conflict resolution · culture · violence · war

AN ANALYSIS OF WAR GAME THEORY AND GAME TREES

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If you were a child of the 1980’s you probably remember watching the movie WarGames with Matthew Broderick and perhaps even developed fascination with computers and the possibilities for gaming.  In the case of the film NORAD’s computer Joshua becomes involved in a serious war game after a teenage computer hacker attempts to play a set of computer games on the machine.  While the film ends happily with Joshua discovering that there is no winner in any of the nuclear war scenarios he attempts it also provides us with a brief introduction into the concepts of War Game Theory.  This paper will discuss and analyze the video lectures section 1.4, 1.5.1 and 1.5.2 of Dr. Campbell’s series in International War and Terrorism.  It is important to understand that “game theory provides a flexible, useful tool to create formal models of the strategic interaction presented in theories of war.”   I will begin with a an exploration of basic game theoretics and game tree construction.  Following the introduction I will move on to an analysis of the various components and characteristics of games and game theory.   Finally I will explore various concepts of balance of power and coalition formation as well as concepts of state stability and how it contributes to how war games and assessments are conducted.  

Game Theoretics and Game Tree Construction and begins with a discussion of the construction of a basic game tree.  Game trees are visual representations of decision based non-cooperative games (DBNG).  War games are usually structured battles between competitors in which we attempt to determine the opponent’s moves and countermoves.  The War Games Handbook defines a war game as an “attempt to get a jump on the future by obtaining a better understanding of the past.”  In these games there will be a winner and a loser.  The emphasis is on gamer decisions and options, which lead to outcomes, specifically the cost-benefit outcomes of war.  Each possible choice involves risk and the risk is weighed against the party’s desirable outcome.  There are many possible scenarios.  These game trees can be very simple or very complicated and have nothing to do with logic trees.  War games are assessed in terms of decision based non-cooperative games because war is inherently non-cooperative.  

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Game trees are a temporal representations of all of the possible outcomes of a game.  This means that moves can be made independent of the other party’s choices and prior to or after their actions are made.  Party 1 can act first, Party 2 can act first or they can act simultaneously.  All options must be represented and preserved on the tree regardless of which party acts first.  These actions and choices in a war game involve escalation or de-escalation of the conflict.  The game tree allows for a strategic analysis of the available choices.  The point of a choice is to escalate or de-escalate.  Disengaging or de-escalating on the game tree does not always lead to the end of the conflict and sometimes escalation is the only way to end the war.  In a basic war game at least 2 decisions are required by the parties to reach an outcome.  You can assess the outcome based on 4 decisions per game. Outcomes are generally ranked in the order of maximum to minimum number of casualties representing the consequences of the decisions made by each party.  

There are numerous assumptions of the War Game and Game Tree.  First, we must always assume that the actors are rational – that they will act in their own best interest.  This concept can be highly problematic, as human beings do not always act rationally.  People are highly driven by emotions such as anger or pride and will often act out in ways that are not in their best interest.  For a person or group that seeks retribution the concept of rational choices is moot.  There can also be vastly diverging interests between political leaders and the public resulting in more irrational behavior.  Second, actors seek to minimize the total number of casualties.  This concept is also problematic considering that actors are not in actuality always rational.  Take, for instance the case of conflict in Israel-Palestine.  Leaders and the people seem very intent on annihilating the other party.  While they attempt to minimize casualties in actuality casualties continue to occur and often are in high numbers.  Third, no actor knows the decision of the other actor in the game.  You can contemplate your opponent’s possible actions but you do not know what they will actually chose.  Lack of trust also coincides with the lack of knowledge.  Neither side can trust the other party.  If you have more information the game can be played more efficiently.  Knowledge in war is vital.  You must know what you know and know what you don’t know.  You must imagine the possibilities.  For example you may know that your opponent has bombs but you may not know the exact number or type of bombs they have.  Finally, decisions, once made are irreversible, they cannot be taken back.

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The next step in understanding a game tree is to identify the parts of the tree.  First you have a decision node, usually represented by a point.  The decision node represents an individual point of choice between various options.  For instance while traveling down a road you may come to a fork in which you must choose to go left or right.  You have to choose one and only one.  Next is a move, represented by a line or arrow.  These are the options from decision nodes and are exclusively disjunctive meaning that you can have one choice or the other, but not both.  After the moves you have the outcomes or terminal nodes.  The terminal nodes represent the consequences of the moves that are chosen.  Finally, you have the information set which the collection of decision nodes and moves, the completed game tree.  

At this point we must construct a hypothetical game tree for conflict escalation.  In our case let’s imagine that a brother and sister are fighting.  The brother is angry and has the option to hit his sister or walk away from the fight.  The sister at the same time has the option of hitting her brother (either before or after he acts) or walking away.  Let’s assume that the brother and the sister both chose to escalate the fight and hit each other.  This will result in “punishment” by the parents for both of them in the form of being grounded.  The second option will be for the brother to hit the sister and for the sister to walk away.  In this case the sister get’s a bruise and the brother gets away with the punch.  In the next possibility the brother choses to deescalate but the sister decides to sucker punch him.  In this case the brother loses and ends up with a bruise.  The final option will be for both to walk away from the conflict completely, in which both sides end up without injuries.  

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We can use the above illustration to analyze and assess the outcomes for each party.  First, E+E = punishment for both parties (or in the case of war maximum casualties for each side.)  Second, E+D = temptation for the brother (or in the case of war, maximum enemy casualties).  The third option D+E = the brother being sucker-punched by his sister (or in the case of war, maximum allied casualties.)  Finally, D+D = reward, neither sibling is injured (or in the case of war we have peace or minimal/no casualties.)    With this simple game tree we can see that there is a 25% likelihood of peace, with a 75% chance that some casualties will occur.  In non-cooperative games attaining peace requires de-escalation by all parties, however not knowing the opponents choice and opting for de-escalation can lead to the worst possible outcome – the highest casualties for your own party.  If both parties escalate then the worst overall possible outcome will occur – mass casualties for both parties.  .

Once we understand the basic game tree we can delve deeper into war game strategies and assessments.  We must always begin with knowing what we know and infer from the known unknown the possibilities of the game.  Once again, you know that your opponent has bombs but you do not know how many or what type.  In building and assessing your options you must take into account that they could have cluster bombs, dirty bombs or simple grenades.  You must be prepared for each possibility.  Next you must weigh and list the outcomes in order of your preference.  Many times those involved in war or war games will posture for escalation in the hopes that the other party will de-escalate.  You must be committed to using the moves that lead to the most practical (not necessarily the best) outcomes or goals and must also remember that the tree is a temporal and moves can be made at the same time.  

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In the next video we move along to section 1.5.1 or “The On-going Game-Theoretic Revolution.”  “Game theory provides a flexible, useful tool to create formal models of the strategic interaction presented in theories of war.”  Game theory allows us to examine and more deeply analyze and understand the game functions.  In non-cooperative gaming theory we are interested in the strategic interactions of the gamers or actors.  Non-cooperative game theory is part of decision theory.  What happens if a party refuses to decide?  You cannot determine the outcome because inaction can indirectly cause escalation.  We are only concerned with the choices and consequences of those direct decisions.  The actions are considered perfect if they serve the best interest of the actor who made the choice.  Since we don’t know the other parties true interests or choices we can only assess the likelihood of their decision.  

Perfection is a test of credibility.  If escalation is the best move for state A but state A choses D then the action is imperfect and it undermines state A’s commitment to winning the game.  If state A postures for escalation but then fails to follow through the state can be seen as weak.  States must historically maintain credibility by following through with what it says it will do in any given circumstance.  If I repeatedly tell Mexico we are going to invade them if they fail to stop drug-lords and then after the given time period refuse to invade it will reduce my credibility.  Repeated instances of this will further undermine credibility and result in a “Boy Who Cried Wolf” mentality.  The other party will realize that my threats are hollow.  Credibility and perfection can also result in deterrence as outlined by deterrence theory (DT).  Making a threat and having the credibility to back that threat can result in the de-escalation of the conflict.  

There are many game solutions that could be reached during the course of the game.  As more information is added to the knowledge pool strategies change and the game becomes more efficient.  Games are generally solved or ended by reaching equilibrium.  Equilibrium does not suggest balanced or peaceful outcomes.  Equilibrium should also not be thought of as the best of all possible solutions or situations.  Rather it should be considered the best possible attainable or practical state.  Successful strategic planning of a solution can lead to deterrence.  It is vital to remember that in our original game tree example there was a 75% chance for escalation and a 25% chance for peace.  The most practical solution would be for the brother to punch his sister and win or get away with it rather than walk away because he risks the possibility of getting punched.  

This once again leads to the role of commitment in game theory.  Commitment refers to the relationship between a states posturing and the likelihood that the state will act in a predicable fashion.  When a state says it will defend itself, for example, it defends itself.  There are however complications in analyzing state commitment.  First, commitment is compromised if other states don’t acknowledge the threat.  Many times this occurs when a state fails to follow through with a threat.  You lose credibility if you don’t fully commit to your posturing.  You are viewed as not being serious, that your talk is cheap.  Second, commitment is compromised in power transition cases where a new regime fails to ensure the old regime that it will not completely destroy the entire political status quo.  Once party A realizes that party B is taking power A will require some insurance that the entire structure they built up will not be dismantled.  Perfection allows us to test the credibility of commitment within the game. One party can look at how credible the other party is historically.  We must also assume that parties will act in their own best interest so that their actions will be perfect actions.  We can use this idea of perfection in order to inform our own options and responses.  

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At this point we must examine the role of limited information in game theory.  Since information is how you win the game the amount of information you have will increase your efficiency.  First, information is limited if parties in conflict have limited historical data – making it hard to anticipate decisions and actions of the other party.  Second, persuasion, signaling and bluffing are all representative features of limited information.  These are actions we see commonly in poker where we seek to deceive our opponent or deny them information.  This manipulation of information is power.  Third, information that is only available to one actor is identified as private information.  I have information that the other party does not know I have.  We can use the roles of snitches, moles or spies in order to use private information to our advantage within the game.  Private information is inferred from actions.  Because there is information that we do not have the sign given to us is often posturing or bluffing.  We can only infer from the other party’s actions what their actual intent is at any give time.  In war strategies we must be able to bluff successfully and use all knowledge to our greatest advantage.  

There are methods of application for perfection and private information within a game.  First, if we know that they are aware that we do not bluff and we have superior military capabilities combined with our posturing that says we will engage if they commit certain acts our actions will be perfect if we engage them when those acts occur.  In other words our hand was forced and we have reinforced our commitment.  Second, in an instant where temporal factors are observed and we see a party escalating despite our posturing we must recognize that they may have some sort of private information that justifies their escalation.  In many cases this could be an unknown weapon or an attempt to preserve power.  Those attempting to preserve their power have nothing to lose and will escalate regardless of historical commitment.  A recent example of this in current events is the situation in Libya.  Quaddafi repeatedly ignored threats from NATO and the United States.  He refused to stop escalation of violence because he feared losing his power.  Eventually NATO and the U.S. intervened resulting in his ultimate downfall.  Syria however is a different case altogether.  Bashir al-Asad appears to have much more military power then Quaddafi and there have been no significant threats posed by outside forces for him to discontinue killing of the opposition forces within the country.  Although, historically we have backed up our threats, we seem to be failing when addressing issues in Syria.  If for example a man brings a gun to a knife fight we must assume that they likely know something we do not know. You must try your best to plan for the “unknown, unknown” in cases such as this.  

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It is vital that we understand the use of intelligence in strategic planning.  Let’s examine a possible scenario.  I am party 1 and party 2 is being challenged and power transition is possible.  Party 2 is much better equipped then I am militarily and poses a significant threat.  I have been given private knowledge that the opposition is sympathetic to my cause and I have the means to privately equip the opposition.  With this information should I chose to escalate or de-escalate the conflict?  If I choose to escalate the conflict and arm the opposition party there are several possibilities that could occur.  First, the opposition could be successful and party 1 would lose power.  Second, I could arm the opposition and party 1 is too powerful destroying the opposition, putting me back into a situation of great risk.  There is also a possibility that party 1 could discover my assistance of the opposition and seek retribution.  A final option would be to avoid arming the opposition but that would result in a significant greater risk to me as my security would be placed in jeopardy.   With all of the available information I would make the choice to arm the opposition because the formation of a coalition would be in my interest.  

The next point that we must examine in game theory is the balance of power and coalition formation.  We must begin with an understanding of the two concepts of stability.  First, there is system stability.  System stability occurs when no states are eliminated or pushed out of the system.  All states are potentially secure.  The second concept is that of resource stability.  Resource stability occurs when resources are never transferred from one state to another.  These two concepts or components are vital in order to properly analyze stability and coalition formation.

First we have to discuss resources and system stability in a two state system.  If state A and state B both have equal amounts of resources then the system is both resource and system stable because there is a balance of power.  There is no need to transfer resources from state to state when even distribution exists between two states.  Also, since the states have equal resources and power it is highly unlikely that either will be ejected from the system, providing system stability.  The system is balanced.  However, if state A has more than half of the available resources the system is unstable because A has the power or resources to overtake state B.  It is impossible to have a system stability only in a two state system as any transference of resources in this case would lead to destabilization as a cause of power imbalance.

Resource and system stability can occur in a 3 state system.  If for example state A has exactly half of the available resources in the system, with state B and C owning the other half the system is therefore stable and resource stable.  C can combine forces with B in order to ensure their position in the system and protect themselves against A.  In this case the two weaker states must align themselves if aid is needed as it is in their best interest to defend each other against the stronger state.  The state sitting on the sideline would be eliminated next if they did not align.  There can also be system stability only in a 3 state system.  If A has 120 units of a resource, B has 100 units of a resource and C has 80 units of a resource then C can easily transfer 30 units to B in order to give them an advantage over A.  Resource transfer has occurred so the system is not resource stable but since no states can be pushed out or eliminated the system is considered to be stable.  

In some cases where there are more than three states the condition to create resources and system stability is that just one state needs exactly half of the resources.  The other states can then align in order to defend against the strongest state.  For example. State A is the most powerful with 120 units, B has 80, C has 60 and D has 40.  Resource transference will occur and all states will be considered essential when D transfers 30 units to B allowing B to have a majority of units – thus securing their place in the system.  How exactly do we determine if a state is essential?  First, we must look at total resource distribution (300.)  Next we ask how much the most powerful state has (120).  Third we ask how far the most powerful state is from attaining half the total distribution (30).  Finally does the weakest state have enough units to contribute to the stronger state in order to reach half the total distribution, without completely using all resources?  If the smallest state can contribute and still exist they have secured their place in the system and have illustrated that they are essential within the system.  

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In essence War Game Theory shows us the natural and inherent nature of the war system.  There is a built in uncertainty in regards to the risks in warfare and we must be aware of the risks of each choice and move we make.  One misstep or wrong move could result in mutually assured destruction of the parties involved.  The major problem in game theory is that it is based on human behavior and choices.  While we can assume that actors will perform rational functions we must remember that not everyone will act rationally all the time, especially in situations in which emotions are high.  We must always be aware of the consequences of our choices and as such be willing to live with the consequences that arise out of our choices in war.

Bibliography

Campbell, Jason J.  International War and Terrorism Lectures. YouTube. http://www.youtube.com/watch?v=nUjVBqgbKpc

 

War Games Handbook.  “What is a War Game?” http://www.hyw.com/Books/WargamesHandbook/1-what_i.htm.
Midlarsky, Manus I. Handbook of War Studies II. “ The On Going Game Theoretic Revolution.” James D. Morrow.  The University of Michigan Press: Ann Arbor.  2008.

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