(Application of the revelation principle: first-price sealed- bid auction) (20%) Recalled the simple first-price sealed-bid auo- tion presented in class. When viewed as a mechanism and using the notions introduced for mechanism design, the set of types for bidder i, ie {1,2), is O, = [0, 1] and the set of messages (the action space) for agent i is M, = R.. The decision rule f is such that for eachcombination of messages (actions) (m,, ma) E Mix M,, if m, > my, agent i obtains the object and pays m,, where j e {1, 2} and j # t We know that the following strategy profile constitutes a Bayesian Nash equilibrium: for each fe {1,2} and each 0, c O., S my(e.) 2 The revelation principle states that the above equilibrium can be represented by an IC direct mechanism. Construct a direct mechanism in which truth-telling is a Bayesian Nash equilibrium and this truth-telling Bayesian Nash equilibrium represents the above equilibrium