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Game Theory

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OBJECTIVE: Christian Game Theory

With "Diamond" Jack Holgroth, Game Theoretician

What Is Game Theory?

I have found that when I tell my fellow Christians that I am a Game Theoretician that most of them do not know what this means. Some think that it has something to do with sports medicine while others mistakenly accuse me of being a professional gambler! This is most unfortunate, since if more Christians were aware of the scientific field of Game Theory -- which is what a Game Theoretician studies -- then they would be better able to apply apologetics when dealing with non-Christians and would also gain an understand of the logic behind many of the Lord's Truths.

So just what is Game Theory? Game Theory is the scientific and mathematical study of games. When I say the word "game" you probably think of something like baseball or canasta -- meaningless diversions and entertainments that people play. While it is true that those are games, a Game Theoretician uses the term "game" more broadly to also encompass such things as politics, war, relationships, and economies. In Game Theory, a game is any situation where participants can experience gains and losses through time depending on their actions or choices.

What is gained or lost differs depending on the particulars of the game, but games in very different situations can have important similarities. Game Theory seeks to categorize and study different classes of games to find patterns that can be applied in real world situations. In game theory, we seek to identify different strategies in games that will either maximize or minimize gains, so that we may pursue or avoid them.

In general, there are two main categories of games: zero-sum games and those that aren't. A zero-sum game is one in which every gain made by a participant is paid for by a loss, either to himself or to another participant. These games are called "zero-sum" because of the way that Game Theoreticians represent games mathematically. We assign positive or negative values to different strategies, and in zero-sum games when we add up all the values we get a sum of zero, since all the negatives and positives cancel each other out. An example of a zero-sum game would be poker, where a fixed amount of money put in by the participants is battled over. If anyone leaves the table richer than they were at the beginning, then someone else must be poorer.

A non-zero-sum game is one in which adding up all the values -- all the gains and losses -- will give a sum other than zero. This sum can be positive or negative. If it is positive, this means that it is possible for all participants to come out ahead after having played the game -- so-called "win-win" situations -- although not all strategies will lead to this outcome. On the other hand, with negative non-zero-sum games it is possible for all participants to lose if the wrong strategies are employed. Most subjects of interest in Game Theory tend to be non-zero-sum games and research into this branch informs much of Game Theory's application to politics and economics. For instance, an example of a win-win strategy in a game would be workers spending their income thereby increasing production demands thereby increasing both corporate profits and worker wages. A lose-lose example would be a nuclear arms race that ends in mutually assured destruction.

When we Game Theoreticians examine a game, we create what we call a payoff matrix. This is simply a chart showing the relative gains and losses -- expressed numerically -- of different strategies for the participants. This helps us quantify and examine the strategies to determine which are the best and worst. I will illustrate a payoff matrix using the classic game of the Prisoner's Dilemma:

Prisoner's Dilemma Payoff Matrix

. Keep Quiet Testify
Keep Quiet 1,1 0,5
Testify 5,0 3,3

Two criminals are taken prisoner and are both charged with their crime. If one testifies against the other he will be set free and the other will serve five years. If they both testify against each other they will both serve three years. If neither testifies they will both serve one year. In this example the values represent losses, so a larger number is a greater loss.

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Application of Game Theory to Christian Apologetics

Game Theory aims to tell us what are the best strategies to produce a positive outcome in a given game. Christianity does tell us what are the best ways to conduct ourselves in order to live positive lives. If Game Theory is a valid science, then its findings must agree with the Word of the Lord. And fortunately for the sake of my job, they do!

Take for instance the Prisoner's Dilemma game as illustrated above. According to the payoff matrix for this game, the best policy for minimizing losses is to testify against the other criminal. Since both criminals will realize this, the natural outcome is for both criminals to testify, thereby resulting in them both being punished for breaking the law. This outcome is in agreement with traditional Christian morality which teaches that we should not commit crimes and that we should tell the truth.

This leads us to a realization that we can use Game Theory to illustrate the Truth of Christianity. We do this not to justify the teachings of the Lord -- for we already have Faith and Knowledge that they are True as they come from the Lord of Truth -- but to show the non-believer that Christianity is a rational and sensible reality and not merely another religion. In short, Game Theory is a powerful weapon to be used in the arsenal of Christian apologetics.

Game Theory allows the Christian to compare and contrast the strategies of the Lord with those that are contradictory, thereby showing the apologetic target the merits of the Lord's teachings. For example, let us consider two different strategies for interacting with our fellow Man. One is given to us by the Lord: "Therefore all things whatsoever ye would that men should do to you, do ye even so to them: for this is the law and the prophets" (Matthew 7:12, which we will abbreviate as "Do unto others", as it is popularly known). The other comes to us from noted Satanist, Aleister Crowley: "Do what thou wilt shall be the whole of the Law". This produces the following payoff matrix for two participants:

Golden Rule vs. Satanist Credo Payoff Matrix

. Do unto others Do what thou wilt
Do unto others 2,2 1,-1
Do what thou wilt -1,1 0,0

When the two participants differ in strategy it is a zero-sum game since one gains at the other's expense. When they agree to be self-serving the sum is zero but no one gains. When they agree to follow the Golden Rule they both gain more than either could by thinking only of their own desires.

If one participant chooses the self-serving strategy, he will hurt the other who will then act selfishly himself in order to even the score, thereby leading to a world where all follow the Satanist's credo and thus no one wins. If, however, all participants follow the Golden Rule as our Lord tells us to do, all will win. The Lord is teaching us the proper strategy for human interactions, and Game Theory shows that He is correct.

Another way we can see the rational Truth in Christianity is by considering how many of the things that the Lord teaches against are actually zero-sum games where one gains at the expense of another. For instance, all gambling games -- which the Lord considers to be a form of the sin of covetousness -- are zero-sum games. Homosexuality is a zero-sum game as well since one man plus another man equals zero children.

Salvation, however, is not a zero-sum game. By accepting Christ into one's heart, a participant can gain infinite rewards at no cost to other players. Also, an evangelism strategy does not lead to a zero-sum game. By helping more people to find Salvation, we are not diminishing the value of our own Salvation or that of anyone else's, but are bringing gain to others. Salvation itself is an unique case in Game Theory in that it is a positive Infinite-Sum Game, whereby choosing Salvation is always the strategy that maximizes your gains. This leads us to Pascal's Wager...

Pascal's Wager

Blaise Pascal
Blaise Pascal, formulator of the apologetic game called Pascal's Wager.

Perhaps the most famous Christian apologetic game is that of Pascal's Wager. (the Pascal's Wager game belongs to a branch of Game Theory called Decision Theory which deals with games involving an individual forming a decison or belief.) It was formulated by the brilliant 17th century mathematician and philosopher Blaise Pascal as a means to express the differing outcomes of the strategies of the Atheist and the Believer in mathematical terms. It seeks not to prove God to the Atheist -- who will blindly deny the existence of such proof no matter how much of it you point out to him -- but rather to show the Atheist that belief in the reality of the Lord is both rational and in his own best interests.

Pascal's Wager is formulated thusly: There are two options -- either the Lord exists or He doesn't. (This is a true dichotomy, since the Lord is defined as an Infinite Being and thus there cannot be a partial Lord.) If the Lord exists then those that believe in Him will receive the infinite reward of Salvation and those that do not believe in Him will suffer the infinite pains of not being saved and spending eternity cast out of Heaven. If, however, the Atheist is correct and the Lord doesn't exist, then those that believe in Him are merely wasting some of their time while those that do not believe in Him have more free time that they can devote to watching secular television programs or some such thing. Pascal's Wager can be more formally represented in Game Theory using a payoff matrix such as I have done below:

Pascal's Wager Payoff Matrix

. Believer Atheist
God Exists +infinity -infinity
God Doesn't Exist -1 +1
Total: infinity-1 =
Infinite Gain
1-infinity =
Infinite Loss

A payoff matrix for the Pascal's Wager game makes it clear to the Atheist that his infinitely best choice is to accept the existence of God. Atheist and Believer represent different strategies the single participant can choose. Positive values represent gains, and negative ones losses. The value of -/+1 represents the time wasted/saved due to the pointlessness of spiritual activities in a Godless Universe. Subtracting or adding any finite number from or to infinity gives the result of infinity.

We can now address the Atheist and say: "The payoff matrix doesn't lie, dear Atheist. It is in your best interest to believe in the Lord. If you will not accept the evidence of His existence before your eyes, then consider the infinitely unlosable strategy of the Believer that the science of Game Theory has shown you. You just can't go wrong by believing!" Once the Atheist accepts the winning strategy of Belief, he will then be open to standard forms of apologetics and will be able to finally see the proof of the Lord that is all around us.

As you can see, the same science of Game Theory that I and my fellow Defense Department tacticians used to defeat the Godless Soviets during the Cold War can be used to defeat Godlessness here in our own land. It is up to us Christians to learn and deploy this powerful weapon in our war against ignorance of the Lord.

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