Exercise 1: Two buyers, J1 and J2 take part in a first-price sealed-bid auction.

The bidders can only bid 100 or 200 . Each of them knows his/her own valuation and moreover:

J1 believes that J2's value is 200 .

J2 believes that J1's value is 0 with probability or 300 with probability .

You are asked to:

a) Represent the decision tree of the game.

b) Determine the strategy set of each buyer.

c) Find Bayesian Nash equilibria.

Exercise 2: In the auction of the previous exercise, assume now that each bidder

knows his own value and moreover:

J1 believes that J2 has a value of 100 with probability and of 200 with

probability .

J2 believes that J1 has a value of 0 with probability and of 300 with

probability .

You are asked to:

a) Represent the decision tree.

b) Determine the strategy set of each buyer.

c) Find Bayesian Nash equilibria.