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The Revelation Game

mathew

[ Traducción al Español / Spanish translation ]

The Revelation Game is an interesting abstract analysis, like a game theory version of Pascal's Wager. The players are H, a human, and G, a superior being.

Each player has two strategies. H can either believe or not believe in the existence of G. G can choose to reveal its existence to H by providing confirming evidence, or can choose to not do so.

Each player has two goals, a primary and a secondary goal.

H's goals

Primary:: Must have evidence before believing in the existence of G.
Secondary:: Would prefer to believe in the existence of G.

G's goals

Primary:: Wants H to believe in him.
Secondary:: Prefers H to believe without evidence.

Outcomes

We rank the outcomes for each player on a scale:

4: Both goals obtained.
3: Primary goal obtained but not secondary.
2: Secondary goal obtained but not primary.
1: Neither goal obtained.

We then have the following payoff matrix, where the first score is the payoff for H, the second the payoff for G:

Payoff Matrix
		G
		Reveal	Not Reveal
H	Believe	(4,3)	(2,4)
H	Not Believe	(1,1)	(3,2)

We see that the dominant strategy for G is to not reveal itself to H regardless of H's strategy, since 4 > 3 and 2 > 1. Thus H, being aware of G's goals, knows that G will not reveal. H is thus forced to choose between the payoffs 3 and 2. Hence the dominant strategy is for G to not reveal and for H to not believe.

Whether or not this game is valid psychologically or philosophically, it is and interesting and new approach. For further reading into game-theoretic theology consult Steven J. Brams, Superior Beings: If They Exist How Would We Know?: Game-Theoretic Implications of Omnipotence, Omniscience, Immortality, and Incomprehensibility, 1983, 2006 Springer-Verlag, NY.

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