There is no dominant strategy for Man.
If God intends to reveal Her existence, then Man wants to believe in God. If God does not intend to reveal Her existence, then Man
doesn’t want to believe in God. Knowing that Man is rational isn’t enough to tell us what Man will do. In contrast, God does have a dominant strategy: regard- less of Man’s belief or disbelief in God, God prefers to hide Her existence. Doing so yields a payoff of 4 versus 3 for when Man believes in God and a payoff of 2 versus 1 when Man does not. A rational God will then hide Her existence.
If Man believes that God is rational, then Man knows that God will hide Her existence, since that is a dominant strategy for God. Given that God hides Her existence, Man’s optimal strategy is not to believe in God. We conclude that
70 CHAPTER 3: ELIMINATING THE IMPOSSIBLE: SOLVING A GAME WHEN RATIONALITY IS COMMON KNOWLEDGE
FIGURE 3.13 Existence-of-God Game
3,4 1,1
4,2 2,3 God
Man
Reveal
Hide
Believe Do not believe
3.3 Solving a Game when Players Are Rational and Players Know That Players Are Rational 71
the answer to the riddle is that Man should not believe in God and God should hide Her existence from Man.*