CHAPTER 16
Game Theory
Games combining chance and skill give the best representation of human life. . . . It would be desirable to have a complete study made of games, treated mathematically.
—Gottfried Wilhelm von Leibniz
I. Two Difficult Decisions
We will begin with two classic tales of characters facing difficult decisions involving love, life, and death. One is the biblical patriarch Abraham and the other Florio Tosca, the title character of Giacomo Puccini's famous opera Tosca. We will examine how game theory, a mathematical field created in the 20th century, provides insight into their ultimate behavior.
A. Abraham
The Binding of Isaac (in Hebrew, 
, Akedat Yitzhak) is one of the most dramatic and troubling stories of the Old Testament. God tests Abraham by demanding a human sacrifice.
Chapter 22 of the book of Genesis begins:
Some time later God tested Abraham. He said to him, “Abraham!
“Here I am,” he replied.
Then God said, “Take your son, your only son, whom you love—Isaac—and go to the region of Moriah. Sacrifice him there as a burnt offering on a mountain I will show you.”
God has directed Abraham to commit an almost unthinkable act: willingly kill his son. Should he comply with God's directive, or should he refuse? What would be the consequences of Abraham's decision? How would God respond to the action Abraham does or does not carry out?
It is abhorrent to us to think ...
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