1. Consider a rst price auction with two players. 1. Assume that each player has a valuation drawn from interval [0, 2] according to a uniform distribution. Find an equilibrium in which bids are linear in valuations. 2. Assume that each player has a valuation drawn from interval [1, 3] according to a uniform distribution. Find an equilibrium in which bids are linear in valuations. 3. Consider a second price auction in the case with valuations on [1, 3]. Find an equilibrium in weakly dominant strategies 4. Consider a second price auction in the case with valuations on [1, 3]. Find a Nash equilibrium in which player 2 always wins