Two risk averse individuals with utility functions over money given by u(x) = x, face a first price sealed bid auction. Each agent i = 1, 2's valuation for the good sold is v_i monetary units. This valuation is private information, but it is known that valuations are random variables independently and uniformly distributed in the interval [0, 1].

(a) Describe the situation as a Bayesian game.

(b) Find a bayesian Nash equilibrium of the form b_i(v_i) = _i*v_i . What is each bidder's expected utility in equilibrium?