Question

SECOND PRICE AUCTIONS

What are the implications of the Nash equilibrium? For instance, does one player have an advantage? Is the equilibrium inefficient relative to another outcome in the game? Does the equilibrium have an intuitive explanation?

Answer 1

The Nash equilibrium in a second price auction is for every player to bid his valuation which is a weakly dominant strategy. The amount paid to the player who bids the highest is equal to the amount bid by the second highest bidder.

Let B is the highest bid of all players other than players, there can be three cases (i) when player bides less than B, it implies player i will not win regardless of whatever other player choose. (ii) bi is greater than B and B is greater than vi which is the valuation of player i, here player i would win and pay equal to B. In this case player wins but has to pay greater than his valuation which will make him worse off. (iii) vi is greater than B then the player is better off bidding his valuation.