Microdynamics • 235

Real options arise in a variety of business settings.13 In the mid-1990s, AnheuserBusch purchased minority interests in brewers in several developing nations, including Mexico’s Grupo Modelo and Asia Brewery in the Philippines. By taking small stakes in these companies, Anheuser-Busch was able to learn about different markets and identify those that merited larger investments. This was a more profitable strategy than immediate, large-scale investment. Economists Tom Arnold and Richard Shockley estimated that modest investments of a few million dollars in each brewery had real options value of hundreds of millions of dollars.

Also taking advantage of real options, Airbus and Boeing offer airlines the option of canceling or downsizing orders. Airlines exercise these options when the demand for air travel falls, as it typically does during economic downturns. Airbus and Boeing use the option valuation formula to determine the extra benefit that this flexibility provides to their customers and adjusts the pricing accordingly. As a final example, Hewlett-Packard (HP) customizes some of its products (e.g., ink-jet printers) to particular foreign markets. Traditionally, it would customize the product at the factory and ship it in finished form to individual foreign markets. This was a risky strategy because demand in foreign markets was difficult to predict, and HP often guessed wrong and ended up shipping too many or too few printers. HP now ships partially assembled printers to large overseas warehouses and then customizes the printers for different markets once it has definite orders for them. This increases HP’s production costs, but it allows the company to tailor the quantities of different printer models to demand conditions in different markets.

The HP example illustrates two important points. First, firms can often create real options by altering the way in which they configure their internal processes. This implies that a key managerial skill is spotting the potential to create value-enhancing real options. Second, real options often do not come for free; they typically involve trade-offs. In the case of HP, the company traded higher production costs for the added flexibility that came from delaying the customization of printers until it gained more definitive demand information in its individual markets.

Another implication of real options is that the timing of a firm’s investments should depend on the degree of uncertainty about future business conditions. By delaying investment decisions, firms postpone any of the benefits of the investment, but they also learn valuable information that can be used to modify the investment. When conditions are volatile, there is more to learn, suggesting that firms should postpone investments when business conditions become more uncertain. Economists have developed formulas for the optimal timing of investments under dynamic uncertainty.14 Ryan Kellogg studied investment decisions by oil companies and found that these formulas do an excellent job of predicting the timing of drilling of new oil wells.15

Competitive Discipline

The Cournot, Bertrand, and Stackelberg models characterize different situations with regard to the competitive variables (e.g., quantity versus price) and the timing of competitive choices. Despite these differences, the models have one thing in common: total industry profits are less than what could be achieved if the firms acted like a cartel, choosing the monopoly price and output. Few if any industries act like cartels, either explicitly or implicitly. This raises two fundamental questions:

1.Why do firms seemingly act against their mutual best interests?

2.Under what circumstances can firms minimize the harmful effects of competition?

236 • Chapter 7 • Dynamics: Competing Across Time

Dynamic Pricing Rivalry and Tit-for-Tat Pricing

The starting point for our analysis is the premise that, all else being equal, firms would prefer prices to be as close as possible to monopoly levels. Antitrust laws prohibit open coordination of market prices and quantities, and the penalties for collusion are severe. This means that if managers are to maintain high prices, they must do so unilaterally. In this section we explore conditions under which firms might unilaterally arrive at prices that approach collusive levels. (Alternatively, we explore the reasons why it is difficult for unilateral actors to achieve collusive pricing.)

We learned from the Bertrand model that if prices exceed marginal costs there is a strong temptation for each firm to “cheat” by lowering price and grabbing market share. But remember that the Bertrand model is static: firms do not believe that their rivals will respond to price reductions. This is not a very realistic assumption. The economist Edward Chamberlin argued that sellers recognize that the profit they gain from cutting price below the monopoly level is likely to be fleeting:

If each seeks his maximum profit rationally and intelligently, he will realize that when there are two or only a few sellers his own move has a considerable effect upon his competitors, and that this makes it idle to suppose that they will accept without retaliation the losses he forces upon them.

Since the result of a cut by any one is inevitably to decrease his own profits, no one will cut, and although the sellers are entirely independent, the equilibrium result is the same as though there were a monopolistic agreement between them.16

To better understand Chamberlin’s argument, suppose that Shell and Exxon Mobil are the only two sellers of a commodity chemical. They currently charge a price somewhere between the Bertrand price of $20 and the monopoly price of $60, say $40 per hundred pounds. Suppose that Shell is under pressure from shareholders to boost profits and is considering raising its price to the monopoly level of $60. You might think that it would be foolish for Shell to raise its price to $60. After all, if Exxon Mobil keeps its price at $40 it will capture 100 percent of the market and earn $12 million per year, which exceeds the $8 million annual profit it would get by following Shell’s lead and charging $60.

But suppose that prices can be changed every week, so that Shell can rescind its price increase without suffering too much loss in profits. In this case, Shell’s decision to raise price carries little risk. If Exxon Mobil refuses to follow, Shell can drop its price back to $40 after one week. At most, Shell sacrifices one week’s profit at current prices (roughly $115,400 or $0.1154 million). Not only is the risk to Shell low from raising its price, but if Shell puts itself in Exxon Mobil’s position, it would see that Exxon Mobil has a compelling motive to follow Shell’s price increase.

To see why, suppose that both firms use a 10 percent annual rate to discount future profits. On a weekly basis, this corresponds roughly to a discount rate of 0.2 percent (i.e., 0.002).17 Shell reasons as follows:

•Exxon Mobil should anticipate that we will drop our price back down to $40 after the first week if it does not match our price increase. By keeping its price at $40, Exxon Mobil will get a one-week “bump” in profit from $0.1154 million to $0.2307 million per week ($0.2307 5 12/52). However, after we rescind our price increase, Exxon Mobil’s weekly profit would go back to $0.1154 million. The discounted present value of Exxon Mobil’s

weekly profit (expressed in millions of dollars) under this scenario would be 0.2308 1

0.1154/(1.002) 1 0.1154/(1.002)2 1 0.1154/(1.002)3 1 . . ., which equals $57.93 million.18

238 • Chapter 7 • Dynamics: Competing Across Time

•If Exxon Mobil follows us and raises its price to $60, we each will earn annual profits of $8 million, which translates into a weekly profit of $153,846 or $0.1538 million. By follow-

ing our price increase, the discounted value of Exxon Mobil’s weekly profit is 0.1538 1

0.1538/(1.002) 1 0.1538/(1.002)2 1 0.1538/(1.002)3 1 . . ., which equals $77.05 million. Clearly, Exxon Mobil is better off following our lead, even though for the first week it would be better off if it refused to raise its price to $60.

Because Exxon Mobil has much to gain by matching Shell’s price and Shell loses little if Exxon Mobil does not match, it makes sense for Shell to raise its price to $60. If Exxon Mobil behaves rationally, then it will behave the way Shell expects it to behave (as described by the preceding reasoning), and Exxon Mobil will match Shell’s price increase. A simple calculation reveals that the monopoly price is sustainable as long as Exxon Mobil’s weekly discount rate is less than 50 percent, which corresponds to an annual discount rate of 2,600 percent! The same logic can be extended to an arbitrary number of firms and to pricing periods of arbitrary lengths (e.g., one month, one quarter, or one year). As long as the number of firms is not too large and the length of time it takes for firms to respond to each other’s prices is not too long, it makes sense for firms to adopt a strategy of always matching each other’s prices. Once a market “leader” sets the collusive price, the others will follow. But if a firm tries to lower its price, others must match it in order to deter such disruptive business stealing. This is known as tit-for-tat pricing.

Why Is Tit-for-Tat So Compelling?

Tit-for-tat is not the only strategy that allows firms to sustain monopoly pricing as a noncooperative equilibrium. Another strategy that, like tit-for-tat, results in the monopoly price for sufficiently low discount rates is the “grim trigger” strategy:

Starting this period, we will charge the monopoly price PM. In each subsequent period, if any firm deviates from PM, we will drop our price to marginal cost in the next period and keep it there forever.

The grim trigger strategy relies on the threat of an infinite price war to keep firms from undercutting their competitors’ prices. In light of other potentially effective strategies, such as grim trigger, why would we necessarily expect firms to adopt a tit- for-tat strategy? One reason is that tit-for-tat is a simple, easy to describe, and easy to understand strategy. Through announcements such as “We will not be undersold” or “We will match our competitors’ prices, no matter how low,” a firm can easily signal to its rivals that it is following tit-for-tat.

Another reason for firms to choose a tit-for-tat strategy is that they probably do well over the long run against a variety of different strategies. A compelling illustration of this is discussed by Robert Axelrod in his book The Evolution of Cooperation.20 Axelrod conducted a computer tournament in which entrants were invited to submit strategies for playing a (finitely) repeated prisoners’ dilemma game. Each of the submitted strategies was pitted against every other, and the winner was the strategy that accumulated the highest overall score in all of its “matches.” Even though tit-for-tat can never beat another strategy in one-on-one competition (at best it can tie another strategy), it accumulated the highest overall score. It was able to do so, according to Axelrod, because it combines the properties of “niceness,” “provocability,” and “forgiveness.” It is nice in that it is never the first to defect from the cooperative outcome. It is provocable in that it immediately punishes a rival that defects