Question #63497

Consider a two player game with payoff matrix

L R

X

Y

Z

3, θ 0, 0

2, 2θ 2, θ

0, 0 3, −θ

where θ ∈ {−1, 1} is a parameter known by Player 2. Player 1 believes that θ = −1

with probability 1/2 and θ = 1 with probability 1/2. Everything above is common

knowledge.

(a) Write this game formally as a Bayesian game.

(b) Compute the Bayesian Nash equilibrium of this game.

(c) What would be the Nash equilibria in pure strategies (i) if it were common

knowledge that θ = −1, or (ii) if it were common knowledge that θ = 1?

L R

X

Y

Z

3, θ 0, 0

2, 2θ 2, θ

0, 0 3, −θ

where θ ∈ {−1, 1} is a parameter known by Player 2. Player 1 believes that θ = −1

with probability 1/2 and θ = 1 with probability 1/2. Everything above is common

knowledge.

(a) Write this game formally as a Bayesian game.

(b) Compute the Bayesian Nash equilibrium of this game.

(c) What would be the Nash equilibria in pure strategies (i) if it were common

knowledge that θ = −1, or (ii) if it were common knowledge that θ = 1?

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