Consider the bilateral trade under incomplete information environment, in which buyer and seller valuations are independently drawn on the iffteryakcording to distribution functions (v) and G(c), respectively. The traders play the following game. The buyer and seller simultaneously proposes an o/er priced an asking price If the asking price and the o/er price are compatible, lie.a + b, then trade takes place at the price p= atb; otherwise trade does not take place.
(a) Denote the equilibrium o/er functionbby) and the equilibrium asking functionalby). Derive an expression for the buyer's expected surplus when she submits bnhasea valuationv, and her opponent uses the asking function (HINT: You may and it useful to denote the inverse asking function(a)y and work with this function instead. Thusa) denotes the cost of the seller type that submits an asking pricea.) Assuming that(c) is a strictly increasing function, the highest cost typbose asking price is belov equalsh(b). Hence the expected surplus of a buyer when she submits an o/er band has valuation equals Z h(b) Up (bjv) = v2 b+ a(c) g(9)dc 0 2