Consider allocating an object to one of two players when each player's preferences are her private information. Player 1's value for the object, denoted by v1 is drawn from a continuous distribution with [1;2] as its support. Player 2's value for the object, denoted by v2, is likewise drawn from the interval [0;1]. 1. What is the equilibrium in dominant strategies if a second price auction is used to allocate the object. Is the outcome ex-post efficient? 2. For what pairs (v1;v2) should Player 1 and Player 2 respectively be allocated the object in a mechanism that maximizes expected revenue for the seller?

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