A Game of Torts

Introduction

If something can go wrong, it will.
— Murphy's Law

When there is a vehicular accident, the driver, if there is fault or negligence on his part, is obliged to pay for the damages caused by his or her act or omission.¹ What if there is no driver, who pays?

On 7 May 2016, Joshua Brown died when the autopilot sensors of his Tesla Model S failed to detect a white tractor-trailer and crashed full speed under the said truck.² This was the first known death caused by a self-driving car.³ According to the National Transportation Safety Board (NTSB), part of the probable cause of the crash was the driver’s inattentiveness due to his over-reliance on the autopilot mechanism of the car.⁴ As a result, the NTSB said that the car manufacturer, Tesla, is not at fault⁵ in line with the finding of the National Highway Traffic Safety Administration (NHTSA) which found no defect in the self-driving system of Tesla.⁶ However, the reason for this is because the Tesla self-driving car is only a level 2 system⁷ wherein the driver’s engagement during the operation is still necessary.⁸ Once a car reaches Level 3 automation, “the responsibility for monitoring the driving environment shifts from the driver to the system.”⁹

In that case, a difficulty arises in finding who should be liable in case there is an accident as the driver is no longer the one primarily responsible for the safety of his journey. The problem becomes more apparent in cases of Level 5 autonomous vehicles,¹⁰ or fully autonomous cars requiring no human intervention. Once the roads are filled with fully autonomous cars, who would be held liable if there is an accident? In other words, who will be at fault if a vehicle gets into an accident when there is no more human driver because only the computer artificial intelligence (AI) is in control?¹¹ While autonomous vehicles may be safer,¹² the question of liability cannot be neglected as accidents are inevitable. In the words of Vladeck, “[n]o matter how well-designed and programmed self-driving cars are, factors beyond the machine’s control virtually guarantee that at some point the car will have an accident that will cause injury of some kind, and will act in ways that are not necessarily ordained by their programming.”¹³

The law on torts governs such circumstance. There is difficulty because the principles of reasonability, foreseeability, and causation are the primary bases for liability in the law on torts.¹⁴ Given the autonomous and unpredictable nature of AI systems, it is unclear how these principles apply.¹⁵ Can there be such a thing as a reasonable AI? If so, by what standard? If we cannot determine the reasonability of an AI’s action, how can we ascertain the foreseeability of an accident? Who or what will be considered as the proximate cause of the accident? These questions all lead to the main question of, “who pays?”

There are several liability regimes under the law on torts which may be used in determining “who pays” such as strict liability, vicarious liability, and comparative negligence. These different regimes affect the behavior of the people in different ways. Still, they all point to the primary tort law goal of preventing accidents and minimizing losses.¹⁶ Law is a mode of regulating people¹⁷ in order to achieve social order.¹⁸ The specific social order sought by the law on torts is the protection of people from injuries caused by other members of society, whether through willful intent or through negligence.¹⁹ This objective is done through the imposition of liability for whoever causes injury by breaching the mutual duties imposed by the society, as measured by the legal rights of each member of society.²⁰ Such imposition of liability “substantially affects how categories of actors respond to the risks they create or confront.”²¹ Thus, different liability regimes lead to different behaviors. For instance, if no liability is imposed on motorists when they injure pedestrians, then there would be no incentive for them to exercise due care leading to the inference that they would not exercise due care thereby increasing the number of accidents.²²

This Paper will attempt to compare different liability regimes as applied in the case of accidents involving autonomous vehicles by determining how they might affect the behaviors of different actors in society such as motorists, manufacturers, or pedestrians by using game theory. Game theory is defined as “a set of tools and a language for describing and predicting strategic behavior.”²³ Strategic behavior arises when there are at least two interacting actors and their decisions depend on the expectation of each actor of what the others will do.²⁴ This means that “our behavioral decisions are intertwined”²⁵ and such fact must be taken into account in predicting outcomes and in regulating behaviors such as in a legal system.²⁶ Thus, game theory may be able to provide assistance in determining “who pays” by providing insights as to how different liability regimes may affect the way people will behave.²⁷ Such predicted behaviors will then be juxtaposed with the underlying values and objectives of tort law.

Torts

Definition

The word “tort” is a French term which originated from the Latin word torquere which means “to twist.”²⁸ This is because a tortious conduct is a conduct that is considered twisted or crooked.²⁹ It is an “unlawful violation of private right, not created by contract, and which gives rise to an action for damages.”³⁰ It is also defined as “an act or omission producing an injury to another, without any previous existing lawful relation of which the said act or omission may be said to be a natural outgrowth or incident.”³¹ Thus, the basic elements of a tort are:

1. Damages suffered by the plaintiff;
2. Fault or negligence of the defendant, or some other person for whose acts he must respond; and
3. Connection of cause and effect between the fault or negligence of the defendant and the damages incurred by the plaintiff.³²

Thus, tort law deals with situations where a person injures another person by breaching his legal duty not to violate the right of another member of society.³³ Consequently, it is the law governing cases of vehicular accidents. In determining “who pays,” it is thus necessary to look into the underlying values of tort law and its purposes.

Purpose

Tort law contributes to the objective of the law to reduce, or if possible, to eliminate risks in society by providing deterrence to harmful activities.³⁴ However, since it is impossible to totally eliminate injuries because “men voluntarily accepts risks as a quid pro quo for their needs,” tort law provides the alternative of providing redress to anyone injured,³⁵ i.e., allocating risks and liabilities in the society.³⁶ Jurists are in agreement that the central aim of tort law is the reduction of accidents.³⁷ In line with this, the major purposes of tort law are:

1. to provide a peaceful means for adjusting the rights of parties who might otherwise take the law into their own hands
2. to deter wrongful conduct
3. to encourage socially responsible behavior
4. to restore injured parties to their original condition, insofar as the law can do this, by compensating them for their injury.³⁸

In addition, tort law also aims to balance conflicting interests.³⁹ As Dean Wright explained, doing all the things that constitute modern living necessarily leads to some losses or injuries.⁴⁰ Thus, according to her,

[t]he purpose of the law of torts is to adjust these losses and to afford compensation for injuries sustained by one person as the result of the conduct of another…The study of the law of torts is, therefore, a study of the extent which the law will shift losses sustained in modern society from the person affected to the shoulder of him who caused the loss or more.⁴¹

Theoretical Justification

There are two main theoretical perspectives justifying tort law and the shifting of losses — the moral and social perspective.⁴²

Under the moral perspective, liability may be imposed on a tort because such act or omission is considered a moral wrong.⁴³ This perspective is in line with the maxim Ubi jus ibi remedium — there is no wrong without a remedy.⁴⁴ It may be said that the liability imposed by tort law is deemed as a private penalty for the wrong done because of one’s moral shortcoming.⁴⁵ As such, if no wrong is done, there should be no basis to impose liability under this perspective.

The social perspective justifies the imposition of liability for tortious conduct “because of the good that it will do to the society as a whole and its function of encouraging socially responsible behavior.”⁴⁶ This perspective is in line with the idea that law is a mode of regulating behavior. It is also reflected in the purpose of tort law of balancing conflicting interests.⁴⁷ From this perspective, the imposition of liability encourages certain behaviors which contribute to the social order and deters others which may be detrimental to the social order.

A slight variation of the social perspective is the economic perspective which views tort law as a system of allocating risks in order to maximize wealth and minimize costs.⁴⁸ The statement of the Court in Phoenix v. IAC⁴⁹ that “[o]ur law on quasi-delicts seeks to reduce the risks and burdens of living in society and to allocate them among the members of society”⁵⁰ is reflective of the economic perspective.⁵¹ The economic perspective may also be used to justify liabilities not arising from fault or negligence, i.e., strict liability torts.

Classifications

In order to cover the wide spectrum of injuries and accidents, tort liabilities are classified into three: intentional torts, negligence, and strict liability.⁵² Intentional torts are those wherein the injury caused is actually intended by the person who caused the injury.⁵³ In contrast, negligence torts are committed when one fails to do an act or omission with due care and causes foreseeable harm to another.⁵⁴ Lastly, strict liability torts are those wherein one may be held liable regardless of the existence of fault or negligence on his part.⁵⁵

These classifications translate to different liability regimes which may be used in allocating liabilities in accidents involving autonomous vehicles. This paper will limit itself to the following liability regimes: strict liability, strict liability with the defense of contributory negligence, and no liability.

To understand how autonomous vehicles may disrupt tort principles, an inquiry into AI systems and autonomous cars is in order.

Autonomous Vehicles

Brief History

Throughout history, humans have been continuously aspiring to make life easier and better.⁵⁶ One way of achieving such aspiration is to make artificial creatures capable of doing our tasks for us. We call these creatures robots.

In the year 1961 robots were first employed in the automobile industry.⁵⁷ The UNIMATE robot was used by General Motors in manufacturing cars to perform spot welding and to extract die-castings.⁵⁸ Soon after, they looked beyond creating more cars using robots but to create cars that are robots — fully autonomous cars.⁵⁹ However, mass adoption of robotic technology only began in the early 1980s when Japanese car industry began to use robots on a large scale in their factories thereby decreasing costs and increasing the quality of their products.⁶⁰ Eventually, the industrial robot industry became dominated by car manufacturers. It is therefore natural that several states, organizations, and private companies began to seriously pursue the project of creating autonomous cars, or unmanned ground vehicles (UGV) as they called it.⁶¹

In 1987—1995, the European Commission funded the Eureka Prometheus Project (Programme for a European Traffic of Highest Efficiency and Unprecedented Safety) to research on driverless cars.⁶² In the late 1990s, the Defense Advanced Research Projects Agency (DARPA) was authorized “to organize a series of prize competitions for driverless cars in order to develop the military sector of UGVs and make one-third of ground military forces autonomous by 2015.”⁶³ In the first race of the DARPA Grand Challenge competition on 13 March 2004, none of the cars was able to complete the race.⁶⁴ After a year and a half, five vehicles were able to finish the second race.⁶⁵ On 3 November 2007, Carnegie Mellon won the third DARPA race at a speed of 22.53 kph.⁶⁶ Fast forward to the present, autonomous cars no longer just run in DARPA races at 22.53 kph. Cars capable of partial or conditional automation are now available for the public.⁶⁷ We are now closer than ever in achieving the goal of turning our cars into robots.

Levels of Automation

Cars may be classified into six categories depending on the level of automation:

• Level 0 — No Automation
• Level 1 — Driver Assistance
• Level 2 — Partial Automation
• Level 3 — Conditional Automation
• Level 4 — High Automation
• Level 5 — Full Automation.⁶⁸

Level 0 cars are the traditional cars we have where there is totally no automation.⁶⁹ Level 1 systems have driver assistance wherein, under certain conditions, the car can control either the steering or the speed but not both at the same time.⁷⁰ An example of a level 1 system is an adaptive cruise control.⁷¹ Level 2 systems offer partial automation wherein the car is capable of steering, accelerating, and breaking in certain circumstances.⁷² In level 2 systems, the responsibility for monitoring hazards still primarily belong to the human driver.⁷³ Level 2 systems are pretty common now such as Tesla autopilot, Audi Traffic Jam Assist, and Mercedes-Benz Driver Assistance Systems.⁷⁴

The shift from Level 2 to Level 3 is pivotal as the responsibility for monitoring the driving environment now belongs to the system rather than the human driver.⁷⁵ In Level 3 systems, the car can manage most aspects of driving and only prompts the driver to intervene in instances it cannot handle.⁷⁶ Thus, the driver must still be available to take over the car at any time.⁷⁷ Upon reaching level 4 automation, human oversight or input is no longer necessary under certain conditions such as when driving in a highway.⁷⁸ Take note that the availability of the human driver to take over at any time is no longer necessary. Thus, under certain conditions, the computer system is fully in control of the vehicle. In Level 5 systems, the car achieves full automation.⁷⁹ This is like Level 4 systems but there is no longer any condition. As such, the car has the capability to drive and control itself under any condition. Consequently, the involvement of the human driver is limited to entering his destination.⁸⁰ There are currently no Level 5 systems yet, but some companies are already working towards developing one such as Waymo,⁸¹ which recently has been testing Level 4 autonomous vehicles in Arizona.⁸²

This Paper limits itself to accidents involving Level 5 autonomous cars where there really is no more human driver, and everyone can ride as a passenger. Further, it does not aim to deal with cases wherein there is negligence on the part of either the manufacturer, designer, suppliers, or the owner. As such, situations such as when the manufacturer fails to follow certain regulations or when there is an obvious bug in the software system are not covered in this Paper as they may be adequately handled by the current tort law principles such as strict liability for defective products or even liability due to negligence in accordance with the doctrine of res ipsa loquitur.⁸³ Likewise, instances where the accident is due to the negligence of the owner in the maintenance of his autonomous vehicle is out of the scope of this Paper as such is sufficiently addressed by the rules on negligence and foreseeability.

Thus, the circumstance being contemplated in this paper is when the accident was due to the autonomous car’s own decision. Since we do not know how AI systems really “think,” or how they arrive at a particular decision,⁸⁴ such a situation is problematic under the traditional paradigm of tort law imposing liability on who is at fault or at least who is presumed to be at fault. Thus, “for the first time ever, legal systems will hold humans responsible for what an artificial state-transition system ‘decides’ to do.”⁸⁵

Since it is difficult to apply the traditional principles of tort law in determining “who pays,” this Paper will instead study the behavior being encouraged or deterred by different liability regimes and compare those behavior to that sought to be achieved by tort law. Rather than ask the question of “why we should choose this liability regime,” this paper will instead ask “what happens if we choose this liability regime.” This is where game theory comes in.

Game Theory

Brief Overview

Law is a mode of regulating behavior.⁸⁶ By prescribing punishments, imposing liabilities, and giving incentives, law directs members of society to behave in a certain way.⁸⁷ As such, a law may be examined depending on how it affects the behavior of people. One way of examining such is using game theory.

Game theory is “a set of tools and language for describing and predicting strategic behavior.”⁸⁸ A core concept in this definition is “strategic behavior.”⁸⁹ When two or more persons interact with each other and each person’s decision depends on what that person expects the others will do, there is what we call a strategic behavior.⁹⁰ Because law regulates behavior, game theory becomes a useful tool in providing insights as to how the laws regulate the behavior of people.⁹¹

In game theory, interactions are modeled into a “game.”⁹² One known model is called the “normal-form game” or “strategic form” of a game.⁹³ The normal-form game has three elements:

1. the players in the game
2. the strategies available to the players
3. the payoff each player receives for each possible combination of strategies.⁹⁴

An Illustrative Example

The easiest way to explain the game is by using an example. For the illustration, an accident involving a traditional motorist and a pedestrian under a regime where there is no imposition of liability will be used.⁹⁵ The players in the game are the actors so they would be the motorist and the pedestrian. The options available to them constitute their strategies. For the purpose of studying the effect of tort law, the option of whether or not to exercise due care is appropriate.⁹⁶ In this context, due care means reasonable care, e.g., not driving too fast, following traffic regulations, carefully crossing the road, or not jaywalking.⁹⁷

When determining the payoff structure, the possible combinations of the available strategies shall be looked at and an outcome for each will be specified.⁹⁸ For instance, we can say that there will always be an accident unless both players exercise due care. Also, since it is impossible to altogether eliminate accidents, there would still be a ten percent chance of an accident when both exercise due care. Further, a value shall be attached for each strategy and outcome representing the costs thereof. In example, an accident costs 100 for the pedestrian because he will be the one injured and taking due care costs 10. Now that we have all the elements, we are now ready to “play” the “game” and analyze the expected behavior of the players in a regime where the costs of the losses are not allocated.

	No Care	Due Care
No Care	P: -100, M: 0	P: -100, M: -10
Due Care	P: -110, M: 0	P: -20, M: -10

Figure 1. Regime of no loss allocation in the context of traditional cars.

Payoffs: Pedestrian (P), Motorist (M)

As we can see here, the pedestrian suffers the losses from the accident amounting to 100 whenever he exercises no care. If he exercises due care and the motorist does not, he still suffers the losses from the accident (which is 100) in addition to the cost of exercising due care (which is 10), amounting to 110. Lastly, if both exercise due care, the pedestrian only suffers a total of 20 which is the amount of exercising care (which is 10) and the losses from the probable accident (which is ten percent of 100 or 10).

On the other hand, the motorist does not suffer any losses whether there is an accident or not, except for the cost of exercising due care. It is already apparent that the motorist will not exercise due care given that there is no incentive to do so. However, game theory provides tools for formally “solving” this “game” to find the strategy combination which the players will most likely choose.⁹⁹

The tools used to “solve” games are called solution concepts which are “general precepts about how rational parties are likely to choose strategies and about the characteristics of these strategies given the players’ goals.”¹⁰⁰

The fundamental assumption in game theory is that the players make choices in a rational manner such that they would “consistently prefer outcomes with higher payoffs to those with lower payoffs.”¹⁰¹ Once the players are presumed rational, then the preferred strategy of the motorist now becomes clear. Since the cost of exercising due care (which is 10) is always greater than the cost of not exercising care (which is 0) regardless of the choice of the pedestrian, then the motorist is most likely to pick the strategy of not exercising care.¹⁰² We can see that the choice of not exercising due care is “strictly dominant.” Strictly dominant strategies are those which is the best choice for the player for every possible choice of the other players.¹⁰³ In this case, if the pedestrian does not exercise due care, the payoff for the motorist is -10 if he exercises due care and 0 if he does not. It is thus only rational for him not exercise due care. If the pedestrian exercises due care, the payoff for the motorist is still the same, that is -10 if he exercises due care and 0 if he does not. Thus, for every possible choice of the pedestrian, the best choice for the motorist is not to exercise due care because it gives the highest payoff. The strategy of exercising due care is then called a “strictly dominated” strategy because it is always the worse option for every choice of the other player.

The concepts of “strictly dominant” and “strictly dominated” strategies are components of this solution concept: “A player will choose a strictly dominant strategy whenever possible and will not choose any strategy that is strictly dominated by another.”¹⁰⁴ However, this solution concept alone is not enough to solve the game. As we can see, the pedestrian has no dominant strategy available. If the motorist chooses not to exercise due care, then the better choice for the pedestrian is also not to exercise due care since it yields a payoff of -100 as opposed to -110. However, if the motorist exercises due care, the better strategy for the pedestrian is to also exercise due care since it yields a payoff of -20 as opposed to -100 which is the payoff if the pedestrian chooses not to exercise due care. As such, the first solution concept is inadequate to predict the likely strategy of the pedestrian.

When there is a dominant strategy for one player, then it makes sense for the other player to predict that such player would always choose the dominant strategy. Based on this, the other player needs only to compare his payoff when the other player chooses a dominant strategy. This solution concept is called iterated dominance, which states that

[a] player believes that other players will avoid strictly dominated strategies and acts on that assumption. Moreover, a player believes that other players similarly think that the first player will not play strictly dominated strategies and that they act on this belief. A player also acts on the belief that others assume that the first player believes that others will not play strictly dominated strategies, and so forth ad infinitum.¹⁰⁵

Applying this solution concept to this game, the pedestrian believes that the motorist will choose not to exercise due care as it is a strictly dominant strategy and exercising due care is a strictly dominated strategy. The pedestrian is then likely to choose not to exercise due care as it is the one with the better payoff when the motorist chooses not to exercise due care.

Based on our solutions, the likely outcome is that there will be more accidents when there is no law imposing liability on the negligent actor. The motorist has little incentive to exercise due care because the payoff for not exercising due care is always better than that of exercising due care. Thus, the outcome of the game is that the motorist will likely not exercise due care and the pedestrian will probably not exercise due care as well. Thus, it becomes apparent that a regime where there is no liability allocation invites accident by not giving incentives to exercising due care.

This is how a situation may be modelled and solved as a “game.” Now, it is time to apply these tools in the context of autonomous vehicles.

Games between an owner of an autonomous vehicle and a pedestrian

Regime of no loss allocation

As a base case, the first game will be that of an owner of an autonomous car and a pedestrian. The players will be the owner and the pedestrian. The strategies available for the pedestrian would be the same, i.e., to exercise due care or not. On the other hand, the exercise of due care in driving will not be available to the owner because he is not the driver of the vehicle anymore. Having no control over how the autonomous vehicle drives itself, the owner has no option to exercise due care in driving. As such, the choice available for an owner would whether to use his autonomous vehicle or not.

As for the payoff scheme, accidents still cost 100 but since autonomous vehicles are presumed to offer a safer driving environment,¹⁰⁶ there would only be fifty percent chance of accident if an autonomous car is used even if the pedestrian does not exercise due care. If the autonomous car is not used, there would be no chance of accident as there will be no car to hit the pedestrian. If the pedestrian exercises due care, the probability of an accident reduces to only five percent. Exercising due care in this game still amounts to 10. An additional cost of 20 would have to be introduced as when the owner does not use his autonomous car because he is presumed to want to take advantage of the technology of self-driving cars given its benefits.

Given these elements, the normal-form game in a regime of no loss allocation would look like this:

	Not Use	Use
No Care	P: 0, O: -20	P: -50, O: 0
Due Care	P: -10, O: -20	P: -15, O: 0

Figure 2. Regime of no loss allocation in the context of autonomous cars.

Payoffs: Pedestrian (P), Owner (O)

In this game, the strategy of using the autonomous vehicle for the owner is a strictly dominant strategy and that of not using the car is a strictly dominated strategy for the owner. The strategy of using the autonomous vehicle will always give a better payoff (which is 0) as compared to the strategy of not using an autonomous vehicle (which is -20) regardless of the choice of strategy of the pedestrian, thereby making it a strictly dominant strategy. Following the first solution concept of choosing strictly dominant strategies, then the owner would likely choose to use his autonomous car.

As for the pedestrian, following the second solution concept of iterated dominance, he would likely exercise due care since the payoff (which is -15) is better than not exercising due care (which is -50) when the owner uses the autonomous vehicle.

It can be seen in this game that the players are already likely to choose the most efficient strategy combination even without any loss allocation. Even though a regime of no loss allocation would not likely lead to a total elimination of accidents,¹⁰⁷ it was able to balance the conflicting interests of reducing accidents and utilizing the available technology. If we look at the sum of payoffs for every cell, the maximum of -15 (as compared to -20, -50, and -30) is achieved when the pedestrian exercises due care and an owner uses autonomous car. Thus, it seems that a no-liability regime is sufficient to achieve the optimum result from an economic perspective of tort law. The key difference here is the presumably safer driving environment brought about by the automation of vehicles thereby reducing human error. Thus, in a regime of no loss allocation, a pedestrian is encouraged to exercise due care and at the same time, the owner is given incentive to use an automated vehicle.

Regime of strict liability

A regime based on negligence does not seem to be applicable because there is no way for us to determine whether the AI system acted negligently or with reasonable diligence.¹⁰⁸ Hence, in the next game, we are going to use a regime of strict liability for the owner based on the doctrine of respondeat superior.¹⁰⁹ The autonomous car would be treated as a servant of the owner for which the latter, as the master, will be liable for the actions of the former. As such, the losses due to an accident would always be shifted to the owner. According to Posner’s Economic Analysis of Law,

the economic rationale for strict liability rules like respondeat superior is best explained in terms of incentives on defendants to alter the rate at which they undertake particular kinds of activity, Courts applying negligence standard typically examine how carefully a particular kind of activity is carried out, but do not question the level at which that kind of activity is engaged in the first place. Strict liability addresses that need, for potential injurers subject to strict liability can be expected to take into account possible changes in activity levels and expenditures on care, in deciding whether to prevent accidents.¹¹⁰

Thus, a strict liability regime is a proper regime if we want to alter not the degree of care of the motorist in driving (because the “motorist” is merely a passenger in this case) but the frequency of using an autonomous vehicle. While the only frequencies to be used are always and never, the game will still be able to show how a regime of strict liability would affect the activity level of the owner. All the rules and values assigned would be the same and only the liability regime would be different so that we can see how a different liability regime may affect the behavior of the players and the total efficiency of the system.

	Not Use	Use
No Care	P: 0, O: -20	P: 0, O: -50
Due Care	P: -10, O: -20	P: -10, O: -5

Figure 3. Regime of strict liability in the context of autonomous cars.

Payoffs: Pedestrian (P), Owner (O)

In this regime, the pedestrian is likely to not exercise due care as such strategy is the strictly dominant strategy. Whether the owner uses an autonomous vehicle or not, the payoff of 0 would always be better than the payoff of -10. Thus, according to the first solution concept, the predicted behavior of the pedestrian is to not exercise due care. In accordance with the solution concept of iterated dominance, the owner would be deterred from using an autonomous vehicle as the payoff of -50 when using the autonomous car is worse than the payoff of -20 when not using the car, given that the pedestrian would likely behave recklessly and not exercise due care.

Thus, in a regime of strict liability, the owner is discouraged from using the autonomous car and the pedestrian is encouraged not to exercise due care. While this encouraged behavior can eliminate accidents, it comes at the expense of not using the autonomous vehicles which we have been trying to develop since 1961.¹¹¹ A regime of strict liability would unduly deter the usage of autonomous vehicles given that there is an available choice of minimizing accidents when pedestrians exercise due care. Further, if we look at the total cost of this solution (-20), it yields more costs than the strategy combination of using the autonomous car and exercising due care (-15).

Regime of strict liabilit with the defense of contributory negligence

Given that the strict liability regime is too harsh which would lead to hampering technological advances, an alternative might be strict liability with the defense of contributory negligence. In this regime, the losses will always be shifted to the owner unless the pedestrian did not exercise due care. If the pedestrian does not exercise due care, then he cannot be compensated.

	Not Use	Use
No Care	P: 0, O: -20	P: -50, O: 0
Due Care	P: -10, O: -20	P: -10, O: -5

Figure 4. Regime of strict liability with the defense of contributory negligence in the context of autonomous cars.

Payoffs: Pedestrian (P), Owner (O)

In this regime, the dominant strategy of the owner would be to use the autonomous vehicle since he would always be better off what ever strategy the pedestrian adopts (0 against 20 when the pedestrian does not exercise due care and -5 against -20 when the pedestrian exercises due care). Following the iterated dominance, the likely strategy of the pedestrian would be to exercise due care since he would have a payoff of -10 as opposed to -50 if he does not exercise due care. The result therefore is similar to that of a regime of no loss allocation in that the use of autonomous vehicle is encouraged together with the exercise of due of the pedestrian. The key difference, however, is the allocation of the losses. In this regime, the costs of the accident are borne by the owner who takes the risk of using his autonomous vehicle. Thus, there will be compensation for the losses suffered by the pedestrian in an accident in case such pedestrian exercises due care as opposed to the regime of no loss allocation wherein the pedestrian suffers all the losses in an accident.

Take note of the major purposes of tort law which are:

1. to provide a peaceful means for adjusting the rights of parties who might otherwise take the law into their own hands;
2. deter wrongful conduct;
3. to encourage socially responsible behavior; and
4. to restore injured parties to their original condition, insofar as the law can do this, by compensating them for their injury.¹¹²

In this regime, the foregoing purposes are achieved. First, the regime was able to provide a peaceful means of adjusting the rights of the parties by providing allocating the costs of the accident whenever the pedestrian was exercising due care. Consequently, the regime is compensatory such that a pedestrian who exercises due care only incurs the cost of taking due care because the losses are shifted to the owner. Looking at the predicted behavior of the parties, not exercising due care which may be considered as a wrongful conduct is deterred and corollary thereto, the exercise of due care which is a socially responsible behavior is encouraged.

In addition, the purpose of balancing conflicting interests is also achieved. While the use of autonomous vehicles introduces risks which may lead to accidents, such also provides the comfort and convenience of riding as a passenger on a safer car. Thus, a balance must be made. While strict liability deters the use of autonomous vehicles, it is counterweighed by the defense of contributory negligence which insulates the owner from liability in case the pedestrian was negligent.

Given the foregoing, it seems that among the three regimes, the one that best reflects the purposes of tort law is the strict liability with the defense of contributory negligence. The above-mentioned games may also be applied to interactions between manufacturers/designers/programmers (MDP) and pedestrians.

Games between an MDP of autonomous vehicle and a pedestrian

Regime of no loss allocation

In a game between an MDP and a pedestrian, the strategies available to the pedestrian would still be to exercise due care or not. On the other hand, if we want to see how a liability regime affects the behavior of an MDP towards minimizing accidents and maximizing profits, a good strategy choice for the MDP would be whether to invest in research and development towards making autonomous cars safer than they already are or not.

As to the payoff structure, investing in research and development for safer cars would cost 10, similar to the cost of exercising due care. For the purpose of the games between MDP and pedestrian, the probability of accidents in the previous section shall be disregarded. As such, in this game, the default probability of accidents is sixty percent and the investment for safer cars will result to the probably of accident being reduced to thirty percent. In addition, when the pedestrian exercises due care, the probability of accidents is reduced by fifteen percent. Also, it is presumed that the owners of autonomous vehicles opt to use their cars.

Given these elements, the game in the base case where there is no loss allocation looks like this:

	Not Invest	Invest
No Care	P: -60, MDP: -0	P: -30, MDP: -10
Due Care	P: -55, MDP: 0	P: -25, MDP: -10

Figure 5. Regime of no loss allocation in the context of autonomous cars between MDP and Pedestrian.

Payoffs: Pedestrian (P), MDP (MDP)

In this game, the pedestrian bears the cost of the accident (which is sixty percent of 100) if MDP chooses not to invest. If the pedestrian chooses to exercise due care, the probability of an accident will be reduced by fifteen percent but he incurs a cost of 10 for exercising due care (thus his payoff is forty-five percent of -100 plus -10, or -55). Since the probability of accidents is reduced if MDP chooses to invest, then the payoff to the pedestrian if he chooses not to exercise due care is -30 and -25 if he exercises due care. As to MDP, it is not affected by the probability of an accident at all since there is no allocation of loss.

Pursuant to the first solution concept, MDP is likely not to invest as it is a strictly dominant strategy. Accordingly, the pedestrian will exercise due care pursuant to iterated dominance. Thus, this regime, if coupled with the regime of strict liability with the defense of contributory negligence, maintains the status quo wherein the MDP would not have any incentive to improve the safety of autonomous vehicles. Consequently, the number of accidents in the road would not be reduced.

Regime of strict liability

A possible regime for liability is also a regime of strict liability pursuant to the theory of products liability since the car is a product of the MDP.¹¹³ Given the same set of elements as the previous game with a regime of strict liability, then the game would be like this:

	Not Invest	Invest
No Care	P: -60, MDP: -0	P: 0, MDP: -40
Due Care	P: -10, MDP: -45	P: -10, MDP: -25

Figure 6. Regime of strict liability in the context of autonomous cars between MDP and Pedestrian.

Payoffs: Pedestrian (P), MDP (MDP)

Under this regime, the dominant strategy of the pedestrian is not to exercise due care which leads to an iterated dominant strategy of investing on the part of the MDP. Thus, a regime of strict liability gives the incentive to MDP of investing on safer autonomous vehicles. However, the pedestrian is not given any incentives to exercise due care. Similar to a regime of strict liability between the owner and the pedestrian, if the pedestrian does not incur any loss in any accident, then the pedestrian is likely to be negligent. Pedestrians would likely jaywalk and not look at the roads when crossing. Thus, this regime does not fulfill the purpose of tort law of encouraging socially responsible behavior.

Regime of strict liability with the defense of contributory negligence

Lastly, we can also try the regime of strict liability with the defense of contributory negligence. Similar to the game between the owner and the pedestrian, the pedestrian would be compensated for the losses in an accident unless he was not exercising due care. Given the same set of elements, such a game would be like this:

	Not Invest	Invest
No Care	P: -60, MDP: -0	P: -30, MDP: -10
Due Care	P: -10, MDP: -45	P: -10, MDP: -25

Figure 7. Regime of strict liability with the defense of contributory negligence in the context of autonomous cars between MDP and Pedestrian.

Payoffs: Pedestrian (P), MDP (MDP)

As we can see, if we add a defense of contributory negligence to a strict liability regime, the dominant strategy of the pedestrian becomes exercising due care since the payoff of -10 is always better than either -60 or -30. Consequently, when we iterate dominance, then MDP is likely to invest because the payoff of investing (which is -25) is better than that of not investing (which is -45). Thus, like the game between the owner and the pedestrian, a regime of strict liability with the defense of contributory negligence produces the most efficient strategy combination.

In this regime, the MDP is encouraged to invest which would lead to safer cars, which means lesser accidents. In addition, the pedestrian in encouraged to exercise due care so that the probability of accidents will be minimized. Looking at the total costs for each cell, this is also the most efficient combination as it yields costs of -35 as opposed to -60, -40, and -55. Likewise, it was also able to fulfill the purposes of tort law since there is compensation and incentive for a socially responsible behavior.

Conclusion

“Who pays?”

The question poses difficulty in the context of accidents involving an autonomous vehicle under tort law. The traditional principles of negligence and foreseeability become inadequate given the unpredictable and largely incomprehensible nature of AI systems powering such autonomous vehicles.¹¹⁴

Instead of looking into theoretical perspectives and justifications alone, this Paper aimed to illustrate a way of going around the difficult question by trying out different liability regimes using game theory and to compare the predicted effects thereof on the behavior of certain actors. After all, law is a constraint in behavior.¹¹⁵ As such, the effect of the law on the behavior of the people seems like a good measure of how appropriate the law is. Such behaviors were then juxtaposed with the purpose of tort law to see if they are aligned with each other.

Using game theory, we found out that a regime of strict liability with the defense of contributory negligence is the best regime for both owners of autonomous vehicles and MDPs thereof. Such regime strikes the optimum balance between the conflicting goals of minimizing accidents and utilizing technological advancements. It was the liability regime that fulfilled all the purposes of tort law and encouraged the most efficient behaviors.

To answer the question, this Paper posits the view that the owner and the MDP may both be held liable and thus be obliged to pay, provided that the liability regime is that of strict liability with the defense of contributory negligence. The well-established rule of no-double recovery¹¹⁶ would still be applicable such that the injured party can sue them both but can only recover from either. While it seems at first that such regime may impede the development and adoption of self-driving cars, the results from the games conducted show otherwise.

The key factor is the safety level of autonomous vehicles. Rational players are predicted to accept the risk of strict liability provided that the probability of accidents is low enough the risk of paying becomes lesser than the rewards of developing and adopting.

Thus, this paper has illustrated how game theory might be an insightful tool in policy making, especially in new areas like robotics, by taking the top-down approach starting from the effect of the law, instead of the bottom-down approach starting from the fundamental principles.

In the end, even if we do not know how computers think, we still know how humans react. Consequently, game theory may also be applied to AI actors since they are programmed to act and react like humans. The introduction of AI actors does not change the game, it only changes the players.