This game is the nonzero sum version of Pascal’s wager (see Example 1.21). Since God choosing to…

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This game is the nonzero sum version of Pascal’s wager (see Example 1.21).

Since God choosing to not exist is paradoxical, we change God’s strategies to Reveals, or is Hidden. Your payoffs are explained as in Example (1.21). If you choose Believe, God obtains the positive payoffs A > 0, B > 0. If you choose to Not Believe, and God chooses Reveal, then you receive −γ but God also receives −.If God chooses to remain Hidden, then He receives − if you choose to Not Believe. Assume A, B,  > 0 and α, β, γ > 0.

(a) Determine when there are only pure Nash equilibria and find them under those conditions.

(b) Find conditions under which a single mixed Nash equilibrium exists and determine what it is.

(c) Find player I’s best response to the strategy Y0