Lecture Notes 15: Credibility
We must be merciless. The enemy must not lay hands on a single loaf of bread. Farmers must kill their livestock and burn their grain. Bridges and roads must be dynamited. Forests and buildings must be burned down. Conditions for our enemy must be intolerable.
-Josef Stalin, 1941
Motivating Examples
Houghton Mifflin is a small publishing operation. When Western Pacific, a large corporation, threatened to take over, all of the best authors at Houghton Mifflin threatened to quit. The CEO of Western Pacific thought this was ridiculous at first because he doubted that the writers had any better outside options if they quit. But eventually he got so many letters that he started to take their threat seriously and dropped his takeover bid.
When Rupert Murdock tried to take over The Times, all the writers threatened to quit. He took over anyway and none of them actually quit.
These examples, along with the Stalin quote, capture the essence of strategic moves. You can try to alter an opponent’s behavior by threatening or promising to do something, but the question boils down to whether your opponent believes that you will actually follow through.
Strategic Moves Defined
A strategic move is when you change the game in a way that somehow limits your future freedom of action in order to elicit a particular response from opponents. For example:
• Professors sign a pledge that they will quit if a new administrator is hired. • You promise to give a business partner $1 million if he cooperates with you.
In all cases, the idea is that your opponent will see this commitment and will alter his behavior in a way that is good for you. For example, the professors’ goal is for the school not to hire the administrator in the first example, and your goal is to elicit cooperation from your business partner in the second example.
to adapt to your committed response. More choices are not always better in game theory. Limiting your own freedom of action can actually be good if it forces your opponent to undertake an action that is favorable to you.
Now, in order for a strategic move to be effective, two conditions must hold.
• The strategic move must be observable. It doesn’t do much good for the professors to threaten to quit if the decision-makers don’t know about it.
• The strategic move must be credible. The professors need some way to convince the university that they are actually going to follow through and quit if the administrator is hired. Similarly, your friend needs to actually believe that you will follow through on your promise to give him $1 million if he cooperates.
Classifying Strategic Moves
The simplest strategic move that a player can make is an unconditional strategic move.
• A commitment is a guarantee that a player will undertake a certain action regardless of what moves other players make.
For example, a restaurant might commit to building a restaurant in a particular location no matter what anyone else does, with the intention of keeping competitors away.
A player can also make a conditional strategic move, which is contingent on other players’ actions.
• A threat is a conditional response to hurt another player, depending on his action. For example, a mother might threaten that she won’t give her child dessert if he hits his sister. • A promise is a conditional response to reward another player, depending on his action.
For example, the police might promise to reduce the charges for a criminal if he rats out his co-conspirator.
Conditional strategic moves can be designed either to encourage another player to do something or to encourage another player not to do something.
• A compellent action is designed to encourage another player to do something. For example, a mother tells her child to eat his vegetables or he won’t get dessert.
There is a critical point here. In order to be strategically interesting, a threat has to create mutual harm. If carrying out a threat is actually good for you, this isn’t a threat anymore. It’s just a warning.
As an example, suppose an employee tells his boss that if the boss cuts his salary, then he’s going to quit and find a different job. Assuming that the employee has a better outside job option, this is not strategically interesting. The employee is just doing what is in his own best interest and warns his boss that he will do so. But if the employee threatens to quit his job even without having a better outside option, this is strategically interesting because he needs a way to convince his boss that he is actually serious about his threat.
The same is true for promises. If fulfilling a promise is good for you, this is just an assurance.
For example, when a mother tells her child that she will give him a hug if he is nice to his sister, this isn’t strategically interesting. The mother enjoys giving the hug and just assures her son that she will give him one. The more interesting case is where following through on a promise is costly. For example, suppose a boyfriend promises to give his girlfriend an expensive necklace if she agrees to go to the movie he wants. It’s costly for the boyfriend to follow through on that promise. Why should his girlfriend believe that he will?
The whole essence of strategic moves is that you are stipulating an action that you actually do not
want to take in order to elicit a certain response from opponents.
• Commitment: When you commit to build a restaurant in a certain location regardless of what other firms do, you are committing to an action that will reduce your profits if other firms actually open up restaurants close to yours. But your hope is that your commitment will be enough to keep these other firms away.
• Threat: When you threaten a business partner that you will cancel a deal if he doesn’t increase your share of the profits from 50% to 75%, you are actually threatening to hurt yourself in the case where he doesn’t agree (by cancelling the project and getting no
profits). But you hope that your threat will make him acquiesce to your demands.
• Promise: When you promise to give your girlfriend an expensive jewel if she marries you, it is actually costly for you to follow through on the deal. But you are hoping that this promise will be enough for her to agree to marry you.
Optimal Strategic Moves
Promises are usually better for compellence. Threats are usually better for deterrence. Here’s why.
Compellence can theoretically be achieved with a threat or with a promise. If a mom wants to get her child to clean his room, both options could work:
• Promise: Clean your room and I’ll give you $10
• Threat: Clean your room or I’ll take away your video games.
We usually think that promises are better for compellence. The promise encourages the child to clean his room quickly and show it to his mother. The threat encourages him to slow-walk and hide his room if it isn’t clean. Also, a compellent threat requires a deadline. The promise encourages the child to act quickly and show his room to his mother.
Similarly, deterrence can theoretically be achieved with a threat or with a promise. If a brother wants to get a bully to stop insulting his sister, both options could work:
• Promise: Stop insulting my sister and I’ll buy you lunch. • Threat: Stop insulting my sister or I’ll punch you.
The threat is better in this case. It’s ongoing. The brother only has to make the threat one time, and it works in perpetuity with no expiration date. The promise would require the brother to continue buying the bully lunch.
Whether something is a threat or a promise depends on the status quo. For example, if the status quo is that the child has a lot of video games, then taking them away is a threat. If the default is that the child has no video games, then giving them to him is a promise.
This suggests that, for compellence, you might want to choose a status quo making it easy to provide rewards. If you want to get your child to do something, you should set it up so that the normal condition is that he doesn’t have a lot of video games. This makes it easy for you to provide rewards when he does the things you want.
Examples of Commitments Recall the game of chicken.
Swerve Straight
Swerve 0,0 -1,1
Straight 1,-1 -2,-2
This game has a Nash Equilibrium where player 1 goes straight and another Nash Equilibrium where player 2 goes straight. If we introduce a first stage to the game where player 1 can commit
to going straight, he can guarantee the Nash Equilibrium that is better for him because player 2 will swerve in response.
But how can player 1 make player 2 believe that he’s really committed to going straight? Maybe he can disconnect his steering wheel and throw it out the window! (Of course, we need to make sure that player 2 can see this). Generally, he could acquire a reputation for being tough.
For a second example, suppose that a teacher can either be weak or tough on students who arrive late, and that a student can in turn be punctual or late. The payoffs are shown below.
Punctual Late
Weak 4,3 2,4
Tough 3,2 1,1
The Nash Equilibrium is for the teacher to be weak and the student to come late, and the payoffs from this equilibrium are (2,4). But if the teacher can commit to being tough, then the student prefers to be punctual. This changes the payoffs to (3,2), which is better for the teacher.
Again, the aspect of commitment is important. Here, the teacher is actually committing to being touch, which is a strictly dominated strategy. The teacher must observably maintain the commitment to remain tough. If she’s weak, the student has an incentive to start coming late again.
Examples of Threats
The United States (player 1) and Japan (player 2) can maintain open or closed markets for trading. The payoffs are given below.
Open Closed
Open 4,3 3,4
The Nash Equilibrium is for the US to have open markets and for Japan to have closed markets, generating payoffs of (3,4). But the US can threaten: “If you close your markets, we will too.” If Japan believes that the US will actually follow through on this threat, they are better off keeping their markets open and getting a payoff of 3 than closing them for a payoff of 2. If the threat is credible, the US can change the payoffs to (4,3) by issuing the threat.
But will the US actually exercise this threat? If Japan does close its markets, the payoff to the US falls from 3 to 1 by actually following through on the threat. One option might be for the US Congress to pass a law that mandates closed markets if Japan closes its markets. If the threat is credible, then Japan will keep its markets open and the threat never actually has to be carried out.
Of course, Japan has its own responses to the threat. They could agree in principle to open their markets and just keep delaying it, knowing that at every instant in time it would be costly for the US to follow through on its threats. Or Japan might close off its markets little by little, knowing that at each stage the action is not large enough to make it worth it for the US to take the costly action of pulling the trigger and retaliating.
As another example, consider two countries in an armed conflict. Country 1 can either maintain the status quo or invade country 2. If there is an invasion, the second country can either go with a conventional response, in which case country 1 will be victorious. Or it can go with a nuclear response, which is extremely costly for both sides.
To keep country 1 from invading, country 2 has to threaten a nuclear response to an invasion. But, again, we have a serious credibility problem. If country 1 does invade, would it make any sense for country 2 to actually follow through on the threat? If country 1 realizes that the threat is not credible, it might invade anyway and reason that the threat is not credible.
Examples of Promises
Consider two firms that can set high prices or low prices.
High Low
High 32,32 21,36
Low 36,21 28,28
The Nash Equilibrium is for both firms to set low prices. While they are both better off if they agree to set high prices, this is a prisoners’ dilemma. It is not an equilibrium for the firms to do so since each firm could deviate to setting a low price in order to raise its profit.
But what if we introduce a first stage to the game where player 1 can make a promise to set a high price if and only if player 2 also sets a high price? If the promise is credible, then the equilibrium outcome is for both to set high prices.
Of course, credibility is the main issue. Will player 1 follow through on his promise? He might leave pricing in the hands of a manager who has specific instructions to set a high price in response to player 2 setting a high price. Developing a reputation in a repeated interaction can also help.
Combining Threats and Promises
The US (player 1) and China (player 2) are considering whether to take action on North Korea’s nuclear program. The payoffs are shown below.
Action Inaction
Action 3,3 2,4
Inaction 4,1 1,2
The Nash Equilibrium is for only the US to take action, leading to payoffs of (2,4). But the US prefers for China to take action. How can it encourage this action?
• A commitment doesn’t work. Whether the US commits to action or inaction, China is better off with inaction.
• A promise alone doesn’t help. The US can promise action in response to action by China, leading to a payoff of 3 for China. But if China doesn’t take action, the best response by the US is action, leading to a payoff of 4 for China. Again, China is better off with inaction.
If you combine the above, you can see that what’s needed for the US to elicit action from China is to combine the threat and the promise. The US should threaten to do nothing if China does nothing
and also promise to take action if China acts.
Availability of Strategic Moves
The availability of a strategic movie (i.e. the ability to threaten or promise) can never hurt you. You could always choose not to exercise it. Indeed, having a strategic move available doesn’t help you if the response in question would have been optimal for you anyway. But having the ability to make a strategic move can help you if it allows you to choose a response rule that would not have been optimal for you, as a way to elicit favorable actions by other players.
What if you’re on the receiving end? Allowing yourself to be threatened is never optimal. You might think about trying to make your opponent’s threats less credible. On the other hand, promises can be beneficial for everyone. In the pricing example above, a credible promise to set a high price in response to an opponent setting a high price actually increases profits for both firms.
Some Practical Advice on Credibility
Credibility is the big problem in all of these examples. How can you convince an opponent that you are actually willing to do something against your own best interest when you threaten him or you make a promise? Here are some tips.
Automatic Fulfillment – Tie your own hands
• A country making a nuclear threat might turn over its nuclear response to a computer program. That should certainly convince your opponent that the threat will go through. • Congress might pass laws that automatically retaliate against export subsidies with tariffs.
The response is mandatory by law.
• Congress has passed mandatory minimum sentencing laws that force judges to impose high sentences for some crimes, even if the judges think the sentence is excessive. The hope is that the law deters many crimes from being committed at all.
Again, the key in all of these cases is that you are actually committing to a response that is worse
Delegate Authority
• You might tell a potential employer that you’re going to reject a job offer unless he sweetens the deal. But would you really reject it if you don’t have any other offers? Maybe you should hire an agent to negotiate for you, and the agent only gets paid if she holds out for better terms. You might not have a credible threat to reject offers, but your agent does. It’s important here that the employer believe that your agent actually has the final say to reject offers and that you will not override her.
• To commit to a certain pricing strategy, use a machine to set your product prices rather than setting them yourself. Again, your opponent must believe that you can’t override it.
Burn your Bridges – Don’t give yourself any option to retreat
• An attacking army might burn its own bridges to prevent themselves from retreating. This convinces the enemy force that the attacking army is committed to fighting to the end, and the ememy might back down as a result.
• Japanese Kamikaze pilots carried only enough fuel to reach the enemy ship, not to come back. This is a credible commitment to crash into the ship. The pilot is going to die anyway. • Tearing down the Berlin Wall was a commitment device for communist East Germany to
reform. If they hadn’t reformed, then everyone would have left East Germany.
• Some companies refuse to diversify their product lines as a way to make a credible threat to defend their existing market. By refusing to diversify, they’re all in and protecting the market aggressively is their only choice.1
• The EU decided on a common currency instead of countries’ maintaining their own currencies and setting fixed exchange rates (which is equivalent). This served as a commitment, making it impossible for countries to back out. If countries maintained their own currencies, it would have been possible down the line for a country to abandon the fixed exchange rate if it found it to be unfavorable. But, by changing the whole currency, it would be extremely costly for countries to go back to their local currencies at this point.
Cut off Communication
You might send a threat and then simply refuse to communicate with the other person.
• Republicans in Congress were negotiating the budget with Democrats. If a budget was not passed by a certain date, the government would default on its debts, which is very costly for all sides. The Republicans submitted a budget that was unfavorable to the Democrats and wanted to convince Democrats that they were unwilling to negotiate further. They
1 An amusing quote along these lines is: “Some fools say ‘Don’t put all your eggs in one basket.’ I say put all your
passed the budget and immediately they all left. This left the Democrats with no other choice than to acquiesce to the Republican budget.
• Labor unions that call a strike are required to call a general meeting to agree on contract terms before they can call off the strike. Calling general meetings is very time-consuming. In essence, this means that once the labor union strikes, it is legally impossible to end the strike for several weeks. This might be enough to get concessions out of management.
Maintain a Reputation
• A mechanic promises to do high-quality work on your car, but you know that he has an incentive to provide low-quality work to increase his profit margin. But if you go back to him over and over again, his promise might be credible, since you can punish him for doing shoddy work. It might even make sense to pay him more than the market rate for other mechanics so that he will try to keep you as a customer.
• A country threatens to blow up everyone who takes hostages, even if it kills all the hostages in the process. This seems costly to exercise when it actually has to be implemented, but it might actually save lives over the long-run by establishing a reputation for toughness and refusal to negotiate with hostage-takers. In essence, not following through with the threat could create a short-term benefit to save the hostages, but it creates a huge long-term cost by destroying the country’s reputation and encouraging future hostage-takers.
• A firm had an odd sign on the road: “128 year in business and never a discount!” Why would you advertise that? Well, when companies regularly discount their products, customers just learn to wait for discounts – and, indeed, the company may not have a credible commitment to refuse to offer the discounts since so many of their customers expect it. But by maintaining a reputation of never discounting, the company’s commitment never to lower its price or offer discounts is actually credible. Customers are willing to pay higher prices knowing that the firm will never discount.
• A failed example is tax amnesty programs. A government tells taxpayers that if they admit that they cheated on their taxes, they can pay the back taxes with no additional penalties. But it warns people not to cheat anymore in the future, since this will be the last time the amnesty is offered! Really, really, really, we promise this is the last amnesty… But is that credible? The government makes huge revenues every time they make an amnesty offer.
Move in Small Steps
• Peace treaties between countries often specify small, sequential steps. One party can’t be expected to give up everything immediately on the promise that the other party will fulfill its part later on. (Note that it’s important that there not be any “last” step, or the cooperation can unravel backwards since the person who is supposed to take the last step has no incentive to follow through, then the second-to-last country has no incentive, etc… – the countries should always have an opportunity for future business with each other).
Teamwork
You might think about having people monitor each other. If one person fails to carry out a threat or a promise, the other people in the team are required to inflict some punishment on him.
• Diet centers often apply peer pressure to dieters who fail to follow through on their promises to lose weight.
• The Roman army made it a death penalty offense to retreat in battle. They also made it a death penalty offense to fail to kill someone else who retreated. You could be sure that when the Roman army attacked, the soldiers weren’t going to chicken out.
• Parents often don’t follow through on punishing their kids. But maybe a father’s wife yells at him if he doesn’t follow through on his threat. This could be enough to convince the kids that he’s actually going to follow through. So maybe the kids will decide to behave in the first place.
Irrationality
This is an interesting one. The normal problem is that, if you make an extreme threat, other players won’t consider it to be credible because they know that it would be too costly for any rational person to follow through on the threat. Thus, acquiring a reputation for being a slightly crazy, irrational person might actually help you in this case! When you make threats, other people might think that you’re actually crazy enough to follow through on them. This is called rational irrationality.
Contracts
For a promise, you can easily make a contract with the other party, who can take you to court if you fail to follow through on your promise.
Countering Strategic Moves
Promises can be good for everyone, but what should you do in response to threats from someone else? Is there a way to make your rival’s threats less credible or to disincentivize him from issuing threats in the first place?
Irrationality
This cuts both directions. We argued before that it can be good for a person making threats if his opponent views him as irrational. But a reputation for being crazy can be good for the person on the receiving end of the threats too. If you are so irrational that you would never give into a threat, then your opponent might realize that there’s no point to making and following through on threats.
Cutting off Communication
One way to avoid being threatened is not to be open to threats in the first place. If a child screams loudly enough, the volume can prevent his parents from issuing threats.
Leaving Escape Routes Open
If your opponent burns his bridges down to try to convince you that he won’t retreat, you might consider building them again. If you are being threatened, but you think there is a chance that the other person might not actually follow through on the threat, it’s always a good idea to give your opponent an “out” that lets him escape without too much cost. Don’t insult him and embarrass him when he retreats. That would reduce his motivation to retreat in the first place.
Reducing Reputation Motive
Suppose a seller refuses to cut his price for a transaction with you on the grounds that it would ruin his reputation with other buyers for maintaining a high price. You might promise him that you won’t tell any of the other buyers. This is good for the seller because he can complete the transaction with you and keep his reputation intact.
Salami Tactics
A good way to get rid of an opponent’s threat is to dismantle it little by little. If you take an action that your opponent doesn’t want, but you just do it a tiny amount at a time, he won’t find it worthwhile at any stage to actually exercise the threat. It’s too costly.
• A parent threatens to punish his child if he doesn’t do his homework, but the child dismantles the threat by putting it off 15 minutes at a time. At each stage, it isn’t worth it for the parent to exercise the punishment.
Case Study 1: Job Applications
You end what appears to be a really successful interview with a firm. The firm tells you that it wants to hire you, but it will only hire you if you accept the job immediately and do not search for any additional job offers. If the firm really wants you, will it actually refuse to hire you if you come back tomorrow? If it wants to maintain a long-term reputation in the job market, maybe.
Case Study 2: Free Trade Agreement
The US once hinted at military action against Japan if Japan didn’t start importing more American meat and vegetables. This was a spectacularly stupid exercise of strategic moves.
• The threat was totally non-credible.
• The Japanese would probably reconsider whether to cooperate on anything after such a threat.
• It was actually lose-lose for the US. If the US actually carried out the threat, it would look terrible to the international community. But if the US doesn’t carry out the threat, it loses its reputation and acquires a bad reputation for making empty threats.
• The threat has no connection to the original problem.
This example teaches us a few important things about strategic moves.
• The act of making a threat is itself costly since it can color your future dealings with anyone else who observes that you issued the threat. People might be unwilling to do any business with you at all.
• While it is true that a successful threat wouldn’t actually need to be carried out, there is always a risk of mistakes. For example, someone may misunderstand the instructions. • An excessive threat is actually counterproductive. It is less likely to be credible.
The general lesson here is that, when you have a whole menu of options, you should go with the
smallest threat that will do the job. Excessive threats are not credible and they make you look foolish (i.e. lose your reputation).
Brinkmanship
Suppose that a threat is so large and costly to implement (for the person doing the threatening) that the person making the threat has no credibility. While a threat may be too large to actually pull the trigger, the threat of some probability of the trigger being pulled may have credibility.
incursion, might be too large and lack credibility. But the country making the threat might instead create a situation where there is a continuous escalation of risk that a bad outcome can occur by accident.
Imagine two people fighting on the side of a cliff. If they go over, then both of them die. It’s not a credible threat to push the other person over, because you’ll go down too. But you might think about dragging the fight closer and closer to the edge of the cliff, escalating the risk that you
accidentally go over. What you hope is that the escalation of risk will become intolerable to your opponent before it becomes intolerable to you, and that he will give up.
The key feature of brinkmanship is that the outcome is not totally within the control of the person doing the threatening. Launching the invasion or deliberately pulling the fight over the cliff is not credible, but a continuous escalation of the risk that it might happen – outside of your control – may be credible. Here are a few real-world examples.
• In 1962, the Soviet Union deployed a large number of nuclear missiles to Cuba, less than 100 miles from the US. President Kennedy continually increased pressure on the Soviets to withdraw their missiles. The threat to launch a war outright was not credible, as it would have been devastating for both sides, but Kennedy’s actions really just escalated the chance
that a war might break out by accident (maybe two ships ended up in a confrontation with each other because of a navigation mistake). The Soviets backed down. This is a widely-known example of an effective exercise of brinkmanship.
• Leaders of labor unions sometimes threaten to go on strike, but going on strike is costly both for the employer and for the workers, so employers might not view the threat as credible. Instead, a better strategy by labor unions is brinkmanship, where the risk of the negotiations breaking down continually increases.
• Spouses who are fighting with each other might threaten divorce, but divorce is extremely costly for both spouses. Instead, a spouse might be better off to just escalate the risk that one or the other will “go crazy” and file for divorce.
The common feature of all of these examples is that there isn’t a sharp breaking point, but rather a slippery slope that continuously gets steeper and with an escalating risk of going over the edge.
situation that is dangerous enough to make your opponent back down before it becomes too dangerous for you to keep going.
Exercise of Brinkmanship in Practice
Uncertainty
In order for brinkmanship to be effective, there must be an element of uncertainty. The US can’t simply threaten to attack and give a deadline because the threat is too large to be credible. Although the threat of certain war isn’t credible, the threat of a risk of war materializing might be. This is much like moving in small steps – basically, breaking up a huge threat into a series of small escalations of risk.
Creating and Controlling Risk
Literal randomization won’t work. Suppose the US wants to use brinkmanship with a 50% chance of war materializing. Can it just flip a coin and start a war if it comes up heads? That won’t work Even if the coin does come up heads, the US has no incentive to actually follow through with a costly war.
The essence of brinkmanship is that somehow a risk of war has to be created that isn’t completely within the control of the US. The idea is to create a situation slightly out of control. Go back to imagining two people fighting on a slippery slope. Nobody is actually going to “pull the trigger” and deliberately push the other person over. But, the closer they get to the edge, the higher the risk that someone will slip and they end up over the brink by accident. Hopefully your opponent will give in before you find yourself too close to the edge that you yourself give up.
How can you create a risk of an action that is outside of your control? In the case of the Cuban Missile Crisis, the US claimed that – as it sent more and more ships – the risk of an inadvertent confrontation occurring would continue to rise. Maybe the crazy generals would feel threatened and fire on a Russian ship. Maybe nobody on board the Russian ship would be able to speak English to diffuse the situation. In other words, President Kennedy correctly claimed that the risk of conflict breaking out was largely outside of his own hands.
Similarly, imagine that a captive has a secret and a pirate threatens to kill him if he doesn’t reveal the secret. That’s certainly not a credible threat since the pirate definitely won’t learn the secret if the captive is dead! But the pirate might claim that, if the captive doesn’t tell him, he’ll get angrier and angrier, and then he might kill the captive in a fit of rage. It’s never a rational response to pull the trigger, but his emotions might escalate to the point that the situation is out of control.
Getting off the Brink Safely
If you are going to use brinkmanship, it is important to have an “exit strategy”. Make sure that the risk can be controlled. If it escalates too quickly and gets too far out of control, the bad outcome might actually materialize. For the examples above, the President has to be able to pull the generals back if the Soviets withdraw, and the husband and pirate have to be able to cool down their tempers. You have to actually be able to withdraw the risk once you get what you want.
A poor application of this principle is US trade policy. US trade negotiators often threaten that Congress might go crazy and pass restrictive embargoes (costly for both sides) if the other country doesn’t give some concession that the negotiators want. But the trade negotiators have no control over Congress. A protectionist Congress might pass the trade restrictions no matter what happens in the negotiations, and a market-oriented Congress would never pass trade restrictions.
Falling off the Brink
With any exercise of brinkmanship, there is a danger that the risk will actually materialize and the parties will end up “going over the brink” before either of the parties gives in.
An unfortunate historical example is the Tiananmen Square incident. Protestors kept growing their numbers and refusing to back down. The government continued sending in more troops, which escalated the conflict. The government surely had no credible threat to deliberately kill thousands of people, as that would make the government look terrible. Rather, as the situation became more volatile, the outcome transpired by accident when one soldier mistakenly thought he was being shot at, making the situation explode. Neither side backed down, and 2600 people died. In this instance, the parties actually ended up falling off the brink.
Concluding Remarks
To game theorists, a more cogent argument is that the nuclear arms race is an exercise in brinkmanship. The key ingredient is that neither you nor your rival knows exactly where the breaking point lies. The following quote by political scientist Barry Posen speaks well to the strategic considerations in an exercise of brinkmanship.
Escalation has generally been conceived of as either a rational policy choice, in which the leadership decides to escalate in the face of a conventional defeat, or as an accident – the result of a mechanical failure, unauthorized use, or insanity. But brinkmanship actually falls between the two. It is neither a purposeful act nor an accident. Rather, it is unintended consequences associated with conventional
choices.
Let’s finish with some practical advice on using brinkmanship.
• Start small and safe – You shouldn’t start with the most serious escalation in your arsenal. For example, the labor union shouldn’t call for a strike on the first day of negotiations. • Raise the risk gradually – Maybe you should do some small things that are costly for you
to indicate that you are serious. In the case of the threatened divorce, maybe the husband can hire a lawyer and pay a retainer.
• Try to deduce the other side’s position – Will the other side give in? Maybe the Soviets will never give in to threats. Maybe the owner of the firm can’t afford the labor union’s demands, no matter whether there is a strike or not. In these cases, brinkmanship is pointless since the other side will never concede to your demands.
Problems
1. For each game below, answer the following questions. (i) What is the Nash Equilibrium if neither player uses strategic moves? (ii) Can any player improve his payoff by using a strategic move? If so, what moves?
a. Game 𝐺𝐺1
L R
U 0,0 2,1
D 1,2 0,0
b. Game 𝐺𝐺2
L R
U 4,3 3,4
D 2,1 1,2
c. Game 𝐺𝐺3
L R
U 4,1 2,2
D 3,3 1,4
3. The United States and the Soviet Union play the game given below. Each country can be restrained (𝑅𝑅) or aggressive (𝐴𝐴)
a. If the two countries choose simultaneously, what is the Nash Equilibrium?
b. If the United States moves first and the Soviet Union observes its move, what is the subgame perfect equilibrium?
c. If the Soviet Union moves first and the United States observes its move, what is the subgame perfect equilibrium?
d. Suppose now that the Soviet Union moves first, the United States observes its move, but then the Soviet Union has a chance to change its first move. What is the subgame perfect equilibrium?
e. If the Soviet Union moves first, is it better off by having the flexibility to change its move later on? Give an intuitive explanation in the context of strategic moves.
R A
R 4,3 1,4
A 3,1 2,2
4. Firm 1 can produce product A or produce nothing at all. Firm 2 can produce product B, product C, both products, or neither product. Profits, as they depend on the aggregate production set, are given below. The game proceeds as follows. Firm 2 first decides on whether or not to make a commitment to produce B (leaving its decision open about whether to produce C). Firm 1 then decides whether it will produce A. Firm 2 then makes a decision on its production set. What is the SPE outcome? What would have been the SPE outcome if firm 2 had no ability to make a commitment up front? By how much does the ability to make a commitment increase profit for firm 2?
Production Set Π1 Π2
None 0 0
A only 6 0
B only 0 6
C only 0 10
AB 2 1
AC 4 3
BC 0 8
