The Revelation Game
The Revelation Game is an interesting abstract analysis, though not quite 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.
We rank the outcomes for each player on a scale:
We then have the following payoff matrix, where the first score is the payoff for H, the second the payoff for G:
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 1 and 2. Hence the dominant strategy is for G to not reveal and for H to believe.
This is a trivial result, however, because the game itself is not particularly significant. The way that the game is set up, God only has two goals, and the human only two goals; and the aim of the game is for each player to maximize the fulfillment of his own goals. So fulfilling both of the player's goals is best, but fulfilling just one of them is better than fulfilling none at all.
The result is that God's best bet is not to reveal merely because we've set up the game so that one of his goals is not to reveal! If God is going to try to obtain both of his goals (as the rules mandate), and we set by fiat "don't reveal yourself" as one of his goals, and he "makes the first move," of course he's not going to reveal himself!
Similarly, if the human reluctantly accepts that he's not going to get the evidence of God that he wants, and his only other goal is to believe in God, then he is going to opt to believe simply because fulfilling one of his goals is better than fulfilling none of them. (In real life, of course, it is dubious that one can simply compel himself to believe something by fiat to begin with.) The most problematic aspect of the revelation game, then, is the lack of justification for giving God and the human the two goals the game gives them. Why think that God would have the goals that the game assigns to him, or that a human would have the goals assigned to him? Why think that the assigned goals should have the primary and secondary weights that the game mandates? And why limit the goals to just two each?
Whether or not this game is valid psychologically or philosophically, it is an 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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