“Quantitative Military Ethics: Applying Game Theory to Strategic and Tactical Decision-Making”
Dr. Joanne K. Lekea
Department of History and Philosophy of Science
firstname.lastname@example.org , email@example.com
George K. Lekeas, PhD candidate
In this paper we are demonstrating the importance of thinking military ethics in conjunction with applying game theory to the study of war. We are attempting to use the techniques of philosophical analysis, rational choice theory and game theory, as tools for understanding and resolving applied ethical questions. We believe that ethical dilemmas are best resolved with reference to game theory, as we can thoroughly estimate the situation in hand and accordingly decide what is the optimum course of action with the minimum side-effects.
So, firstly, we are looking at a number of ways we can use in our effort to make ethical decision concerning the conduct of war. One can attempt to resolve military ethics dilemmas contemporary armies face with reference to war literature and poetry or by using philosophical texts relating to them. Another option is to refer extensively to the legal aspects of these dilemmas citing the provisions posed by International Humanitarian Law and every nation’s military legislation. Also, we can discuss moral issues with reference to a particular theory (i.e. the just war theory) and of course we can rely upon a number of case studies to make our students confront difficult questions such as “what should be done in this case?” or “which elements could help me decide which is the best choice?” or “how can I calculate the likely outcome of my actions?”. Our aim is to show that we need a different approach towards reflecting on military ethics, if we want an effective, ethical leadership and a conduct of hostilities accordant to moral and legal rules of war fighting.
Secondly, in relation to the above mentioned, we give a introduction to the basic concepts of game theory, as well as its applications to strategic and tactical decision-making. Furthermore, we try to show that with the use of game theory analysis we can determine the tactical options available to each side by using a sequential algorithm, which assigns a numerical value to each possible outcome (by judging the potential gain or loss of an exchange), calculates all possible strategies and their outcomes, finds each side’s best options at strategic and tactical level, and – finally - determines the expected result of the game by examining whether the possible outcome favors the attacker or the defender. At last, we apply the theory to strategic and tactical engagement scenarios in order to support our argument.
2. SOLVING MILITARY DILLEMAS BY REFLECTING ON WAR LITERATURE/POETRY AND PHILOSOPHICAL TEXTS RELATED TO THE CONDUCT OF WAR.
War literature (Thompson 2004, Sherry 2005, Murlyne/Shewring 1989, Jason/Graves 2000) and poetry (Stallworthy 2003, Stout 2005) related to warrior ethos, the conduct of hostilities or other, specific aspects of war (such as the treatment of prisoners of war or the protection of civilians) can be an excellent source for locating and commenting on ethical dilemmas concerning war. We can easily find material that reflects on similar contemporary issues and further analyze the consequences these ideas have on today’s battlefields. We can clearly see that some ideas expressed in religious and philosophical texts are now part of International Humanitarian Law (Nabulsi 1999: 66-240, Nardin/Mapel/Smith 1993: 62-84, 136-179, 270-296, Nardin 1998: 14-213, Tuck 1999: 1-234).
For example, since the sixth century B.C. Laotse deemed that: “A good general effects his purpose and stops…effects his purpose as a regrettable necessity…effects his purpose and does not love violence” and Sun Tzu believed that the captives should be treated well (Christopher 1999:8-9). Other texts state that poisonous weapons or flame throwers should not be used and those who did not take part in the battle, as well as civilians should be protected (Lekea 2004:20-21).
Moreover, when we look at issues
relating to the protection of civilians, we could recall what Plato wrote in Republic; in particular, he held the
view that the civilian population of the enemy should not be mal-treated or
punished as they are not responsible for the conflict (Bk. V 471a5-b5). Aristotle
thought that war is inevitable, but necessary in order to secure peace (Nichomachean
Ethics, 1177b6) and Euripides observed that it is wrong to harm prisoners
of war (Heracleidae 961-969).
Xenophon and Thucydides commented on various aspects of the just conduct of
hostilities and the right to start a war (Xenophon, Cyropaedia, vii, 1,
41-44 and Anabasis, vii, 1, 29, Thucydides, Historia, VII. 82-87,
Nardin 1992, 62-80). Later in Ancient Rome,
This presentation is suggestive and fragmentary, as it is not the aim of this paper to prove that we can reflect on military ethics using literature, religious or philosophical texts. We wanted, though, to show that texts play an important role when discussing ethical dilemmas. They can provide us with a historical approach of the moral issues that are under consideration nowadays. Analyzing texts may prove a positive element and precious supplement when thinking what action one should take in war, but alone can not help officers or soldiers to solve practical ethical problems. One needs a more systematic approach to deal with them efficiency.
3. UNDERSTANDING MILITARY ETHICS WITH REFERENCE TO A PARTICULAR MORAL THEORY.
As stated in the previous section, scattered ideas on military ethics cannot effectively help a decision-making process, especially when urgent answers are needed, as the problem usually arises in the heat of the battle. Moral theories can provide us with a useful framework, essential in our efforts to think about ethical dilemmas in a more organized context.
For example, just war theory can prove a helpful tool in order to discuss various possible solutions to ethical dilemmas concerning war. Just war theory covers a variety of topics, some related to the beginning of war (jus ad bellum) and some related to the conduct of hostilities (jus in bello). This way, for example, one can cope with dilemmas concerning the use of force in a populated area. Should one choose the use of infantry soldiers as an option, which would ensure the best possible protection of the civilian population, or the use of more powerful weapons (i.e. air bombardment), which would almost certainly harm or even kill civilians, but would protect troops from a hazardous mission?
According to just war theory, for the conduct of war to be just, it must be governed by two principles: those of discrimination and proportionality. The principle of discrimination defines who and what we can attack in a war (Fotion 1996). The principle of proportionality is used to resolve issues such as how one should attack and what kind of weapons one might use in order to achieve the military objectives set without causing disproportional collateral damage (Schmitt 1992:102). It is invoked when there is a possibility of harming or killing non-combatants as a result of the military operation (Predelli 2004:16-26; Brown 2003:171-185, Lekea 2003:234).
In relation to the afore mentioned ethical dilemma concerning the use of force in a populated area, both principles create the ethical obligation for military commanders and other people involved in tactical planning to think carefully about the results of the attack. Civilians and their property should be protected in the best possible way, as it is immoral to deliberately kill non-combatants who are ‘morally and technically innocent, that is, harmless’ (Mapel 1996:67; Holmes 1989:104).
These guidelines given are not obligatory to follow. And of course there is no moral theory of any kind that can give as all the answers to every possible problem that could arise. After all, there has never been any ideal theory that could meet all the challenges effectively. Decision-making in a war is not an easy task. Moral theories can help military and political personnel in charge of planning this kind of operations to realize the ethical perspectives of their choices.
4. APPLYING MILITARY ETHICS USING INTERNATIONAL HUMANITARIAN LAW.
Another way of reflecting on ethical dilemmas and ambiguous cases is by resorting to the rules of conduct as stated in every nation’s military legislation and International Humanitarian Law. In fact, a subset of moral rules with the lapse of time formed the moral baseline of international legislation relating to war issues and actually became a part of International Humanitarian Law. Let us revert to the hypothetical situation discussed in the previous section concerning tactical planning in a populated area. Is everything permissible in order to achieve the objectives set? What kind of weapons should be used? Are there legal obligations towards civilians’ protection?
First of all, non-combatants are excluded from direct, intentional attack and their properties should not be intentionally harmed. According to International Humanitarian Law, we can set out two general categories of illegal ways of fighting and illegal weapons: the mala in se means and the mala prohibita means (O’ Brien 1981:37). Their main difference is that mala in se means are always forbidden because of their inhumane consequences (Murphy/Coleman 1990:12). As an example, genocide is always considered to be a great violation of human rights and is illegal as it turns against the civilian population. The mala prohibita means may satisfy the principles of discrimination and proportionality (Halbrook 1994:4), but their use is also prohibited by international law (O’ Brien 1981:55-62). For example, the use of weapons causing excessive pain or having indiscriminate effects on the civilian population is prohibited. These prohibitions once based on moral grounds, are now a part of international law (Perrakis/Marouda 2001:303-544).
By using International Humanitarian Law, we can also analyze the use and limitations of specific types of weapons, as well as how their use can guarantee the best possible result, on both moral and practical grounds (Lekea 2006). The factors that determine if certain types of weapons are suitable for use operationally are their destructibility rate, as well as their short- and long-term effects on both civilians and the environment. On these grounds, for example, nuclear weapons are deemed to be unsuitable for use due to their high ‘destruction power’, the uncontrollable and long-term harm on non-combatants and the environmental disaster they cause (Hutchinson 2004; U.S. Department of Defense 2004; Hashmi/Lee 2004). Our approach to chemical and biological weapons should be similar (Marrs/Maynard/Sidell 1996; Lederberg 1999; U.S. Department of Defense 2001a). Any possible use of them in an operation would coin it unjust, as they violate the principle of distinction of civilians and potential consequences could be disastrous on both civilians and the environment, making it almost impossible not to violate the principle of proportionality as well (Krickus 1979:501; Butler, 2001:1-12. U.S. Department of Defense 2001b).
We can clearly see that the prohibitions set by international legislation have a strong moral background. We can combine the moral rules and the legal obligations to decide what is best in particular engagements. Is this sufficient though? The answer is negative as both ethical theories and international legislation tend to be rather generic by nature and, thus, unable to deal with situations where a large number of interdependent factors are involved. As an example, what would one do if one of the most wanted terrorists was spotted in an area crowded by civilians? Clearly, international legislation as well as ethical theories tell us that civilian lives should be protected and give us directions about what kind of weapons should not been used, but they do not tell us what kind of weapons should be used or how it should be used, as these are operational parameters.
The combination of ethical theories with international legislation can provide us with valuable directions on which the operation will be based, but can do very little with helping us to design and run it. Game theory, on the other hand, will allow us to cater for these aspects as well in the form of a strategy, assuming rational players with incomplete information about one another abilities, which is true in almost all cases.
5. DOING MILITARY ETHICS WITH GAME THEORY - A SHORT INTRODUCTION TO ITS MILITARY APPLICATIONS.
The application of game theory to the study of war can be of great help (Hargreaves-Heap/Varoufakis 1995: 1-40, Rasmusen 2001:67-271, Myerson 1997: 1-35, Brown 2000:1-44, Brams/Kilgour 1988, Shubic 1983, Haywood 1951). It can provide us with the tools necessary for studying practical issues about the costs and benefits of a war, evaluating ethical questions on the use of force in the battlefield or in urban environments where the protection of civilians is crucial (e.g. fire exchange in the war against terrorism or humanitarian interventions).
Military professionals are charged with making difficult decisions and it is at this point that game theory and rational choice theory prove to be necessary in strategic and tactical decision-making (Straffin 1996: 27-31, Gintis 2000: 357-399, Hastie /Dawes 2001: 47-72, Osborne 2003: 1-358, Colman 1982, Isaacs 1965). The benefits we can enjoy from applying this framework, through which we can examine the available courses of action, include getting answers in uncertain situations, as well as foreseeing the reactions to each course of action taken; identify the pros and cons of each alternative and select that course of action that minimizes cost while maximizing benefits .
In other words, at the strategic level, we can apply those theories to decide when it is best to start (or end) a war, or even take an alternative political or diplomatic course of action according to the calculation of benefits from our actions. Military planners can also apply game-theoretic analysis to tactical operations since it enables them to estimate and confront effectively the capabilities and military choices of the enemy, evaluate how an intelligent (and rational) opponent is likely to behave in a given situation and which side is most likely to win.
The scenarios we use to simulate real-life situations include five elements:
1. players, or decision makers;
2. strategies available to each player;
3. rules governing players' behavior;
4. outcomes, each of which is a result of particular choices made by players at a given point in the game; and
5. payoffs accrued by each player as a result of each possible outcome.
These scenarios assume that each player will pursue the strategies that help him or her to achieve the most profitable outcome in every situation. These features provide the essence of a theoretical model for analyzing conflict situations: two or more players have a range of actions or freedom equivalent to a set of choices and have certain information (although no player has complete information). Each player has a set of preferences for the different possible outcomes and the results of the interaction depend on all the players' decisions. If we assume that each player has a goal, then we may attempt to prescribe actions which will realize it. Game theory prescribes courses of action for the attainment of outcomes, which have certain formal 'optimum' properties.
In order to achieve the aims mentioned above, we are using game theory, as well as mathematics (formal models) to model human decision-making in competitive situations. This way, we hope that we can successfully analyze military situations by conceptualizing the realistic situation in which both sides in war are free to choose their best “moves” and to adjust their strategy over time.
A. STRATEGIC LEVEL.
Generally, at the
strategic level, we can apply game-theory to decide when it is best to start
(or end) a war, or even take an alternative political or diplomatic action
according to the calculation of benefits from our actions. The war against terrorism serves as a good example. After
This scenario involves the
On the other hand, there is the other option of going
after the terrorists and destroying their resources. This would involve actions
like the bombing against Taliban resources in
The following sub-sections describe the strategies involved in the game and the different payoffs that players can enjoy from these strategies.
The strategies available for the U.S. administration are to pre-empt, safeguarding potential targets, or to deter, actively going after the terrorists and making them incapable of launching an attack anywhere in the world as their resources would have been destroyed. The costs involved in the second operation would be much higher, but results will be more ‘persistent.
On the other hand, the terrorists
- by watching what the government does, will have to choose their next move. As
the main objective of this kind of organizations is to launch attacks around
the globe, it is a safe assumption that they will not consider stopping the
attacks, but might only consider changing the place of attack. They might
consider launching an attack against a target based on
Deterrence costs will be dependent upon the level of safety required () and the proportion of hard-liners within the group ph (the assumption here is that the higher the percentage, the higher the costs would be, as hard-liners are more likely to insist on carrying out an operation). The cost would, thus, be written as
CD = f(,ph) with 0 ph 1, > 0 and > 0
(the last two inequalities model the assumption that if the deterrence level or the percentage of hard-liners within the group go up, the deterrence cost will go up as well).
These are the costs related to
safeguarding targets in
If the terrorists attack, then the payoff for the government is - pθ * CD. If they attack abroad the payoff is
–CD – (1- pθ) * δ * Ca + V,
where V is the net payoff for not attacking a
In the case of pre-emption, the costs will be much higher and a function of the proportion of the hard-liners within the organization; thus, the cost of pre-emption Cp >> CD for all values of θ. The cost will equal CP = δ(pβ) * CPS where δ(pβ) is a priority factor and CPS is assumed to be a “constant” cost unit (if the proportion of hard-liners is high, then that organization will have to be destroyed at any cost). The δ(pβ) factor will account for factors like operations planned in uncertain environments, attacks made with the use of special weapons and so on. On the other hand, there would be a cost Cpa for attacks made against U.S. interests abroad – this cost is assumed to be Cpa << Ca in the case of deterrence, as pre-emption would harm terrorist resources.
The costs for the government if
they manage to attack – even if pre-emption is employed – would be –Cp – pA’C
(where pA’ is the probability of terrorists attacking U.S. soil targets even if
pre-emption is chosen and C is the cost for having a successful terrorist
operation on U.S. soil). On the other hand, if they attack abroad, the cost
will be -CP – (1- pA’) * δ * Cpa + T, where T is the payoff for not having
an attack on
For terrorists, if they attack
under pre-emption they have a payoff of S’ depending on the type of event they
choose, whereas if they do not attack
B. TACTICAL LEVEL.
Military planners can also apply game theoretic analysis to tactical operations since it enables them to estimate and confront effectively the capabilities and military choices of the enemy. These applications are particularly important for the war against terrorism as they enable us to see how terrorists are likely to behave in a given situation and which side is most likely to win. The following example shows the ethical difficulties in decision-making process.
Imagine that as the chief of operations you decide to hit a “highly valued” target in a populated area. The target is identified as a possible terrorist training building. Inside the building there are suspects of terrorist acts. Nearby the building there is a hospital and a playground, and people are frequently crossing the area. You have two choices: first, to hit the target using an accurate weapon (such as an accurate guided missile) and second, to send ground troops to capture the suspects and take up the place. If you choose to bomb the target or hit it using a guided missile, there is a possibility of killing civilians who happen to be around. If you choose to enter the building using ground forces, you take up the risk of having casualties amongst your soldiers.
Game theory can help us identify the risks posed by each of our choices. It can also help us calculate any possible threats against our soldiers and civilians who happen to be in the area at the time the operation takes place.
In this case-study, we assume that at the strategic level the decision of pre-emption has been taken and we are now faced with a dilemma at the operational level. This concerns how to attack terrorists; an attack with an accurate weapon will have a high probability of success, while if ground troops are sent in, civilian lives will be ‘secured’. The players are the terrorists and the government – the following sub-sections will describe the strategies and payoffs associated with every choice made.
The strategies available to the government are the different ways through which they can attack and destroy the suspicious building. One way is to use a missile, or another form of an accurate weapon, that almost guarantees success of the operation. However, this strategy is almost guaranteed to end with civilian casualties as well and has the disadvantage that suspects can not interrogated and provide additional evidence for terrorist acts.
On the other hand, as the main
objective of terrorist organizations is to attack governmental buildings, we
can safely assume that this will continue to be the case no matter whether the
building is destroyed or not. Their strategy might change with regards to the
location of their next target – would they attack a building on
The payoffs that the government will receive depend on the type of operation they choose. In the case that the accurate weapon attack is selected, then there is a positive payoff P, as the terrorist’s building is destroyed and the resources of the terrorist organization will be slashed. There is a cost associated with this operation, C, expected to be really high. On the other hand, there is an associated negative payoff due to the number of civilian deaths; this is represented as Ccv(n), where n is the number of civilians who die as a result of the operation. There is another negative payoff that relates to loss of information about other activities of the terrorist organization – this is represented as CLI. The total payoff associated with the operation is:
Cm = P – C – Ccv(n) – *CLI (1),
where is a factor that demonstrates the importance of this organization and will be dependent on the terrorist organization we are trying to defeat. In order, thus, for the person in charge of the operation to proceed with it, the following inequality will need to hold:
P > C + Ccv(n)+ * CLI (2).
If the choice is to send ground troops to capture hostages and destroy the building, the cost of the operation is definitely smaller and equal to C’. There is, also, a negative payoff in the case that there are soldier casualties during the operation, represented by Csd(n), where n is the number of soldier deaths. In the case that hostages are captured, there is another positive payoff which is information that might be secured from them – this is represented in the model as CI (which equals the CLI factor in the previous equation) and will be multiplied in the model by the importance factor for this organization, . The total payoff in this case is:
Cgr = P’ - C’ + * CI – Csd(n) (3),
where P’ represents the payoff for the government if the building is not destroyed but taken over by ground troops with P’ < P. In this case, the operation will go ahead if
P’ > C’ - * CI + Csd(n) (4).
In terms of the strategies of the terrorists, if they choose to attack a target on US soil in case that their training building is destroyed by an accurate weapon, then they will have to incur the cost of overcoming high security measures and replacing the resources destroyed. In order to simplify the mathematics, without leaving out strategic aspects of the model, we are assuming constant costs of running an operation, regardless of its type and form (i.e. normal vs. spectacular, bombing incident vs. hostage-taking incident and so on). The payoff that US gained from slashing the terrorist resources will have to be accounted for as well. However, because of all these difficulties the payoff will be large as well (PT). In this case, the total cost for terrorists will be equal to
PT – P – C’’ (5),
C’’ is the cost for running the operation due to high security measures. If
they choose to attack a target outside of
PT’ – P - CO’’ (6).
In the case that the building is not destroyed, but
ground troops are sent to capture the terrorists in it, the costs for running
the operation on the terrorists’ behalf do not change and remain C’’ if they
attack a target on U.S. soil and C0’’, if the attack is carried out outside
U.S. soil. They will also have to pay the payoffs for information leaks from
terrorists who were captured during the government’s operation represented as CI’.
The terrorist payoffs will be PTG and PTG’ respectively if the target is on
7. FUTURE RESEARCH.
In this paper, a number of assumptions had to be made regarding the costs of operations. We hope to be able to produce more accurate models, if information becomes available.
In our model, we did not include
the possibility of co-operation between terrorist organizations for carrying
out operations either on
We, also, need to look at how terrorist operations influence the organization itself. What happens, for example, after a successful or non-successful operation is carried out? How is the terrorist organization influenced in terms of resources, recruitment and so on?
Finally, policies involving terrorism are rarely organized and run by one country alone. Rather, they involve a combination of counties in different capacities with a number of depending choices about what policy they should adopt (e.g., pre-emption vs. deterrence). It would be interesting to extend the current models to reflect the possibility of having more than two players in this game.
In this paper, we discussed a game-theoretic approach to dilemmas faced by military professionals at both tactical and strategic levels. There have been attempts to resolve these dilemmas by philosophical theories and international legislation; while their contributions are valuable, they miss the most important aspect of decision-making; decisions need to be made fast and with incomplete information. Game-theory comes to the rescue by enabling us to evaluate payoffs and decide on the best strategy to follow. Surely, this research is still at early stages with regards to the model produced, but we hope to be able to develop more complex models that will much more accurately model the war against terrorism.
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Joanne K. Lekea
(BA Athens, MSc Athens, PhD Athens) holds a BA (Hons) in Ancient and Classical
Greek Studies with a specialization in Classical Literature (1999) from the
University of Athens, an MSc (with distinction) in History and Philosophy of
Sciences and Technology and a Ph.D. (with distinction) in Military Ethics
awarded jointly by the University of Athens and the National Technical
University of Athens (NTUA). Her research interests include - but are not
limited to - the Just War Theory, International Humanitarian Law, Military
Ethics, Humanitarian Interventions, Game Theory and Terrorism. She works as a part-time
lecturer with the Hellenic Air Force Academy
and is also a post-doctor researcher and a teaching associate with the
(BSc Athens, MSc Warwick,
The author acknowledges funding support for this
work from “Herakleitos” project, which is co-financed from Op. Education through
ESF (European Social Fund) and National Resources.
 Using all these kinds of texts can be used as a teaching element in the military academies to help cadets realize that ethical dilemmas were always a part of military life. As outlined above, questions relating to the protection of civilians or the treatment of prisoners or the use of specific weapons were intrinsic to military profession. Original texts can prove to be a helpful aid in order to find out how these problems were looked at by different traditions and what solutions were given during the years passed until the current era.
 We chose just war theory because of its long history and flexibility to deal with a variety of situations, as well as its influence on international legislation. Any ethical theory could be fit for this discussion but just war theory has the advantage of standing in the middle with regards to prohibitions of available actions during war.