An improved proof of the truth telling equilibrium of the alternative ascending bid auction

Auctions have received signicant interest in the past few years. An example are the recent radio frequency auctions in the Netherlands, through which the Dutch government allocated 4G frequencies to bidders in the telecom market. These auctions, in which multiple ob- jects are auctioned simultaneously, can be dicult to model, especially when bidders have dependent values for the objects. The broader area of mechanism design, the eld in game theory where we think about the design of games (mechanisms) that allocate goods in a proper (economically ecient) way, has been a topic receiving signicant academic interest in the past few years. The central topic in this thesis is the (alternative) ascending bid auction introduced in [1]. It is an auction for multiple identical goods, in which participants submit a bid (a quantity) in each round. The price for the goods is then increased in each round. What makes the alternative ascending bid auction special is the payment rule. It is structured such that the price to be payed by each player only depends on the bids of all the other players (and not on his own). [1] shows that in this setting, the set of strategies where each player bids truthfully forms an ex post perfect equilibrium. In words this means, that when all players j 6= i bid truthfully, then player i does not have an incentive to deviate from his truthful strategy. This thesis is a critique on the actual proof that is given in [1]. We will argue that the proof given is incomplete and a more thorough mathematical analysis is necessary. We do not contest the result itself. The rest of the thesis is organised as follows. In section 2, we will rst discuss the basic auction framework itself, with its precise mathematical denitions. In section 3 we will introduce the uniform-price ascending bid auction, in which a uniform price is payed by each participant (a simpler version of the alternative introduced in [1]). We will show the concept of demand reduction (an example of a technique through which players can gain advantage by `not telling the truth') in an auction. In section 4, we will turn to Ausubel's alternative ascending bid auction, discuss the precise proof as given in [1] and state our alternative.