Question

Consider the following variant of two-finger morra, where Alice picks an action a ∈ {1, 2} and Bob picks an action b ∈ {1, 2}. Bob pays Alice $(a × b) if a + b is even, and Alice pays Bob $(a × b) if a + b is odd. Note that the payoff is different than that in the example we used in class.

1) If Alice plays 1 finger with probability p and 2 fingers with probability 1 − p, what’s the expected payoff that Bob can achieve if he knows p? How should Alice choose p such that Bob’s payoff is indifferent of his own choices?

2) If Bob plays 1 finger with probability q and 2 fingers with probability 1 − q, what’s the expected payoff that Alice can achieve if she knows q? How should Bob choose q such that Alice’s payoff is indifferent of her own choices?

3) What is the Nash equilibrium strategy for both players? And what is the expected payoff for each if they play the Nash equilibrium strategy?

Answer 1

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