As emphasized in the introduction, the “fewness of firms” in oligopoly markets causes each firm’s demand and marginal revenue conditions, and hence each firm’s profits, to depend on the pricing decisions, output decisions, expansion
Now try Technical Problem 1.
decisions, and so forth, of every rival firm in an oligopoly market. The resulting interdependence and strategic behavior make decisions much more complicated and uncertain. To make the best decisions they can when every firm is trying to anticipate the decisions of every other firm, managers must learn to think strategically.
Perhaps you are thinking, “Sure, interdependence complicates decision making and makes it messy. So what do I as a manager do in such situations? How do I go about making strategic decisions?” We can’t give you a set of rules to follow. The art of making strategic decisions is learned from experience.
We can, however, introduce you to a tool for thinking about strategic deci- sion making: game theory. Game theory provides a useful guideline on how to behave in strategic situations involving interdependence. This theory was developed more than 50 years ago to provide a systematic approach to stra- tegic decision making. During the past 25 years, it has become increasingly important to economists for analyzing oligopoly behavior. It is also becoming more useful to managers in making business decisions. Unfortunately, learning the principles of game theory will not guarantee that you will always “win”
or make greater profit than your rivals. In the real world of business decision making, your rival managers will also be strategic thinkers who will try to pre- dict your actions, and they will try to counteract your strategic decisions. And, to make winning even less certain, many unpredictable, and even unknown, events are frequently just as important as strategic thinking in determining final outcomes in business. Game theory can only provide you with some gen- eral principles or guidelines to follow in strategic situations like those that oli- gopoly managers face.
You might think of the word game as meaning something fun or entertain- ing to do, but managers may or may not find it fun to play the strategic games that arise in oligopoly. To game theorists—economists who specialize in the study of strategic behavior—a game is any decision-making situation in which people compete with each other for the purpose of gaining the greatest indi- vidual payoff, rather than group payoff, from playing the game. In the game of oligopoly, the people in the game, often called “players,” are the managers of the oligopoly firms. Payoffs in the oligopoly game are the individual profits earned by each firm.
In this section, we will introduce you to strategic thinking by illustrating some of the fundamental principles of strategic decision making that can help you make better decisions in one of the more common kinds of strategic situations managers face: making simultaneous decisions about prices, production, advertis- ing levels, product styles, quality, and so on. Simultaneous decision games oc- cur in oligopoly markets when managers must make their individual decisions without knowing the decisions of their rivals. Simultaneous decision games can arise when managers make decisions at precisely the same time without knowl- edge of their rivals’ decisions. However, decisions don’t have to take place at the same time to be “simultaneous”; it is only necessary for managers not to know
game theory An analytical guide or tool for making decisions in situations involving interdependence.
game
Any decision-making situation in which people compete with each other for the purpose of gain- ing the greatest individu- al payoff.
simultaneous decision games
A situation in which competing firms must make their individual decisions without knowing the decisions of their rivals.
I L L U S T R AT I O N 1 3 . 1 How Can Game Theory Be Used in Business
Decision Making?
Answers from a Manager
“Game theory is hot . . . it’s been used to analyze everything from the baseball strike to auctions at the FCC.” So began an article in The Wall Street Journal by F. William Barnett.a
Barnett points out that game theory helps managers pay attention to interactions with competitors, custom- ers, and suppliers and focus on how near-term actions promote long-term interests by influencing what the players do. After describing a version of the prisoners’
dilemma game, he notes that an equilibrium (such as the one we show in cell D of Table 13.1) is unattractive to all players.
Some rules of the road: Examine the number, concentration, and size distribution of the players.
For example, industries with four or fewer players have the greatest potential for game theory, because (1) the competitors are large enough to benefit more from an improvement in general industry condi- tions than they would from improving their posi- tion at the expense of others (making the pie bigger rather than getting a bigger share of a smaller pie) and (2) with fewer competitors it is possible to think through the different combinations of moves and countermoves.
Keep an eye out for strategies inherent in your mar- ket share. Small players can take advantage of larger companies, which are more concerned with maintain- ing the status quo. Barnett’s example: Kiwi Airlines,
with a small share of the market, was able to cut fares by up to 75 percent between Atlanta and Newark without a significant response from Delta and Conti- nental. But, he notes, large players can create econo- mies of scale or scope, such as frequent-flier programs, that are unattractive to small airlines.
Understand the nature of the buying decision. For example, if there are only a few deals in an industry each year, it is very hard to avoid aggressive compe- tition. Scrutinize your competitors’ cost and revenue structures. If competitors have a high proportion of fixed-to-variable cost, they will probably behave more aggressively than those whose production costs are more variable.
Examine the similarity of firms. When competi- tors have similar cost and revenue structures, they often behave similarly. The challenge is to find prices that create the largest markets, then use non- price competition—distribution and service. Finally, analyze the nature of demand. The best chances to create value with less aggressive strategies are in markets with stable or moderately growing demand.
Barnett concludes, “Sometimes [game theory] can increase the size of the pie. But for those who mis- understand [the] fundamentals of their industry, game theory is better left to the theorists.” As we said earlier, strategic decision making is best learned from experience.
aF. William Barnett, “Making Game Theory Work in Practice,” The Wall Street Journal, February 13, 1995.
what their rivals have decided to do when they make their own decisions. If you have information about what your rival has chosen to do before you make your decision, then you are in a sequential decision-making game, which we will discuss in the next section of this chapter.
Making decisions without the benefit of knowing what their rivals have de- cided is, as you might suspect, a rather common, and unpleasant, situation for managers. For example, to meet publishers’ deadlines, two competing clothing retailers must decide by Friday, July 1, whether to run expensive full-page ads in
local papers for the purpose of notifying buyers of their Fourth of July sales that begin on Monday. Both managers would rather save the expense of advertising because they know buyers expect both stores to have holiday sales and will shop at both stores on the Fourth of July even if no ads are run by either store.
Unless they tell each other—or receive a tipoff from someone working at the newspaper—neither manager will know whether the other has placed an ad until Monday morning, long after they have made their “simultaneous” decisions. As we mentioned earlier, making decisions without knowing what rivals are going to do is quite a common situation for managers. Any of the strategic decisions described at the beginning of this chapter could be a simultaneous decision game.
To introduce you to the concept of oligopoly games, we begin with the grand- father of most economic games. While it doesn’t involve oligopoly behavior at all, it is a widely known and widely studied game of simultaneous decision making that captures many of the essential elements of oligopoly decision making. This famous game is known as the prisoners’ dilemma.
The Prisoners’ Dilemma
The model of the prisoners’ dilemma is best illustrated by the story for which it is named. Suppose that a serious crime—say, grand-theft auto—is committed and two suspects, Bill and Jane, are apprehended and questioned by the police.
The suspects know that the police do not have enough evidence to make the charges stick unless one of them confesses. If neither suspect confesses to the se- rious charges, then the police can only convict the suspects on much less seri- ous charges—perhaps, felony vandalism. So the police separate Bill and Jane and make each one an offer that is known to the other. The offer is this: If one suspect confesses to the crime and testifies in court against the other, the one who con- fesses will receive only a 1-year sentence, while the other (who does not confess) will get 12 years. If both prisoners confess, each receives a 6-year sentence. If nei- ther confesses, both receive 2-year sentences on the minor charges. Thus Bill and Jane each could receive 1 year, 2 years, 6 years, or 12 years, depending on what the other does.
Table 13.1 shows the four possibilities in a table called a payoff table. A payoff table is a table showing, for every possible combination of actions that players can make, the outcomes or “payoffs” for each player. Each of the four cells in
Now try Technical Problem 2.
payoff table
A table showing, for every possible combination of decisions players can make, the outcomes or
“payoffs” for each of the players in each decision combination.
T A B L E 13.1
The Prisoners’ Dilemma:
A Dominant Strategy Equilibrium
Bill
Don’t confess Confess
A B
Don’t confess 2 years,2 years 12 years,1 year
Jane C D
Confess 1 year,12 years 6 years,6 years
Table 13.1 represents the outcome of one of the four possible combinations of actions that could be taken by Bill and Jane. For example, cells A and D in the payoff table show the payoffs for Bill and Jane if both do not confess or do confess, respectively. Cells B and C show the consequences if one confesses and the other does not. In each cell, the years spent in prison for each one of the two suspects is listed as a pair of numbers separated by a comma. The first number, shown in bold face, gives Jane’s prison sentence, and the second number, shown in italics, gives Bill’s prison sentence.1 Both suspects know the payoff table in Table 13.1, and they both know that the other one knows the payoff table. This common knowledge of the payoff table plays a crucial role in determining the outcome of a simultane- ous decision game. What the suspects don’t know, since their decisions are made simultaneously, is what the other has decided to do.
The police have designed the situation so that both Bill and Jane will be in- duced to confess and both will end up in cell D (excuse the pun). To see this, put yourself into Bill’s head and imagine what he must be thinking. Bill knows that Jane must decide between the two actions “confess” and “don’t confess.” If Jane does not confess (“bless her heart”), Bill receives a lighter sentence by confessing (“sorry Jane, I promise I’ll visit you often”). If Jane confesses (“Jane, you dirty rat”), Bill still receives a lighter sentence by confessing: 6 years compared with 12.
Therefore, confessing is always better than not confessing for Bill (“Sorry Jane, what did you expect me to do?”)—it gives Bill a lighter sentence no matter what Jane does. The only rational thing for Bill to do is confess. The police, of course, counted on Bill thinking rationally, so they are not surprised when he confesses.
And they also expect Jane to confess for precisely the same reason: Confessing is the best action Jane can take, no matter what action she predicts Bill will take. So both Bill and Jane will probably confess and end up with sentences of 6 years each.
The prisoners’ dilemma illustrates a way of predicting the likely outcome of a strategic game using the concept of a dominant strategy. In game theory a dominant strategy is a strategy or action that provides the best outcome no matter what de- cisions rivals decide to make. In the prisoners’ dilemma, confessing is a dominant strategy for each suspect. Naturally, rational decision makers should always take the action associated with a dominant strategy, if they have one. This establishes the following principle for strategic decision making.
Principle When a dominant strategy exists—an action that always provides a manager with the best outcome no matter what action the manager’s rivals choose to take—a rational decision maker always chooses to follow its own dominant strategy and predicts that if its rivals have dominant strategies, they also will choose to follow their dominant strategies.
Finding dominant strategies, especially in larger payoff tables, can sometimes be difficult. A useful method for finding dominant strategies can be easily illustrated using the payoff table for the prisoners’ dilemma in Table 13.1. Let’s
common knowledge A situation in which all decision makers know the payoff table, and they believe all other decision makers also know the payoff table.
dominant strategy A strategy or action that always provides the best outcome no matter what decisions rivals make.
1Throughout this chapter, we will follow the convention of listing payoffs to players in each cell of a payoff table as payoff to row player, payoff to column player.
begin with Jane: For each column (i.e., for each decision Bill could make), find the cell that gives Jane her best payoff and pencil a “J” in that cell. Following this procedure for this game, you will mark two J’s: one in cell C and one in cell D.
Now repeat this process for Bill: For each row (i.e., for each decision Jane could make), find the cell that gives Bill’s best payoff and pencil a “B” in that cell. Fol- lowing this procedure, you will mark two B’s: one in cell B and one in cell D.
Since all J’s line up in one row, that row (Confess) is a dominant strategy for Jane. Similarly, Bill possesses a dominant strategy because all B’s line up in one column (Confess).
As you can now see, it is easy, once dominant strategies are discovered, to pre- dict the likely outcome of games in which both players have dominant strategies.
Game theorists call such an outcome a dominant-strategy equilibrium. When both players have dominant strategies, the outcome of the game can be predicted with a high degree of confidence. The compelling nature of a dominant-strategy equilibrium results from the fact that, when all decision makers have dominant strategies (and know their dominant strategies), managers will be able to predict the actions of their rivals with a great deal of certainty.
An important characteristic of the prisoners’ dilemma, and one that makes it valuable for understanding oligopoly outcomes, is that cooperation is un- likely to occur because there is an incentive to cheat. To see this, suppose that, before committing their crime, Bill and Jane make a promise to each other that they will never confess to their crime. Once again let’s get into Bill’s head to see what he is thinking. Suppose Bill predicts that Jane will keep her promise not to confess (“Jane loves me; she would never break her promise to me”). He then has an incentive to cheat on his promise because he can get out of jail in just one year instead of two years by confessing (“Oh Jane, come on; I promise I’ll wait for you”). Alternatively, if you think that it’s farfetched for Bill to trust Jane (“Jane never loved me the way I loved her”), then suppose Bill predicts Jane will confess. Now his best decision, when he predicts Jane will cheat by confessing, is also to cheat and confess. Without some method of forcing each other to keep their promises not to confess, Bill and Jane will probably both cheat by confessing.
Despite the fact that both suspects choose dominant strategies that are best for them no matter what the other suspect chooses to do, they end up in a cell (cell D) where they are both worse off than if they had cooperated by not confessing. This paradoxical outcome has made the prisoners’ dilemma one of the most studied games in economics because it captures the difficult nature of cooperation in oli- gopoly markets. We now summarize the nature of a prisoners’ dilemma.
Relation A prisoners’ dilemma arises when all rivals possess dominant strategies, and, in dominant- strategy equilibrium, they are all worse off than if they had cooperated in making their decisions.
As we will explain later in this chapter, managers facing prisoners’ dilemma situations may be able to reach cooperative outcomes if, instead of having only one opportunity to make their decisions, they get to repeat their decisions many
dominant-strategy equilibrium Both players have dominant strategies and play them.
times in the future. We will save our examination of repeated decisions, as well as a more precise discussion of “cooperation” and “cheating,” for Section 13.3. Until then, our discussion will continue examining situations in which managers have only a single opportunity to make their decisions.
Most strategic situations, in contrast to the prisoners’ dilemma game, do not have a dominant-strategy equilibrium. We will now examine some other ways oligopoly managers can make simultaneous decisions when some, or even all, of the firms do not have dominant strategies.
Decisions with One Dominant Strategy
In a prisoners’ dilemma situation, all firms have dominant strategies to follow and managers rationally decide to follow their dominant strategies, even though the outcome is not as good as it could be if the firms cooperated in making their decisions. If just one firm possesses a dominant strategy, rival managers know that particular firm will choose its dominant strategy.
Knowing what your rival is going to do can tell you much about what you should do. We illustrate the value of knowing what your rival is going to do with the following example.
Pizza Castle and Pizza Palace are located almost side by side across the street from a major university. The products of Castle and Palace are somewhat differen- tiated, yet their primary means of competition is pricing. For illustrative purposes, suppose each restaurant can choose between only two prices for its pizza: a high price of $10 and a low price of $6. Clearly, the profit for each firm at each of the prices depends greatly on the price charged by the other firm. Once again, you see that profits of oligopolists are interdependent.
Table 13.2 shows the payoff table facing Castle and Palace. If both charge $10, each does quite well, making $1,000 a week profit, as shown in cell A. If both lower their prices to $6, sales increase some; each restaurant will probably maintain its market share; and, because of the lower price, the profit of each falls to $400 a week, as shown in cell D. However, if either firm lowers its price to $6 while the other maintains its price at $10, the firm with the lower price will capture most of
Now try Technical Problem 3.
T A B L E 13.2 Pizza Pricing:
A Single Dominant Strategy
Palace’s price
High ($10) Low ($6)
A B
High ($10) $1,000,$1,000 $500,$1,200 Castle’s price
C D
Low ($6) $1,200,$300 $400,$400
Payoffs in dollars of profit per week.