In contrast to simultaneous decisions, the natural process of some decisions requires one firm to make a decision, and then a rival firm, knowing the action taken by the first firm, makes its decision. Such decisions are called sequential decisions. For example, a potential entrant into a market will make its decision to enter or stay out of a market first, and then the incumbent firm (or firms) re- sponds to the entry decision by adjusting prices and outputs to maximize profit given the decision of the potential entrant. In another common kind of sequential decision, one firm makes its pricing, output, or advertising decision ahead of another. The firm making its decision second knows the decision of the first firm.
As we will show you in this section, the order of decision making can sometimes, but not always, create an advantage to going first or going second when making sequential decisions.
Even though they are made at different times, sequential decisions nonetheless involve strategic interdependence. Sequential decisions are linked over time: The
Now try Technical Problems 8–11.
sequential decisions When one firm makes its decision first, then a rival firm makes its decision.
best decision a manager can make today depends on how rivals will respond to- morrow. Strategically astute managers, then, must think ahead to anticipate their rivals’ future decisions. Current decisions are based on what managers believe rivals will likely do in the future. You might say a manager jumps ahead in time and then thinks backward to the present. Making sequential decisions, like mak- ing simultaneous decisions, involves getting into the heads of rivals to predict their decisions so that you can make better decisions for yourself. Once again, oligopoly decisions involve strategic interdependence.
Making Sequential Decisions
Sequential decisions can be analyzed using payoff tables, but an easier method, which we will employ here, involves the use of game trees. A game tree is a diagram showing firms’ decisions as decision nodes with branches extending from the nodes, one for each action that can be taken at the node. The sequence of decisions usually proceeds from left to right along branches until final pay- offs associated with each decision path are reached. Game trees are fairly easy to understand when you have one to look at, so let’s look at an example now.
Suppose that the pizza pricing decision in Table 13.2 is now a sequential deci- sion. Castle Pizza makes its pricing decision first at decision node 1, and then Palace Pizza makes its pricing decision second at one of the two decision nodes labeled with 2s. Panel A in Figure 13.3 shows the game tree representing the sequential decision.
Castle goes first in this example, as indicated by the leftmost position of deci- sion node 1. Castle can choose either a high price along the top branch or a low price along the bottom branch. Next, Palace makes its decision to go high or low.
Since Palace goes second, it knows the pricing decision of Castle. Castle’s de- cision, then, requires two decision nodes, each one labeled 2: one for Palace’s decision if Castle prices high and one for Palace’s decision if Castle prices low.
Payoffs for the four possible decision outcomes are shown at the end of Palace’s decision branches. Notice that the payoffs match those shown in the payoff table of Table 13.2.
Castle decides first, so it doesn’t know Palace’s price when it makes its pricing decision. How should the manager of Castle pizza make its pricing decision? As in simultaneous decisions, the manager of Castle tries to anticipate Palace’s deci- sion by assuming Palace will take the action giving Palace the highest payoff. So Castle’s manager looks ahead and puts itself in Palace’s place: “If I price high, Pal- ace receives its best payoff by pricing low: $1,200 is better than $1,000 for Palace. If I price low, Palace receives its best payoff by pricing low: $400 is better than $300.”
In this situation, since Palace chooses low no matter what Castle chooses, Palace has a dominant strategy: price low. Panel B in Figure 13.3 shows Palace’s best de- cisions as gray-colored branches.
Knowing that Palace’s dominant strategy is low, Castle predicts Palace will price low for either decision Castle might make. Castle’s manager, then, should choose to price high and earn $500 because $500 is better than pricing low and earning $400.
game tree
A diagram showing the structure and payoff of a sequential decision situation.
decision nodes Points in a game tree, represented by boxes, where decisions are made.
This process of looking ahead to future decisions to make the best current decision is called the backward induction technique or, more simply, the roll-back method of making sequential decisions.
Notice that the roll-back solution to a sequential decision is a Nash equilib- rium: Castle earns the highest payoff, given the (best) decision it predicts Palace will make, and Palace is making its best decision given the (best) decision Castle makes. We must stress, however, that Palace, by making its decision last, does not need to anticipate or predict Castle’s decision; Castle’s decision is known with cer- tainty when Palace chooses its price. The complete roll-back solution to the pizza
roll-back method Method of finding a Nash solution to a sequential decision by looking ahead to future decisions to reason back to the best current decision. (Also known as backward induction.)
Castle, Palace
$1,000, $1,000
$500, $1,200
$1,200, $300
$400, $400 Palace
High ($10)
Low ($6)
High ($10)
Low ($6) 2
Palace 2 High ($10)
Low ($6) Castle 1
Panel A — Game tree
Castle, Palace
$1,000, $1,000
$500, $1,200
$1,200, $300
$400, $400 Palace
High ($10)
Low ($6)
High ($10)
Low ($6) 2
Palace 2 High ($10)
Low ($6) Castle 1
Panel B — Roll-back solution F I G U R E 13.3
Sequential Pizza Pricing
pricing decision, also referred to as the equilibrium decision path, is indicated in Panel B by the unbroken sequence of gray-colored branches on which arrowheads have been attached: Castle High, Palace Low. Furthermore, the roll-back equilib- rium decision path is unique—a game tree contains only one such path—because in moving backward through the game, roll back requires that the single best deci- sion be chosen at each node of the game.7 We summarize our discussion of this important concept with a principle.
Principle When firms make sequential decisions, managers make best decisions for themselves by working backward through the game tree using the roll-back method. The roll-back method results in a unique path that is also a Nash decision path: Each firm does the best for itself given the best decisions made by its rivals.
First-Mover and Second-Mover Advantages
As you might have already guessed, the outcome of sequential decisions may de- pend on which firm makes its decision first and which firm goes second. Some- times you can increase your payoff by making your decision first in order to influence later decisions made by rivals. Letting rivals know with certainty what you are doing—going first usually, but not always, does this—increases your payoff if rivals then choose actions more favorable to you. In such situations, a first-mover advantage can be secured by making the first move or taking the first action in a sequential decision situation.
In other situations, firms may earn higher payoffs by letting rivals make the first move, committing themselves to a course of action and making that action known to firms making later decisions. When higher payoffs can be earned by reacting to earlier decisions made by rivals, the firm going second in a sequential decision enjoys a second-mover advantage.
How can you tell whether a sequential decision has a first-mover advantage, a second-mover advantage, or neither type of advantage (the order of decision mak- ing doesn’t matter either way)? The simplest way, and frequently the only way, is to find the roll-back solution for both sequences. If the payoff increases by being the first-mover, a first-mover advantage exists. If the payoff increases by being the second-mover, a second-mover advantage exists. If the payoffs are unchanged by reversing the order of moves, then, of course, the order doesn’t matter. We now illustrate a decision for which a first-mover advantage exists.
Suppose the Brazilian government awards two firms, Motorola and Sony, the ex- clusive rights to share the market for cellular phone service in Brazil. Motorola and Sony are allowed to service as many customers in Brazil as they wish, but the gov- ernment sets a ceiling price for cellular service at $800 annually per customer. The two companies know that each plans to charge the maximum price allowed, $800.
first-mover advantage A firm can increase its payoff by making its decision first.
second-mover advantage
A firm can increase its payoff by making its decision second.
7Game theorists refer to the Nash equilibrium path found by implementing the roll-back method as a subgame–perfect equilibrium path because best decisions are made at every node or “subgame” in the game tree.
Motorola and Sony can both provide either analog or digital cellular phones.
Motorola, however, has a cost advantage in analog technology, and Sony has a cost advantage in digital technology. Their annual costs per customer, which remain constant for any number of customers served, are as follows:
Motorola Sony Annual cost of analog service $250 $400 Annual cost of digital service $350 $325
Demand forecasters at Motorola and Sony work together to estimate the total demand for cellular phone service in Brazil. They discover that Brazilians do not care which technology they buy, but total sales will suffer if Motorola and Sony do not agree to offer the same technology. The desire to have a single technology arises because the two technologies will probably not be compatible: Analog cus- tomers and digital customers will not be able to communicate. (Motorola and Sony can solve the compatibility problem, but it will take several years to solve the problem.) Demand estimates show that, at a price of $800 per year, a total of 50,000 Brazilians will sign up for cell phone service if Motorola and Sony provide the same technology, but only 40,000 will sign up at $800 per year if the two firms offer different technologies. Motorola and Sony expect that sales will be evenly divided between them: 25,000 customers each if the same technologies are chosen or 20,000 customers each if they choose different technologies.
You can see from the payoff table in Figure 13.4 that Motorola and Sony both make greater profit if they choose the same technologies than if they choose opposite technologies: Cells A and D are both better than either cell C or B. If the technology decision is made simultaneously, both cells A and D are Nash equilibrium cells, and game theory provides no clear way to predict the outcome. Motorola, of course, would like to end up in cell A since it has a cost advantage in analog technology and will sell more analog phone service if Sony also chooses analog. How can Motorola entice Sony to choose analog technology so that the outcome is cell A?
The clever manager at Motorola sees that, if Motorola chooses its (analog) technology first, cell A is the predicted outcome. To see why cell A is the likely outcome, we turn to Panel B, which shows the game tree when Motorola goes first. To find the solution to this sequential game, Motorola’s manager applies the roll-back method. First, the manager finds Sony’s best decisions at Sony’s two de- cision nodes. At the decision node where Motorola chooses Digital, Sony’s best decision is Digital, which is the outcome in cell D. At the decision node where Motorola chooses Analog, Sony’s best decision is Analog, which is the outcome in cell A. Then, rolling back to Motorola’s decision, Motorola knows that if it chooses Digital, then it will end up with $11.25 million when Sony makes its best decision, which is to go Digital. If Motorola chooses Analog, then it will end up with $13.75 million when Sony makes its best decision, which is to go Analog.
Roll-back analysis indicates Motorola does best, given the choice Sony will later make, by choosing Analog. This Nash equilibrium path is shown in Panel B as the gray-colored branches with arrows.
To have a first-mover advantage, Motorola must receive a higher payoff when it goes first compared with its payoff when it goes second. In this game, Motor- ola does indeed experience a first-mover advantage because roll-back analysis shows that Motorola earns only $11.25 million when Sony goes first. (You will verify this in Technical Problem 13.) Thus Motorola gains a first-mover advan- tage in this game of choosing cellular phone technology. We summarize our discussion of first-mover and second-mover advantage with a relation.
Relation To determine whether the order of decision making can confer an advantage when firms make sequential decisions, the roll-back method can be applied to the game trees for each possible sequence of decisions. If the payoff increases by being the first (second) to move, then a first-mover (second-mover) advantage exists. If the payoffs are identical, then order of play confers no advantage.
Sony, Motorola
$11.875, $11.25
$10, $13.75
$9.50, $11
$8, $9
$11.875, $11.25
$8, $9
$9.50, $11
$10, $13.75
Sony Sony’s
technology
Digital
Analog Analog
Digital
Digital
Analog 2
Sony 2 Digital
A
C
B
D
Digital
Analog
Analog
Payoffs in millions of dollars of profit annually
Motorola's technology
Motorola 1
Panel B — Motorola secures a first-mover advantage Panel A — Simultaneous technology decision F I G U R E 13.4
First-Mover Advantage in Technology Choice
As you probably noticed, we did not discuss here how Motorola gains the first- mover position in this game of choosing cellular phone technology. Determining which firm goes first (or second) can be quite complex, and difficult to predict, when both firms recognize that going first (or second) confers a first-mover (or second-mover) advantage. We will now examine several strategic moves that firms might employ to alter the structure of a game to their advantage.
Strategic Moves: Commitments, Threats, and Promises
As we have emphasized, strategic decision making requires you to get into the heads of your rivals to anticipate their reactions to your decisions. We now want to take you a step beyond anticipating your rivals’ reactions to taking actions to manip- ulate your rivals’ reactions. We will now examine three kinds of actions managers can take to achieve better outcomes for themselves, usually to the detriment of their rivals. These strategic actions, which game theorists refer to as strategic moves, are called commitments, threats, and promises.
These three strategic moves, which, in most cases, must be made before rivals have made their decisions, may be utilized separately or in combination with each other. Strategic moves will achieve their desired effects only if rivals think the firms making the moves will actually carry out their commitments, threats, or promises. Rivals will ignore strategic moves that are not credible. A strategic move is credible if, when a firm is called upon to act on the strategic move, it is in the best interest of the firm making the move to carry it out. Making strategic moves credible is not easy, and we cannot give you any specific rules that will work in every situation. We will, however, provide you with the basic ideas for making credible strategic moves in the discussions that follow.8 We first discuss commit- ments, which are unconditional strategic moves, and then we turn to threats and promises, which are conditional moves.
Managers make commitments by announcing, or demonstrating to rivals in some other way, that they will bind themselves to take a particular action or make a specific decision no matter what action or decision is taken by its rivals.
Commitments, then, are unconditional actions the committing firms undertake for the purpose of increasing their payoffs. A commitment only works if rivals believe the committing firm has genuinely locked itself into a specific decision or course of action. In other words, commitments, like all strategic moves, must be credible to have strategic value.
Generally, a firm’s commitment will not be credible unless it is irreversible. If some other decision later becomes the best decision for the committing firm, rivals will expect the committing firm to abandon its commitment if it can. Rivals will
Now try T echnical Problems 12–13.
strategic moves Three kinds of actions that can be used to put rivals at a disadvantage:
commitments, threats, or promises.
credible
A strategic move that will be carried out because it is in the best interest of the firm making the move to carry it out.
commitments Unconditional actions taken for the purpose of increasing payoffs to the committing firms.
8To get a more thorough and richer development of the practical application of strategic moves to business decision making than is possible in one or two chapters of a textbook, we recommend you read two of our favorite books on the subject: Avinash Dixit and Barry Nalebuff, Thinking Strategically:
The Competitive Edge in Business, Politics, and Everyday Life (New York: W. W. Norton, 1991); and John MacMillan, Games, Strategies, and Managers (New York: Oxford University Press, 1992).
believe a commitment is irreversible only if it would be prohibitively costly, or even impossible, for the committing firm to reverse its action. In short, only cred- ible commitments—those that are irreversible—successfully alter rivals’ beliefs about the actions the committing firm will take.
To illustrate how credible commitments can improve profitability, sup- pose that Motorola and Sony make their choices between analog and digital technologies simultaneously according to the payoff table shown in Panel A of Figure 13.4. The outcome of the simultaneous game is difficult for either firm to predict since there are two Nash equilibrium cells, A and D. The manager of Motorola, however, decides to make a commitment to analog technology before the simultaneous decision takes place by building a facility in Brazil specifically designed for manufacturing and servicing only analog phones. Both firms know that the cost of converting Motorola’s new plant to production of digital cellular phones is enormous. Consequently, Motorola is unlikely to incur the huge costs of converting to digital technology, so Sony views Motorola’s action as irreversible.
Thus Motorola’s strategic move is a credible commitment because Sony believes Motorola’s action is irreversible.
Notice that Motorola’s commitment transforms the simultaneous decision situ- ation in Panel A into the sequential decision situation shown in Panel B. Motorola, through its use of credible commitment, seizes the first-mover advantage and en- sures itself the outcome in cell A. We have now established the following principle.
Principle Firms make credible commitments by taking unconditional, irreversible actions. Credible commitments give committing firms the first moves in sequential games, and by taking the first actions, committing firms manipulate later decisions their rivals will make in a way that improves their own profitability.
In contrast to commitments, which are unconditional in nature, threats and promises are conditional decisions or actions. Threats, whether they are made explic- itly or tacitly, take the form of a conditional statement, “If you take action A, I will take action B, which is undesirable or costly to you.” The purpose of making threats is to manipulate rivals’ beliefs about the likely behavior of the threatening firms in a way that increases payoffs to the threatening firms. For example, firms that are al- ready producing a product or service in a market and earning profits there may try to deter new firms from entering the profitable market by threatening, “If you enter this market, I will then lower my price to make the market unprofitable for you.”
Threats do not always succeed in altering the decisions of rivals. For threats to be successful in changing rivals’ behavior, rivals must believe the threat will actually be carried out. Following our discussion about credible strategic moves, a threat is credible if, when the firm is called upon to act on the threat, it is in the best interest of the firm making the threat to carry it out.
Consider again the simultaneous technology decision in Panel A of Figure 13.4.
Suppose, before the simultaneous decisions are made, Motorola threatens Sony by saying to Sony, “If you choose digital technology for your cellular phones, we will choose analog.” In making this threat, Motorola wants Sony to think, “Since Motorola is going to go analog if we choose digital, then we might as well choose
threats
Conditional strategic moves that take the form: “If you do A, I will do B, which is costly to you.”