Can auctions select people by their level-k types?

In this paper, we seek to determine if auctions can be used to select players according to their level-k types. To do so, we embed auctions into the p-beauty contest game. We find that by using different designs, we can get the auction winners to be either the lower level-k types or the higher level-k types. In particular, when the value of winning the auction is increasing in the level-k types of all the players, higher level-k players bid higher. When the value of winning the auction is decreasing in the level-k types of all the players, the lower level-k players bid higher. Taken together, our experiment confirms that we can use auctions to select players by their level-k types. This shows that auctions can allow an economic designer to affect the outcome of a game through the selection of level-k types entering to play the game.