Chapter 16: Economics of Uncertainty and Game Theory

Chapter 16: Economics of Uncertainty and Game Theory

Decision Making Under Uncertainty

As I previously mentioned, economics is about decision making in our daily living. Our decision making may not always be done under certainty but sometimes under uncertainty or risk. More precisely speaking, risk is measurable (uncertainty) whereas (genuine) uncertainty is unmeasurable. As a matter of fact, our life may be more uncertain or risky rather than certain or safe. We are not able to foresee what will happen tomorrow. Nobody knows what will wait for us when we die. We believe that we will be in paradise (in spirit) or the kingdom of God (in spiritual body) as Jesus promises us (Luke 23:43; John 3:16, 5:24, 14:2-3).

Uncertainty in the Bible

Did Adam know what would happen to him when he eats (the fruit) of the tree of the knowledge of good and evil although God told him that he would surely die when he eats of it (Genesis 1:17)? Absolutely not! If he had known what would wait for him, he would have forbidden Eve from eating of it and he himself would not have eaten of it, or he had forsaken Eve not to be tempted by the serpent along with her.

            Did Noah know for sure there would be the great flood? Probably not. He built an ark for one hundred years without knowing when there would be the great flood. The Book of Hebrews describes about Noah’s faith in Hebrews 11:7: “By faith Noah, being warned by God concerning events as yet unseen, took heed and constructed an ark for the saving of his household; by this he condemned the world and became an heir of the righteousness which comes by faith.” Noah patiently built the ark for a century and thus could save himself and his family.

God promised to Abraham three things – land, nations, and blessings. Did Abraham know whether God surely would give him and/or his descendants all those three promises? Probably not. Although Abraham was a man of faith, he was not quite sure whether God would keep his promise. That was why he was a little upset when God appeared to him in Genesis 15:1 and asked him in Genesis 15:2 about his promise of offspring/nations: “O Lord GOD, what wilt thou give me, for I continue childless, and the heir of my house is Elie'zer of Damascus?” Then, he said sarcastically in Genesis 15:3: “Behold, thou hast given me no offspring; and a slave born in my house will be my heir.” The greatness of Abraham is not that he knew God more than other people or his conduct was perfect but that he believed God with a simple mind whenever God promised although he did not know what would happen to him on the next day. God credited Abraham’s faith to him as righteousness (Genesis 15:6). The Book of Hebrews describes about Abraham’s faith in Hebrews 11:8-19: “⁸By faith Abraham obeyed when he was called to go out to a place which he was to receive as an inheritance; and he went out, not knowing where he was to go. … ¹⁷By faith Abraham, when he was tested, offered up Isaac, and he who had received the promises was ready to offer up his only son.” Abraham’s decision making of departing his home land, Ur of the Chaldeans, offering of his son Isaac, and others was done under uncertainty, without knowing what the outcomes would be.

Many people of God – Isaac, Jacob, Joseph, Moses, Joshua, Caleb, Rahab, Samuel, David, and others – kept their faith and obeyed God, believing God’s promises without knowing what would happen to them in the future. Today, many Christians live by faith under uncertainty, believing that they would enter the kingdom of God.

Game Theory

Game theory in economics tries to explain an individual’s or a firm’s behavior or decision making when they do not know the other party’s behavior or decision making. The prisoner’s dilemma is a basic standard game in which two rational players/persons make decisions for their own self-interests when they are placed in two separate rooms without being allowed to communicate with each other. That is, two individuals or players make a rational decision under uncertainty about the other player’s decision, seeing the possible outcomes depending upon their decisions. This kind of game is called a noncooperative game.

            I was interested in interpreting believers’ decision making under uncertainty in the Bible using game theory when I was a graduate student who studied game theory. While I was preparing for this book, I found that there were few scholars who discussed about game theory in the Bible.[1] However, I want to explain game theory for the following examples using my own payoff tables.

1.      Adam versus God

To form a payoff table for the game between Adam and God, my a-priori (prepositional) assumptions are that God exists and God’s promise or command may be either fulfilled or not fulfilled (bluffed).

		God
		Fulfill	Not Fulfill
Adam	Obey	(+∞, +∞)	(-α1, +θ1)
	Disobey	(-∞, -∞)	(+α2, -θ2)

God’s command to Adam is in Genesis 2:16b-17, “^16bYou may freely eat of every tree of the garden; ¹⁷but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall die.”

When Adam obeys God and God’s command is valid, Adam will enjoy eternal life in the garden of Eden. So, his payoff is infinity (+∞) or extremely large. As God is very much well pleased with Adam’s obedience, his payoff is also infinity (+∞) or extremely large.

When Adam obeys God and God’s command is not valid, that is, he will not punish Adam but there is no eternal life for Adam, either. Then, Adam will be very much disappointed and his payoff, -α₁, may vary from any negative number to negative infinity, depending upon Adam’s character. God is pleased with Adam’s obedience although he does not have any intention to fulfill his command or promise. So, his payoff, +θ₁, is some positive number.

When Adam disobeys God and God’s command is valid, Adam will surely die and cannot enjoy eternal life in the garden of Eden. So, his payoff is large negative number or (close to) negative infinity (-∞). As God is very much displeased with Adam’s disobedience, his payoff is also (close to) negative infinity (-∞, see Genesis 6:6-7).

When Adam disobeys God and God’s command is not valid, that is, God does not punish Adam and there is no eternal life for Adam, either. Then, Adam gains some knowledge as he eats of the tree of the knowledge of good and evil, and thus his payoff, α₂, is some positive number. God is displeased with Adam’s disobedience although he does not have any intention to fulfill his command or promise. So, his payoff, -θ₂, is some negative number.

What should be Adam’s rational decision without knowing God’s intention? He does not have a dominant strategy with the given payoff table, which is the best and rational strategy regardless of God’s intention. So, his decision is up to his faith in God. In Genesis 3:6, he decided to disobey God’s command, eating of the tree of the knowledge of good and evil, and as a result of his disobedience, he was expelled from the garden of Eden (with his wife Eve) and lost eternal life.

2.   Abraham versus God

For the game between Abraham and God, my a-priori (prepositional) assumptions are the same. That is, God exists, and God’s promise may be either fulfilled or not fulfilled (bluffed).

		God
		Fulfill	Not Fulfill
Abraham	Faith	(+∞, +∞)	(-α1, +θ1)
	No Faith	(-∞, -∞)	(+α2, -θ2)

God’s promise to Abraham is in Genesis 12:1-3, “¹Go from your country and your kindred and your father’s house to the land that I will show you. ²And I will make of you a great nation, and I will bless you, and make your name great, so that you will be a blessing. ³I will bless those who bless you, and him who curses you I will curse; and by you all the families of the earth shall bless themselves.”

When Abraham obeys God and God’s promise is valid, Abraham and his descendants will obtain the land of Canaan, become great nations, and enjoy God’s blessings. So, his payoff is large positive number or (close to) infinity (+∞). As God is very much well pleased with Abraham’s obedience, his payoff is also (close to) infinity (+∞).

When Abraham obeys God and God’s promise is not valid, that is, he will not keep his promises to Abraham. Then, Abraham will be very much disappointed and his payoff, -α₁, may vary from any negative number to negative infinity, depending upon Abraham’s character. God is pleased with Abraham’s obedience although he does not have any intention to fulfill his promise. So, his payoff, +θ₁, is some positive number.

When Abraham disobeys God and God’s promise is valid, Abraham cannot attain God’s promise of the land, great nations, and blessings. So, Abraham will be very much disappointed, and his payoff is large negative number or (close to) negative infinity (-∞). As God is very much displeased with Adam’s disobedience, his payoff is also (close to) negative infinity (-∞, see Genesis 6:6-7).

When Adam disobeys God and God’s promise is not valid, then Abraham did not lose anything. Abraham did not have to leave his home country, Ur of the Chaldeans. He could enjoy extra time for other things in his home town, and thus his payoff, α₂, is some positive number. God is displeased with Abraham’s disobedience although he does not have any intention to fulfill his promise. So, his payoff, -θ₂, is some negative number.

What should be Abraham’s rational decision without knowing God’s intention? He does not have a dominant strategy with the given payoff table, like in the case of Adam. So, his decision is up to his faith in God. However, he decided to believe God’s promise (Genesis 12:4, 15:6; Hebrews 11:8-19). As a result of his obedience out of faith, he and his descendants attained the land of Canaan, became great nations, and enjoyed God’s abundant blessings.

3.   Person versus God

For the game between any person and God, we may remove the above a-priori assumptions. That is, there was indeed historical Jesus, but people are not sure about the existence of God and of Heaven and Hell. Although God exists, Jesus’ promise may be valid (existence of Heaven/Hell) or not valid (non-existence of Heaven/Hell). If God does not exist, then Jesus’ claim is invalid, and all believers waste their time and life (see 1 Corinthians 15:16-19). I do not consider this case here.

		Jesus Christ/God
		Heaven/Hell	No Heaven/Hell
Person	Faith	(+∞, +∞)	(-α1, +θ1)
	No Faith	(-∞, -∞)	(+α2, -θ2)

God’s promise to people through Jesus Christ is in John 3:16 and some other similar verses, “For God so loved the world that he gave his only Son, that whoever believes in him should not perish but have eternal life.”

When Person has faith in Jesus Christ and Jesus’ (or God’s) promise is valid, Person will enter the kingdom of Heaven where Person will have eternal life. So, Person’s payoff is positive infinity (+∞). As God is very much well pleased with Person’s obedience, his payoff is also (close to) positive infinity (+∞).

When Person has faith in Jesus Christ and Jesus’ (or God’s) promise is not valid, that is, there is neither Heaven nor Hell. Then, Person will be very much disappointed, and thus Person’s payoff, -α₁, may vary from any negative number to negative infinity, depending upon Person’s character. God is pleased with Person’s faith although he does not have any intention to fulfill his promise. So, his payoff, +θ₁, is some positive number.

When Person does not have faith in Jesus Christ and Jesus’ (or God’s) promise is valid, Person cannot go to Heaven but to Hell. So, Person will be very much disappointed, and thus Person’s payoff is (close to) negative infinity (-∞) as Person will suffer there eternally. As God is very much displeased with Person’s disbelief, his payoff is also (close to) negative infinity (-∞, see Genesis 6:6-7).

When Person does not have faith in Jesus Christ and Jesus’ (or God’s) promise is not valid, then Person does not lose anything. Rather, Person enjoys the secular worldly life without any guilty feeling, and thus Person’s payoff, α₂, is some positive number. God is displeased with Person’s disbelief although he does not have any intention to fulfill his promise. So, his payoff, -θ₂, is some negative number.

What should be Person’s rational decision without knowing God’s intention? He does not have a dominant strategy with the given payoff table, like in the cases of Adam and Abraham. So, Person’s decision is up to Person’s faith in Jesus Christ. Which one between faith and no-faith is a better choice to reduce danger under uncertainty? When you have faith in Jesus Christ but there is no Heaven/Hell, what is your worst loss? Your loss includes your time that you spend for worship and other church activities, money that you offered to the church. When you do not have faith but there is Heaven/Hell, what is your worst loss? Your loss will be unbearable suffering from eternal dying. Although there is no dominant strategy for any individual in this game, a rational choice seems to be obvious.

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[1] Bob Becking, “Biblical Games: Game Theory and the Hebrew Bible,” Ars Disputandi, Vol. 3 (2003), 91-93. In his article, Becking discusses about Steven J. Brams’ book, Biblical Games: Game Theory and the Hebrew Bible (Cambridge MA 1982).