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Our analysis of the game tree is now complete. N will select Pm in the first stage. E will select “In.” Second-year competition will be Cournot. This outcome is shown by the heavy solid line in Figure 6.3.
According to this analysis, limit pricing fails because the incumbent’s pre-entry pricing does not influence the entrant’s expectations about postentry competition. It seems that the intuitive appeal of limit pricing has run up against the cold hard logic of the game tree. It turns out that there is one additional ingredient that bolsters the intuitive justification but is not captured by the game tree. That ingredient is asymmetric knowledge about industry conditions. To understand the importance of such asymmetries, it is helpful to first discuss another entry-deterring strategy for which simplified economic models and intuition sometimes diverge.
Predatory Pricing
Predatory pricing occurs when a large incumbent sets a low price to drive smaller rivals from the market. The purpose of predatory pricing is twofold: to drive out current rivals and to make future rivals think twice about entry. The second purpose is reminiscent of the goal of limit pricing. Predatory pricing causes rivals to rethink the potential for postentry profits, while the predatory incumbent expects that whatever losses it incurs while driving competitors from the market can be made up later through future monopoly profits.14
The Chain-Store Paradox
The idea that an incumbent should slash prices to drive out rivals and deter entry is highly intuitive. Yet a relatively simple example reveals a potential flaw in the argument. Imagine that a rational incumbent firm operates in 12 markets and faces entry in each. In January, it faces entry in market 1; in February, it faces entry in market 2; and so on. Should the incumbent slash prices in January so as to deter entry later in the year?
We can answer this question by working backwards from December to see how earlier pricing decisions affect later entry. The most important thing to note is that regardless of what has occurred in prior months, the incumbent will not benefit from predatory pricing in December. By this time, there is no further entry to deter and therefore no reason for the incumbent to continue slashing prices. The entrant in the twelfth market knows this and should enter regardless of previous price cuts. Now let us back up to November. The forward-looking incumbent knows that it cannot deter entry in December and therefore concludes that it cannot benefit from slashing prices in November. The potential November entrant can figure this out too and so enters without fear of retaliation. In this way, the problem completely unravels, so that the incumbent realizes that it has nothing to gain from predatory pricing in January! The striking conclusion: in a world with a finite time horizon in which entrants can accurately predict the future course of pricing, we should not observe predatory pricing. Just like limit pricing, predation seems to be an irrational strategy. This idea is astonishing but does have some empirical support, as we describe in Example 6.5.
The apparent failure of the intuition supporting predatory pricing strategies has given rise to a puzzle in economics known as the chain-store paradox.15 The paradox is that many firms appear to engage in predatory pricing, despite the theoretical conclusion that the strategy is irrational. Standard Oil, whose pricing policies in the nineteenth century drove rivals into bankruptcy, is a quintessential example. Rivals of Wal-Mart have occasionally accused it of predatory pricing. In 2003, the German
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Supreme Court agreed with a lower court ruling that Wal-Mart’s low prices undermined competition and ordered Wal-Mart to raise its prices; the retailer subsequently sold its German stores and stopped doing business there. Wal-Mart has never lost such a predatory pricing challenge in the United States but has settled at least two cases out of court.
Rescuing Limit Pricing and Predation: The Importance of Uncertainty and Reputation
The economic theories presented above suggest that limit pricing and predatory pricing are irrational strategies, yet firms continue to pursue them. One possible explanation is that firms set prices irrationally. If this explanation is correct, then this analysis should warn firms that set low prices to deter entry: Don’t do it! We doubt that many firms will consistently pursue irrational strategies, especially firms like Wal-Mart that have ample opportunity to correct their “mistakes.” This leaves two other possible explanations: the theories are wrong, or they are incomplete. We don’t believe the theories are wrong—the internal logic is undeniable. But they are almost certainly incomplete, as they require many simplifying assumptions that can artificially drive the results. By lending richness to the chain-store paradox and other models, game theorists have added important nuances to the theories, helping to reconcile the apparent inconsistencies between theory and fact.
Game theorists have shown that predatory actions may be profitable if entrants are uncertain about market conditions. To illustrate the importance of uncertainty, we will revisit the limit-pricing game. The argument against the incumbent’s limit-pricing strategy goes something like this:
If the entrant is certain that the low pre-entry price is due to a limit-pricing strategy, then it has every reason to believe that the incumbent will come to its senses after entry and allow prices to increase. As far as the entrant is concerned, limit pricing is like a sunk cost and can have no bearing on future pricing. If the incumbent wants to sacrifice profits prior to entry, that is the incumbent’s problem.
This argument presumes that the entrant knows with certainty why the incumbent has set a low pre-entry price. But suppose that the entrant is uncertain about the reasons behind the incumbent’s pricing strategy. For example, the entrant might not be certain whether market demand is “meeting expectations” or is “below expectations.” Or it might be uncertain whether the incumbent has “typical costs” or “low costs.” If market demand is low, or the incumbent has low costs, then it might be sensible for the incumbent to set a low price without regard to strategic considerations. And if the incumbent has low cost or if demand is below expectations, the entrant might prefer staying out of the market. It may even be possible that the incumbent is trying to maximize sales rather than profits. This would again cause the incumbent to set a low price.
All of this uncertainty allows us to rescue limit pricing. Suppose that market demand meets expectations and that the incumbent has a typical cost structure and is trying to maximize profits, but the entrant does not know this. By setting a low price, the incumbent may persuade the entrant that demand is low, that its costs are low, or even that it does not care about profits. This might be enough to keep the entrant out of the market. Remember, this approach only works if the entrant is uncertain about the market demand, the incumbent’s costs, or the incumbent’s motivations. Without such uncertainty, limit pricing falls victim to the theoretical arguments discussed previously.
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EXAMPLE 6.5 PREDATORY PRICING IN THE LABORATORY
Predatory pricing is a violation of antitrust laws in most developed nations. Yet there have been very few successful prosecutions for predatory pricing, and most antitrust economists doubt that it happens very often in practice. One reason is that it is difficult, in practice, to distinguish between low prices designed to boost the market shares of efficient firms from abnormally low prices designed to drive rivals from the market. The former is an acceptable business practice that no court would want to outlaw. The rival seems unacceptable but may have no practical impact on consumers if new rivals emerge. Thus, the courts may be hesitant to block any price reductions, regardless of apparent intent.
Economists have wondered whether it is possible to generate true predatory pricing even under laboratory conditions. The relatively new field of experimental economics provides an opportunity to find out. Experimental economists conduct small-scale simulations of business situations, frequently enlisting the participation of undergraduate and graduate students. One of the first important simulations involves participants who “play” a repeated prisoners’ dilemma, with cash awards determined by which game cell is played. In the past two decades, the experiments have become more sophisticated, with several experiments exploring predatory pricing.
Mark Isaac and Vernon Smith published the results of the first predatory pricing experiment in 1985.16 Here was the setup. Two participants competed in a market where they would sell up to a total of 10 units. Each player was “endowed” by Isaac and Smith with a cost function displaying increasing marginal costs. The players named their own prices and the maximum amount they were willing to sell at that price. A player who sold one or more units at a price that exceeded the cost got to keep the profits. Lastly, players had to sell at least one unit in a period to earn the right to play the game again.
Isaac and Smith made sure that one player had lower costs than the other. The low-cost player could drive the rival from the market by offering to sell all 10 units at a price that was below its own marginal cost of selling its last unit, but also below the rival’s cost of selling its first unit. This would be a prime example of predatory pricing. Isaac and Smith repeated this experiment with dozens of participants. The lower-cost player never set a predatory price. This explains the title of Isaac and Smith’s paper, “In Search of Predatory Pricing.”
Other experimental economists pointed out that the high-cost rival in Isaac and Smith’s experiment had no opportunity to make money if it exited the market. This might give the rival a strong incentive to match the low-cost player’s predatory pricing, even if it meant losing money in the short run. This, in turn, might have discouraged the low-cost player from preying. Economists modified Isaac and Smith’s setup to allow high-cost rivals to make money in other markets. In these experiments, lowcost players often did set predatory prices. Other economists have modified Isaac and Smith’s experiment by allowing for a series of potential entrants, so that even if the low-cost player drives one rival from the market, it will face future potential rivals. Once again, this seems to encourage low-cost players to set predatory prices.
It is now commonly accepted that predatory pricing occurs in laboratory settings. Does this imply that predation occurs in the real world? It certainly suggests that relative novices can figure out the potential benefits of predation and are willing to take short-run losses provided they are playing with someone else’s money. As with the entire field of experimental economics and similar studies of tit-for-tat strategies, price discrimination, commitment, and other game theoretic situations, there is considerable debate as to what this implies for experienced strategists making real-world decisions that involve millions of their own dollars.
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A little bit of uncertainty can also increase the effectiveness of predatory pricing. Predatory pricing appears to be irrational because all of the entrants can perfectly predict incumbent behavior. But suppose that the last entrant is uncertain about whether the incumbent would actually maintain low prices after entry. As with limit pricing, this could stem from uncertainty about market demand, the incumbent’s costs, or the incumbent’s objectives. Incumbents can exploit this uncertainty by slashing prices, thereby establishing a reputation for toughness. In an experiment, Yun Joo Jung, John Kagel, and Dan Levin found that when students playing a predation game were unsure about the incumbent’s tendencies, incumbents did slash prices to deter entry.17
The chain-store paradox not only sheds light on the role of uncertainty; it also reminds us of the importance of asymmetry. In our analysis, it is reputation, not incumbency per se, that matters. An entrant might come into the market and slash prices. An incumbent that is uncertain about the entrant’s costs or motives may elect to exit, rather than try to ride out the price war.
Wars of Attrition
Price wars harm all firms in the market regardless of who starts them, and are quintessential examples of wars of attrition. In a war of attrition, two or more parties expend resources battling with each other. Eventually, the survivor claims its reward, while the loser gets nothing and regrets ever participating in the war. If the war lasts long enough, even the winner may be worse off than when the war began because the resources it expended to win the war may exceed its ultimate reward. An interesting example of price wars is provided by online penny auctions. In these auctions, bidders bid for items such as consumer electronics, clothing, and even cash awards. The high bidder claims the item, but all bidders must pay their bid. Under these rules, every bidder has an incentive to raise his or her bid above the prevailing high bid, even if the high bid exceeds the value of the item being auctioned. (For example, suppose that the item being auctioned is worth $200. It is better to win the item at a bid of, say, $220, than to submit a losing bid of $180.)
Besides price wars, many other types of interactions are wars of attrition. The U.S./Soviet nuclear arms buildup between 1945 and the late 1980s is a classic example. Both countries spent huge sums to increase their nuclear arsenals, each hoping that the other country would be the first to make concessions. Eventually, the Soviet Union fell apart, and Russia acknowledged that it could not afford to carry on the buildup.
Firms that are engaged in a price war should do all they can to convince their rivals that they have no intention of dropping out, so as to hasten their rivals’ exit. Firms might even claim that they are making money during the price war, or that they care more about winning the war than they do about profits. (An analogy in the arms race is Ronald Reagan’s pronouncement that the United States could survive and win a nuclear war.)
Asymmetries can profoundly influence the outcome of a price war. Suppose that two firms are engaged in a price war and one of the firms has made sunk commitments to workers and other input suppliers. The other firm may as well give up. A firm that has made sunk commitments has low incremental costs of remaining in the market. Any rival who persists in fighting the price war should expect a long battle that is probably not worth fighting.