5. The following static game of complete information (Matching Pennies) has no p

Question

5. The following static game of complete information (Matching Pennies) has no pure-strategy Nash equilibrium but has one mixed-strategy Nash equilibrium: each player plays H with probability 1/2. Provide a pure-strategy Bayesian Nash equilibrium of a corresponding game of incomplete information such that as incomplete information disappears, the play ers' behavior in the Bayesian Nash equilibrium approaches their behavior in the mixed-strategy Nash equilibrium in the original game of complete information (Hint: Consider the "Battle of the sexes game" in the lecture notes.)

Explanation / Answer

Let us find pure strategy Bayesian nash equilibrium.

The method works directly on the Bayesian normal form representation which is most easily done by converting the game into the corresponding payoff matrix.

The method for finding the Bayesian Nash equilibrium converts the game into an equivalent bigger fame in which the different types of each player are treated as separate players.

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