Strategy, Bargaining, and Commitment

Why does every request become urgent?

Two project teams use the same testing unit. Each needs routine work completed during the coming scheduling period. The unit offers normal processing and a rush channel. Rush requests receive priority, but interrupting the schedule consumes resources and delays other work. When both teams rush, neither gets much of an advantage.

Each team would prefer a world in which both used normal processing. Yet each worries about being the only team waiting in the ordinary queue. If the other team rushes, asking for priority may be the best available defense. If the other team does not rush, priority may be an attractive advantage.

The resulting congestion need not mean that either manager failed to think. It may be the result of both managers thinking about their own teams under the existing rules.

The organization, requests, and numerical payoffs in this chapter are fictional. The opening example contains no genuine emergencies. We are examining how routine work can become a priority contest, not arguing that urgent work should always wait.

Chapter 3 compared prices while initially holding competitors’ offers fixed. A strategic situation arises when the consequence of your decision depends on choices made by someone who is also considering your response. The other participant might be a rival, supplier, employee, or another team in the same organization. Strategy begins by taking that person’s choices seriously.

Specify the situation before predicting behavior

Five questions organize the analysis. Who chooses? What can each participant do? What does each care about? What does each know when choosing? In what order are choices made?

Here the players are Team A and Team B. Each can submit a normal request or a rush request. They choose without seeing the other’s current submission and cannot revise their requests afterward. Calling the choices simultaneous means neither observes the other’s choice before deciding; it does not require both managers to click a button at the same instant.

The payoff is the value a participant places on an outcome. For this construction, use a common net-value scale that accounts for completion benefits, delay, and actual rush costs. Each team chooses to maximize its own entry. We also assume the entries can be added to represent organizational value, with no other affected parties omitted. They are not estimated dollars or arbitrary satisfaction scores.

That last assumption matters. In an actual organization, a manager might care about a bonus, a deadline, a supervisor’s opinion, or colleagues’ workloads. A payoff model must reflect the incentives doing the work. A convenient table cannot make unmeasured effects disappear.

Read one participant’s choice at a time

Table 4.1 gives the four possible outcomes. A chooses the row; B chooses the column. In each pair, the first number is A’s payoff and the second is B’s. The row position does not mean that A chooses first.

On a small screen, scroll the table sideways to see all columns.

If both use normal processing, each gets 20. If A alone rushes, A gets 28 while B gets 8. Reverse the choices and the payoffs reverse. If both rush, each gets 12 after the disruption and rush costs.

To decide what A should do, first hold B’s choice fixed at normal. A compares 20 from normal with 28 from rush. Rush is better by 8. Now hold B’s choice fixed at rush. A compares 8 from normal with 12 from rush. Rush is better by 4.

A best response is the action giving the highest payoff for the specified choice of the other participant. Rush is A’s best response to either of B’s actions. It is therefore a strictly dominant action in this game: it is better regardless of which action B takes.

Now check B using the second number in each pair. If A uses normal, B compares 20 with 28. If A rushes, B compares 8 with 12. B also prefers rush in both cases. The symmetry saves arithmetic only after we understand which numbers belong to whom.

The important comparison is not “28 is the biggest number in the table.” A team cannot choose its own action and the other team’s action together. It chooses between the outcomes available given what the other team does.

Equilibrium does not mean a good joint outcome

Both teams rush. At that outcome, neither can improve its payoff by changing its action alone. If A switches to normal while B continues rushing, A falls from 12 to 8. The same is true for B.

This is a Nash equilibrium: each participant is choosing a best response to the other’s choice. Nash’s 1950 paper provides the underlying equilibrium definition. In our game, mutual rush is the only equilibrium because each team strictly prefers rush at either action of the other.

But normal/normal produces 20 + 20 = 40 total units, compared with 12 + 12 = 24 from rush/rush. Each asymmetric outcome produces 28 + 8 = 36. Mutual normal processing gives the highest combined value and leaves both teams better off than mutual rushing.

Why is normal/normal not an equilibrium? Starting there, A could gain by rushing while B stayed normal: 28 rather than 20. B faces the same temptation. A joint improvement is not necessarily supported by individual incentives.

This structure is often called a prisoner’s dilemma. In the classic story, two prisoners are questioned separately. Each can confess or remain silent without knowing the other’s choice. Suppose both silent means 1 year each; one confessing alone goes free while the silent prisoner gets 5 years; both confessing means 3 years each. These are hypothetical sentences, not a description of legal practice. Each cares only about a shorter own sentence, with no enforceable agreement or later consequences.

If the other stays silent, confessing gives 0 years rather than 1. If the other confesses, confessing gives 3 rather than 5. Both therefore confess, although both would prefer 1 year each to 3. Silence corresponds to normal processing and confession to rushing: the numbers differ, but the ordering of each person’s choices is the same.

The useful point is the conflict between individually attractive actions and a better joint outcome. The rush game is not a zero-sum situation: the combined payoff changes with the choices. There is value to recover, not merely a fixed prize to take from someone else.

An equilibrium is a conditional prediction, not a guarantee that every person will act this way. Managers may care about consequences omitted from the table, misunderstand the options, or face rules we have not included. If observed behavior differs, investigate the model rather than treating the difference as proof of irrationality.

Change the rule, not just the announcement

A senior manager could ask both teams to stop rushing. That request communicates a desired outcome, but it does not by itself change either payoff comparison. If supervisors still reward each team for getting its own work through first, the request conflicts with the incentives.

Consider a specific rule change. Each rush request now incurs an additional internal charge of 9 payoff units, paid to a central account outside both teams. Assume the charge reduces the result that each team actually cares about, is announced before requests are submitted, and cannot be routinely waived afterward.

If B uses normal processing, A now compares 20 from normal with 28 − 9 = 19 from rush. If B rushes, A compares 8 from normal with 12 − 9 = 3 from rush. Normal is better in both cases. B faces the same comparisons, so mutual normal processing becomes the unique equilibrium.

The charge changes behavior by changing the team’s consequence of choosing rush. It does not work merely because an accountant writes “charge” beside the request. If it has no effect on the team’s budget, evaluation, or other valued outcome, the original incentives may remain.

Nor is an internal payment automatically a resource loss to the firm. What the team pays, the central account receives. The original payoffs already include the real rush costs. Counting the extra charge as another organizational cost would confuse a transfer with resources consumed. Designing the rule, monitoring requests, and resolving disputes can consume real resources, and those costs still matter.

The amount matters too. With a charge of only 3, rushing gives 25 against normal and 9 against rush. Those still exceed 20 and 8 respectively. Both teams continue rushing. A penalty can look serious in a policy document yet fail to change the relevant comparison.

The 9-unit charge is not an optimal policy established for a real business. Genuine emergencies could make rushing valuable enough to justify its costs. An exception rule would need a way to identify those cases without making every routine request an “emergency.” Alternatively, a coordinator could allocate priority using evidence about the value of timely completion. That assigns someone a new decision right and creates a new information and monitoring problem.

The managerial question is therefore which feasible rule improves coordination after its own costs are counted. An appeal to goodwill, a charge, and centralized approval are different arrangements, not interchangeable labels for cooperation.

When future work changes today’s incentives

The original, uncharged example is a one-shot game: one interaction with no later consequences. Rushing is each team’s best response regardless of the other’s choice. In a repeated game, the teams face the same situation again, and their choices today may affect how the other team acts tomorrow. An informal understanding to use normal processing might now affect later treatment as well as today’s queue position.

When B uses normal, A can gain 28 − 20 = 8 today by rushing. But if the departure is observed and leads to a lasting return to mutual rushing, A loses access to future cooperative outcomes. Each future period of mutual normal processing gives 20 rather than 12, a difference of 8.

Repeated interaction can support cooperation when the expected future loss, valued today, exceeds the immediate gain. The comparison must allow for whether the teams will actually meet again, how much they value later outcomes, and whether a response will occur. There is no need to assume that repetition changes anyone’s character; it can change what an action costs.

Three practical questions follow. Can a departure be detected and distinguished from a genuine emergency? Does the same team bear the later consequences? Is the threatened response feasible and believable when the time comes?

A manager about to leave may receive today’s advantage while a successor bears the later loss. A team unable to observe requests may not know whether a delay reflects another team’s conduct or a testing failure. A threatened response that would be abandoned immediately may create little deterrence. In the original matrix, continued mutual rushing is at least individually defensible because rush remains a best response to rush. That does not establish that destroying future cooperation is desirable for the organization.

Repetition also does not remove the end of a relationship. If everyone knows that a particular round is the last, the same payoffs apply, and there are no consequences afterward, rush is again the dominant action in that round. Anticipating that result can weaken cooperation in the preceding round, and the reasoning can work backward. Merely scheduling several future meetings does not establish a self-enforcing agreement.

In practice, the task is to understand the relevant horizon and consequences rather than promise that a repeated relationship will solve the problem. Clear records, stable responsibilities, and a fair way to distinguish emergencies from opportunistic requests may help. They also take effort. Repeated dealings and formal rules can complement one another without making oversight unnecessary.

Bargaining starts with what happens without agreement

Strategic interaction can also concern how to divide gains from a transaction. Consider a separate fictional purchase. A buyer needs a replacement pump for a project worth $12,000 before paying for the pump. A reliable outside supplier offers an equivalent pump for $8,200, with the same quality, delivery, and payment conditions.

The buyer is negotiating with another supplier whose avoidable production cost is $6,000. Accepting this order would displace a different job yielding $1,000 contribution after its costs. Both alternatives are available during the negotiation. Assume no other costs, risks, or future effects differ.

An outside option is a feasible alternative if this agreement is not reached. Without agreement, the buyer can complete the project using the $8,200 pump and retain $12,000 − $8,200 = $3,800. The negotiating supplier can take its other job and earn $1,000.

The pair of payoffs if negotiations fail is the disagreement point: here, ($3,800, $1,000), with the buyer first. The outside options are the alternative transactions; in this example, their returns determine the disagreement payoffs. These are the baselines against which each side judges an agreement—not zero, and not the prices they announce.

Suppose they agree on a price of $7,600. The buyer retains $12,000 − $7,600 = $4,400, which is $600 better than its outside option. The supplier earns $7,600 − $6,000 = $1,600, which is also $600 better than its outside option.

Neither party should compare agreement with receiving nothing. The buyer already has a way to obtain the pump, and the supplier already has another use for its capacity. This is Chapter 2’s opportunity-cost reasoning applied to negotiation.

Find the range before arguing about the split

The supplier needs at least $6,000 + $1,000 = $7,000 to match its alternative. The buyer will pay no more than $8,200 for an equivalent pump under these conditions. These are reservation prices, the limits at which agreement just matches the respective alternatives.

The joint gain available from this agreement is $8,200 − $7,000 = $1,200. Table 4.2 shows three ways the price could divide it.

On a small screen, scroll the table sideways to see all columns.

At either endpoint, one side is indifferent. Both gain strictly at prices between the endpoints. The middle row divides the gain equally, but nothing in the facts makes that price inevitable. We have not specified who makes offers, how long bargaining can continue, what each knows about the other’s alternatives, or the cost of delay.

This separates two questions. Can an agreement create value compared with disagreement? How will the participants divide that value? Moving the price within this range changes the division, not the combined gain. Changing delivery terms or the resources required to produce the pump could change the gain itself.

The buyer’s project value of $12,000 is not its price ceiling in this negotiation, because it can buy the equivalent pump elsewhere for less. The supplier’s $6,000 production cost is not its floor, because supplying the pump sacrifices another profitable job. Ignoring either alternative gives the other party a misleading picture of what agreement is worth.

A stronger outside option can narrow acceptable terms. If the buyer obtains a genuinely comparable $7,600 offer elsewhere, the available gain with this supplier falls to $600. That does not tell us the exact new price. It tells us that the buyer no longer needs to accept the old ceiling.

Alternatives must be usable, not merely asserted. A cheaper quote arriving after the project deadline is not automatically equivalent. Nor can the supplier claim the same capacity for two mutually exclusive jobs. Negotiating skill cannot make an unavailable alternative available.

A forceful statement is not a commitment

Suppose the buyer announces, “I will not pay more than $7,000.” The supplier then makes a final $7,600 offer. At this stage, assume the buyer can only accept or reject and buy the equivalent outside pump; there are no later bargaining rounds or reputation effects.

Acceptance saves the buyer $600 compared with its $8,200 alternative. The announcement has neither improved the buyer’s disagreement payoff nor removed its ability to accept. A stronger outside option and a binding restriction on later choices are different ways to affect bargaining. If the supplier understands these choices, the declaration alone gives it no reason to believe the buyer will reject $7,600.

To assess a threat, begin at the point when it would have to be carried out. Would the person still want, and be able, to do what was announced? Working backward from that later choice is often more informative than judging how determined the original statement sounded.

A credible commitment changes or reliably constrains that later choice. A purchasing representative might genuinely lack authority to exceed a limit, with no possibility of obtaining an exception before the offer expires. That is different from being told to bargain firmly while retaining immediate access to an approving supervisor. The supplier must also know the restriction exists for it to influence the supplier’s offer.

Schelling’s “An Essay on Bargaining” (1956) develops the role of binding one’s later choices in bargaining. The managerial lesson is not to eliminate flexibility indiscriminately. A restriction can strengthen a position, but it can also prevent a worthwhile agreement when circumstances change. A rule that can be quietly reversed may provide neither reliable commitment nor useful discipline.

A deposit changes the reservation decision

Commitments can also support cooperation rather than demand a larger share. Continue with the pump transaction, but now suppose the parties have agreed on $7,600 and the buyer wants capacity reserved before giving the final instruction to manufacture.

Once the supplier reserves that capacity, its alternative job is lost. A buyer’s promise to proceed leaves the supplier exposed if the buyer later cancels. Consider an arrangement that collects a $1,000 deposit before reservation, credits it toward the agreed price on delivery, and lets the supplier retain it if the buyer cancels. Assume these consequences are observable and effective in this illustration.

With delivery, the buyer pays $1,000 now and $6,600 later. Total revenue is still $7,600, not $8,600. Calling the payment a deposit does not create another $1,000 of surplus.

If the buyer cancels after reservation but before manufacture, assume the supplier incurs none of the $6,000 production cost and no additional loss beyond the forgone job. Retaining the $1,000 then compensates the specified outside contribution. Before reserving, the buyer knows it cannot later cancel and recover that payment.

Once paid and genuinely unrecoverable, however, the deposit is sunk. At the later decision, the buyer compares the remaining benefits with the remaining $6,600 and its feasible alternatives. It should not proceed merely to “get the deposit back.” The arrangement changes the payment needed to continue and the consequences anticipated before reservation; it does not justify proceeding merely because the deposit has already been paid. Cancellation can still be the better choice after circumstances change.

The arrangement has limits. A buyer deposit does not guarantee that the supplier will deliver, and a payment retained despite supplier failure could create another incentive problem. The parties would need clear responsibilities, observable events, and workable safeguards. These are economic requirements to investigate, not conclusions about the legal enforceability of particular terms.

Giving up flexibility is itself a cost. A reservation arrangement should be compared with waiting, buying an available pump elsewhere, or paying for more flexible capacity. Chapter 11 examines more extensively how vulnerable investments and incomplete agreements can affect business relationships and ownership.

Strategy is also a question of organizational design

The rush game asks how internal rules can make individually sensible choices costly for the organization. The pump negotiation asks how feasible alternatives limit an agreement and how present arrangements affect later incentives. Both require looking beyond the action management wants someone to take.

For the testing unit, the next step would be to investigate actual delays, rush costs, and emergency needs before choosing a charge or approval process. A rule also needs an owner: who grants priority, who reviews exceptions, and whose evaluation reflects the disruption imposed elsewhere? Those decisions connect strategy to the agency costs and decision rights introduced in Chapter 1.

For the pump, the buyer should establish comparable alternatives and the supplier should count displaced work. Neither should treat a bargaining statement as a constraint without asking what makes it effective. The purpose is not to win every concession. It is to find an arrangement that creates value, divides it on acceptable terms, and gives each participant reason to carry out the agreement.

Study map

Identify the players, choices, payoffs, information, and timing. Find best responses while holding the other participant’s action fixed. Separate equilibrium from joint value. Ask whether a rule change or future consequence actually changes incentives. In bargaining, compare agreement with feasible outside options. Judge commitments at the point of execution, including the value of flexibility given up.

Practice and discussion

These are public practice questions. Keep the original assumptions unless a question changes one explicitly.

1. Read the game. Use Table 4.1 to identify each team’s best response to each action of the other team. Explain why normal/normal is not an equilibrium even though it produces the highest combined payoff. What can A obtain by switching alone from rush/rush to normal?

2. Test a rule. Deduct an internal charge of 3 from the payoff of any team that rushes. Calculate all four payoff pairs and find the equilibrium. Repeat with a charge of 9. If both nevertheless rush under the 9-unit charge, what are the teams’ combined net payoffs and the central account’s receipts? Why are those receipts not a resource loss?

3. Examine future consequences. Return to the uncharged game. A can gain 8 now by rushing while B uses normal. Suppose A values the entire expected future loss from this departure at only 3 today. Is the departure deterred? Explain how observation, staff turnover, and a known final round could change the effectiveness of an informal agreement.

4. Change an outside option. First lower the buyer’s equivalent outside quote to $7,600, keeping the supplier’s original costs and alternative. Find the acceptable price range and joint gains. Separately, restore the original $8,200 quote but raise the supplier’s alternative-job contribution to $2,500. Is there now a price that leaves both at least as well off as their alternatives?

5. Evaluate the reservation. In about 150 words, explain what the $1,000 deposit changes and what it does not guarantee. Include the balance payable on delivery, the supplier’s specified loss on early cancellation, and one new fact you would need before recommending the arrangement in practice.

Check your arithmetic

For question 1, A would fall from 12 to 8. For question 2, the 3-unit charge gives pairs (20,20), (8,25), (25,8), and (9,9), read across the rows. Rush/rush remains the equilibrium. The 9-unit charge gives (20,20), (8,19), (19,8), and (3,3); normal/normal is the equilibrium. If both rush under that charge, team payoffs total 6 and central receipts total 18, recovering 24 before administration costs. For question 3, 8 − 3 = 5, so the departure remains attractive. For question 4, the first range is $7,000–$7,600 with $600 joint gains; in the separate variation, the supplier needs $8,500, above the buyer’s $8,200 ceiling. For question 5, $6,600 remains payable; the specified forgone contribution is $1,000.

Source note

The business cases, payoff matrix, calculations, and exercises are original teaching constructions; the prisoners’ story retells the conventional thought experiment. Nash supplies the equilibrium attribution and Schelling the bounded commitment attribution; neither source provides these hypothetical business returns. Further teaching references are Gendler’s prisoner’s dilemma lecture, Polak’s repeated-game discussion, and the disagreement-payoff definition on slide 7 of Acemoglu’s bargaining discussion. This chapter does not estimate real behavior, derive a formal bargaining solution, or offer contractual legal advice.