Single-object Auction Theory

Abstract

Usually, objects in the markets have a defined price where buyers accept it purchasing the object. However, in some cases, objects are sold in the markets using a competitive game among the potential, few of them generally, buyers pretending that the buyer who likes it more will acquire it. Notice that, if the mechanism is appropriated, the one who likes it more is the one who is willing to pay more for it. This game is called an auction where the buyers are called bidders and what they offer for the object is a bid. The auction (that is, the proposed game) should satisfy certain properties like, for instance, who is willing to pay more for the object needs to be the one getting it. In other words, an auction is not a lottery since in this case the one getting the prize is not necessarily the one who has bought more tickets. In general, in game theory, a game is defined by the number of players, their strategies and the payoff functions of the players (that are the payments of each player for any given strategy profile) (see, [9] An Introduction to Game Theory, Osborne, M.J.). Here, we could differentiate between complete and incomplete information games if we have all the information to know what strategy follows each player is a complete information game and otherwise an incomplete information game. Returning to the auctions, the payoff functions are unknown to the bidders except his own payoff function because if some buyer knows what would be the payoff function of another competitor he would change his bid to win. Thus, an auction is an incomplete information game.