Consider second-price sealed bid auction. We assume that seller's value of the item is 0. There are three buyers whose private valuations θi are distributed uniformly on [0, 1]. All buyers simultaneously submit sealed bids bi ≥ 0. The buyer with the highest bid wins and pays the amount of the second-highest bid to the seller. In Bayesian Nash Equilibrium each buyer has s strategy b_i : [0, 1] → [0,∞), where b_ i(θ_ i) is the bid of buyer i's type θ_ i, that maximizes his expected payoff given the strategy of the other buyer.
- Find Bayesian Nash Equilibrium.
- Is this a truthful mechanism? Why?