

Low Price 12, 5 7, 7

TABLE 9.2

A Price War

Each firm’s optimal strategy is to set a low price.

strategies is driving them to low prices and low profits. One might ask, Why can’t the firms achieve the beneficial, high-price outcome? The answer is straightforward. To set a high price, anticipating that one’s rival will do likewise, is simply wishful thinking. Although high prices are collectively beneficial, this outcome is not an equilibrium. Either firm could (and presumably would) profitably undercut the other’s price. An initial high-price regime quickly gives way to low prices. As long as the firms act independently, the profit incentive drives down prices.

Before leaving this example, we make an additional point. The strategic behavior of rational firms can be expected to depend not only on the profit stakes as captured in the payoff table but also on the “rules” of the competition.8 In the present example, the rules have the firms making their price decisions independently. There is no opportunity for communication or collusion. (In fact, any kind of price collusion is illegal under U.S. antitrust laws.) We say that the firms behave noncooperatively. However, the “rules” would be quite different if the firms were the two largest members of an international cartel. Opportunities for communication and collusion would be freely available. Clearly, the firms would strive for a cooperative agreement that maintains high prices. However, it is worth remembering a lesson from Chapter 8’s analysis of cartels: A collusive agreement can facilitate a mutually beneficial, cooperative outcome, but it hardly guarantees it. Cartels are unstable precisely because of the individual incentives to cut price and cheat. Thus, even a collusive agreement is not ironclad.

CHECK STATION 3 In the price war, suppose that some consumers display a strong brand allegiance for one firm or the other. Consequently, any price difference between the duopolists is expected to produce a much smaller swing in the firms’ market shares. Specifically, suppose that if one firm charges a price of $6 and the other $8, the former sells 4 million units and the latter 2 million (instead of the original 6 million and 1.25 million sales). All other facts are as before. How does this change the payoffs in Table 9.2? What price should each firm set? Explain.

THE PRISONER’S DILEMMA So frequent are situations (like the preceding example) in which individual and collective interests are in conflict that they commonly are referred to as the prisoner’s dilemma. The origin of the term comes from a well-known story of two accomplices arrested for a crime. The police isolate each suspect in a room and ask each to confess and turn state’s evidence on the other in return for a shortened sentence. Table 9.3 shows the possible jail terms the suspects face. If the police can garner dual confessions,

8The example of price competition also serves as an introduction to game theory. Payoff tables, the rules of the game, and the analysis of optimal strategies are all topics taken up in greater depth in Chapter 10.

the suspects will be charged and convicted of a serious crime that carries a five-year sentence. Without confessions, convictions will be for much shorter jail terms.

Obviously, each suspect seeks to minimize time spent in jail. A careful look at Table 9.3 shows that each prisoner’s best strategy is to confess. (If his or her accomplice stays mum, confessing brings the shortest sentence, one year. If the partner confesses, so too must the suspect to avoid a maximum term.) Without the benefit of communication, there is no way for the partners to agree to stay mum. The individual incentive is for each to turn state’s evidence. By cleverly constructing the configuration of possible jail terms, the authorities can induce the suspects to make voluntary confessions, resulting in five-year prison terms.

Suspect 1 Suspect 2 Stay Mum Confess

Stay Mum 2 years, 2 years 8 years, 1 year

Confess 1 year, 8 years 5 years, 5 years

TABLE 9.3

The Prisoner’s Dilemma

Each suspect’s optimal strategy is to confess and turn state’s evidence on the other.

The prisoner’s dilemma should be viewed as a general model rather than as a special (perverse) case. Once one has the model in mind, it is easy to identify countless situations in which it applies:

• In the superpowers’ arms race, it is advantageous for one country to have a larger nuclear arsenal than its rival. But arms escalation by both sides improves neither side’s security (and probably worsens it). • A cartel has a collective interest in restricting output to earn a monopoly profit. At the same time, cartel members can increase their individual profits by cheating on the cartel, that is, exceeding their quotas. (Recall the discussion in Chapter 8.) • Abnormally cold winter temperatures bring the threat of a shortage of natural gas for heating buildings and homes. State and city officials urge residents to turn down their thermostats to conserve natural gas.

Unfortunately, the result is a negligible reduction in use. (Why should

I suffer low temperatures when my personal energy saving will have no discernible impact on the shortage?) • The utilization of public resources, most commonly natural resources, presents similar dilemmas. For instance, many countries fish the

Georges Bank in the North Atlantic. Each country’s fleet seeks to secure the greatest possible catch. But the simultaneous pursuit of maximum catches by all countries threatens depletion of the world’s richest fishing grounds. Similarly, firms in many industries generate air and water pollution as manufacturing by-products, and it is hardly in their self-interest to adopt costly pollution controls. Nonetheless, the collective, social benefit of reducing pollution may be well worth the cost. • The more widely antibiotics are prescribed, the more rapidly drugresistant microorganisms develop.

In each of these cases, there is a significant collective benefit from cooperation. However, the self-interest of individual decision makers leads to quite different, noncooperative, behavior. The key to overcoming the prisoner’s dilemma is to form an agreement that binds the parties to take the appropriate cooperative actions. To halt the arms race, the interested parties must bind themselves to a verifiable arms control treaty. Cartel members can agree to restrict output in order to maximize the collective profit of the cartel. A negotiated treaty on fishing quotas is one way to preserve Georges Bank. The American Medical Association has proposed guidelines calling for conservative practices in prescribing antibiotics. In the natural gas example, a binding agreement among consumers is impossible; rather, the way to encourage cuts in consumption is via higher natural gas prices.

CHECK STATION 4 In the prisoner’s dilemma example, suppose that a minimum sentencing law requires that a defendant entering into a plea bargain must serve a minimum of three years. What entries will this affect in Table 9.3? Explain why this law is likely to backfire in the present instance.

Attack on a Skater

On January 6, 1994, an unknown assailant attacked figure skater Nancy Kerrigan, injuring her right knee and preventing her from competing in the United States Olympic trials. Within days, the police and FBI followed a trail of clues left by the inept perpetrators. They subsequently arrested three men, one of whom was the former bodyguard of rival skater Tonya Harding. At first, Miss Harding and Jeff Gillooly (her former husband, with whom she was living) repeatedly denied any knowledge of the attack. However, after more than 10 hours of interviews with federal investigators, Miss Harding admitted that she learned of Gillooly’s involvement several days after the attack. When Gillooly later found out about Harding’s statement (she had repeatedly assured him she had not implicated him), he named her as a key figure in planning the attack.

In their own inimitable way, Harding and Gillooly entangled themselves in a classic prisoner’s dilemma: whether to hold out or implicate the other. Once again, the cliche that fact imitates theory seems to have been vindicated. Indeed, the case ended in dueling plea bargains. Gillooly pleaded guilty to one charge of racketeering, subject to a maximum jail term of two years, and was fined $100,000. Harding pleaded guilty to minor charges for which she received probation, paid a $100,000 fine, and was forced to withdraw from competitive skating. However, an earlier court injunction enabled her to compete in the Winter Olympics, where she finished eighth. Nancy Kerrigan, who was placed on the U.S. team, finished second and won the Olympic silver medal.

Would the pair have escaped prosecution if they had refused to implicate one another? To this question we probably will never know the answer.

BERTRAND PRICE COMPETITION An extreme case of price competition originally was suggested by Joseph Bertrand, a nineteenth-century French economist. Suppose duopolists produce an undifferentiated good at an identical (and constant) marginal cost, say $6 per unit. Each can charge whatever price it wishes, but consumers are very astute and always purchase solely from the firm giving the lower price. In other words, the lower-price firm gains the entire market, and the higher-price firm sells nothing.

To analyze this situation, suppose that each firm seeks to determine a price that maximizes its own profit while anticipating the price set by its rival. In other words, as in the previous example of quantity competition, we focus on equilibrium strategies for the firms. (The difference is that here the firms compete via prices, whereas previously they competed via quantities.) What are the firms’ equilibrium prices? A little reflection shows that the unique equilibrium is for each firm to set a price equal to marginal cost: P1 P2 $6. This may appear to be a surprising outcome. In equilibrium, P AC MC so that both firms earn zero economic profit. With the whole market on the line, as few as two firms compete the price down to the perfectly competitive, zero-profit level.

Why isn’t there an equilibrium in which firms charge higher prices and earn positive profits? If firms charged different prices, the higher-price firm (currently with zero sales) could profit by slightly undercutting the other firm’s price (thereby gaining the entire market). Thus, different prices cannot be in equilibrium. What if the firms were currently charging the same price and splitting the market equally? Now either firm could increase its profit by barely undercutting the price of the other—settling for a slightly smaller profit margin while doubling its market share. In summary, the possibilities for profitable price cutting are exhausted only when the firms already are charging P AC MC and earning zero profits.

The Bertrand model generates the extreme result that price competition, by as few as two firms, can yield a perfectly competitive outcome. It

When to Cut Price

should be emphasized that this result depends on two extreme assumptions— that (1) all competition is on the basis of price and (2) the lower-price firm always claims the entire market. We already have seen that quantity competition leads to quite a different outcome. Furthermore, even if price is the most important competitive dimension, market shares are unlikely to be all or nothing.9 In models with some degree of product differentiation, competition leads to price reductions, but equilibrium prices remain above the perfectly competitive level.

Pricing has been a focus of attention throughout the first half of this book. Let’s step back for a minute and take stock of the factors that dictate changes in pricing strategy, in particular, that call for price cuts.

Changes in Market Demand. The surest rationale for a cut in price is an adverse shift in demand. As we’ve seen, facing a less favorable demand curve means setting a lower optimal sales target and a lower price. Amid a fall in demand because of a growing recognition of health risks, tanning salons have responded by cutting prices. Seeing buyer demand sapped by the ongoing US recession, Saks Fifth Avenue broke ranks with other upscale retailers by sharply discounting its prices at the start of the 2008 holiday buying season.

Market Skimming. This strategy of price discriminating over time means setting a high price to pioneer adopters (who have relatively inelastic demand), then later lowering the price to attract mass-market users (whose demand is more elastic). Apple’s iphone and ipad both saw significant price discounts during their first years on the market.

The Learning Curve. As a firm gains cumulative experience producing a new product, it can expect to reduce its cost per unit by reengineering and improving the production process. Lower unit costs support lower prices. More important, it pays for the firm to cut a product’s price at the outset in order to induce a “virtuous circle” of profitability. The initial price cut spurs sales and production levels, speeding the learning process, thereby accelerating cost efficiencies and, in turn, supporting further price reductions—with additional profit accruing to the firm at each stage. Strong learning curve effects have been documented for a range of assembly-line products: from aircraft to laptops to photocopiers.

9A good example of the Bertrand model is the case of competitive bidding. Here, the firm that submits the lowest bid price gains the exclusive award of a supply contract. Competitive bidding is taken up in Chapter 16.

Strategic Price Cuts. Increased competition from competitors—whether in the form of advertising, quality improvements, or aggressive pricing—can be expected to have an adverse effect on the firm’s demand and, therefore, might call for price cuts in response. For instance, Neiman Marcus Group, Gucci, Hermes, and several top fashion houses were compelled (albeit belatedly) to follow Saks’s price discounting strategy. Major airlines routinely meet the challenge of a rival introducing additional flights along its routes by offering fare discounts.

Boosting Sales of Related Products. When a firm sells complementary products, cutting the price of one spurs the demand for another, and more importantly, is the path to maximizing the firm’s total profit. Gillette is happy to give away its multiblade razors at minimal cost because the company generates its real profit by selling packs of replacement blades at a price upward of $2 per blade. As long as a consumer is locked into his favorite shaver, the money from blade purchases will keep on coming. Microsoft has long underpriced its Windows operating system because that platform generates significant demand for its applications software such as Microsoft Office. Google generates so much revenue (some $30 billion in 2010) from Internet advertising that it makes sense to tie consumers to Google by giving away free such key online features as e-mail, Google Maps, and its Chrome browser.

The Kindle Once Again. As we saw in Chapter 3, since introducing the Kindle in 2007, Amazon has repeatedly cut its price—from $399 to $259 to $189 to $159. Each of the factors listed above has a bearing on this pricing strategy. A skimming strategy certainly makes sense—setting high prices to hard-core egadget aficionados and subsequently lowering prices to enlist the less sophisticated mass market of buyers. So too has there been a steep learning curve, lowering the production cost of the Kindle over time.

Moreover, as noted in Chapter 6, Amazon has an obvious incentive to lower the Kindle’s sale price in order to boost the lucrative tied sales of its ebooks. Additional e-book sales translate directly into greater total profit. Cutting price is also a logical competitive response. Facing increased price competition from Barnes & Noble’s Nook reader and the threat of losing users to Apple’s multipurpose iPad, Amazon’s Kindle price cuts make sense as a profit-maximizing countermove. Of course, a less charitable interpretation suggests that Amazon might be on the verge of becoming ensnared in a destructive price war. Finally, some book publishers have claimed that Amazon CEO Jeff Bezos’s real goal is to obliterate the hardcover book market altogether and, simultaneously dominate the emerging e-book market. Such an extreme strategy could mean selling the Kindle at a loss and might be far from optimal. In other words, this last price-cutting explanation owes more to psychologically driven (perhaps irrational) behavior than to profit maximization.