When Immediate Responses Fail.

Author:Dothan, Shai
Position:Game theory in laws of war, criminal law, international sales law


  1. INTRODUCTION 1076 II. THE TIT-FOR-TAT STRATEGY AND ITS WEAKNESSES 1080 A. When Tit-for-Tat Is Optimal 1081 B. A Delayed Response Deals Well with Noise 1082 C. Using Stronger Penalties to Sustain Deterrence 1084 III. PROPORTIONALITY AND THE LAWS OF WAR 1086 A. "Armed Attack" and the Accumulation Doctrine 1089 B. Jus Ad Beilum Proportionality 1090 C. Blurring the Lines Between Jus Ad Beilum and 1092 Jus in Bello IV. DISPROPORTIONATE PENALTIES FOR REPEAT 1093 OFFENDERS A. Wny Career Offenders May Deserve a Higher 1096 Penalty B. Incapacitating Career Offenders 1098 C. Improving Deterrence for Career Offenders 1099 V. DELAYED RESPONSES IN INTERNATIONAL SALES LAW 1101 A. Non-Legal Sanctions in Contractual Relations 1103 B. Tit-for-Tat under the CISC 1104 C. The Nachfrist Notice Procedure 1106 VI. CONCLUSION 1107 I. INTRODUCTION

    The rule of law depends on several foundational principles: the procedures that determine the existence of a legal breach and the form of the legal retaliation must be clear, (1) wrongdoers can be punished only after they violate the law, (2) and the response used against them must be proportional to the gravity of the breach (3) and issued close to the time of the breach itself. (4) These principles concur with the attributes of a tit-for-tat strategy, a strategy that was found to lead to cooperation between parties in a variety of situations. A tit-for-tat strategy is clear (easy to understand), nice (does not defect first), retaliatory (responds immediately), and forgiving (responds proportionately). (5)

    Consider the rule that a country may respond to hostilities directed against it by another country that do not amount to an "armed attack" only with steps that are immediate, necessary, and proportional. (6) Or the rule that allows only proportional responses as a countermeasure even against an armed attack. (7) These are clear examples of a tit-for-tat strategy. In interactions between well-organized countries of similar strength, this strategy allows each country to gauge the intentions of the other, promoting cooperation and preventing deterioration into war.

    But in interactions between a stronger, well-organized country and a weaker country that cannot control militants acting from its own territory, a tit-for-tat rule can lead to a cycle of attacks and counterattacks. The stronger country may mistake hostilities by militants acting from the territory of the weaker country as deliberate attacks by the weaker country. If the stronger country responds immediately, the weaker country may retaliate, and both countries will spiral into a series of counterreprisals culminating in war.

    If, however, countries were allowed to delay their response as they analyzed the actions and intentions of the other country and after a while respond with disproportionate force, the deterioration may be prevented. Furthermore, future aggression can be prevented by incapacitating or weakening the enemy, not just by deterring it. If a stronger country is allowed to use disproportionate force, it can minimize the ability--not only the motivation--of the weaker country to harm it. What is needed to serve these goals is simply a doctrine of many-tits-for-many-tats.

    Developments in the international laws of war follow this logic. They allow a country to accumulate several small attacks against it that do not individually constitute an "armed attack" and treat them all as an armed attack that deserves a strong response. (8) Furthermore, even a response to an armed attack is constrained by some level of proportionality, but states can aggregate several armed attacks, using the so-called "pin-pricks" doctrine, and respond to all of them together with a force far greater than that mandated by each individual attack. (9)

    Criminal law offers another example of this dynamic. Usually, criminal sanctions are directed at a specific violation of the law and are proportional to the gravity of the violation. The state therefore uses a tit-for-tat strategy against potential offenders. Some jurisdictions, however, adopt disproportionate penalties against repeat offenders that are intended to remove such offenders from society for a very long time. One form of escalating punishments for repeat offenders is the so-called "three-strikes-and-you're-out" rule. (10) These rules are directed against recidivist offenders that chose a life of crime and are likely to commit more crimes in the future if released (career offenders). The ability to aggregate information over several offenses before a disproportionate response is used allows the state to separate these career offenders from offenders who committed a single offense without adopting crime as a way of life. Even if the state knows that an accused committed an offense with certainty, it is only the accumulation of offenses that allows the state to know this crime is not a result of a mistake or a one-time opportunity, but rather the actions of a career offender.

    A third strike can separate a career offender from society and incapacitate his ability to commit more crimes. (11) The disproportionate response that is meted out as a "third strike" might deter potential career offenders from committing even their first crime because they know they may not be able to avoid committing crimes in the future and therefore a first crime increases the chances that they will end up suffering this greater penalty. (12)

    International sales law offers another example for a legal regime that is generally committed to proportional responses. The United Nations Convention on Contracts for the International Sale of Goods (CISG) (13) allows a party to an international business contract to respond to a breach by the other party in a proportional manner. (14) If the breach is fundamental, the damaged party can avoid the contract, releasing it from all its contractual obligations. (15) If the breach is not fundamental, the damaged party can only take certain countermeasures that are proportional to the gravity of the breach and intended to save the contract. (16) In addition, it can also sue the other side for damages. (17)

    Nevertheless, if a seller--in breach of the agreement--does not deliver the goods on time, the buyer may set an extended period for fulfilling the contract. The buyer has to inform the seller of this extended period in what is known as a "Nachfrist Notice." (18) If the seller does not deliver within the extended period, the buyer can avoid the contract, thereby responding disproportionately to a continuing violation even if it does not constitute a fundamental breach. The grace period given to the seller allows the buyer to gauge the seller's intentions before issuing that disproportionate response. (19)

    These examples demonstrate that legal systems often have a preference for immediate and proportional responses and, by this, favor a tit-for-tat strategy. This Article argues that in some situations--particularly in conditions of uncertainty--a disproportionate and delayed response is preferable as it can deter more effectively and prevent the ability to commit future violations. A strategy of many-tits-for-many-tats that allows the responder to aggregate several wrongful actions toward it before it responds with a strong sanction may therefore be sometimes preferable. This analysis justifies and explains certain legal regimes that contradict the predominant tit-for-tat strategy.

    Part II describes the tit-for-tat strategy, the game theory that supports its use, and the situations in which it will lead to inefficient results. Part III presents the laws of war that usually prevent countries from responding disproportionately to hostilities against them and reviews several cases in which a disproportionate response is nevertheless legal. Part IV presents the benefits of disproportionate penalties for repeat offenders in criminal law. Part V reviews a disproportionate response to breach of contract in international sales law as an exception to the general proportional responses allowed by the CISG. Part VI concludes.


    In some situations, cooperation is a strategically wise choice: all drivers are better off driving on the right side of the road in New York and on the left side of the road in London. These situations are known in game theory as coordination games. (20) They only require a good source of information and a little patience to lead rational players to cooperative behavior that is beneficial to both of them. (21)

    Unfortunately, not all situations in life can be modeled as a coordination game. There are situations in which the rational thing for both parties to do is to betray each other. The most notorious situation of this kind is known as the prisoner's dilemma. The metaphor behind the prisoner's dilemma is a story in which two accomplices are caught in the middle of a crime. The police put them in separate rooms and make each the same exact offer: "If you choose to rat on your friend and he stays silent, you will get out without a penalty and your friend will stay in prison for a very long time. If you confess and so does your friend, you will both get a couple of years in prison. If you both stay silent, you will both go to prison for only one year. Finally, remember that we made your friend the same offer." (22)

    A rational prisoner would quickly realize that the smart thing to do is always to rat on his partner. If the partner stays silent, the snitch would go home scot-free. If the partner confesses, telling the police what you know can reduce your penalty from many years to just a couple of years in prison. Given that both prisoners are rational and egoist, they would always betray each other. (23)

    The tragic thing about the prisoner's dilemma is that if both prisoners confess, they would both go to prison for a couple of years. They could have each spent just one year in prison if only...

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