Question

There is single object to be sold to one of the n potential buyers. Each buyer has a valuation of vi for the object. Consider the auction rule where the winner is the highest bidder, and pays the minimum of all the bids, i.e. min{bi : i ∈ N}. In this game, truthtelling is a dominant strategy equilibrium. Is it true or false ?

Answer 1

Ans. True , that a truthtellimg is a dominant strategy . Because let say if there are N bidder who have a there true bid value are ( b1,b2, b3 ------ ,bN ) which are listen in an descending order that means person 1 has the highest bid value and Nth have the lowest bid value . Than according to the above rule person 1 will win the auction and pay the price equals to bid value of person N . Now assuming person N do not write it's true bid value and rest all write the true bid value. That is person N were to write his bid value as maximum possible which is to be larger enough that it exceeds all other player than player according to the rule person N will win the auction and pay the price b(N-1) that's the true bid value of the person( N-1)th. But in reality the true bid value of person N is bN which is lower than the price it will have to pay b(N-1) . So he will have to bear loss by reporting something above it's true bid value . So reporting the true bid value is the dominant statergy for all the player because there is a possibility of them earning losses.