Game-theoretic analysis of pay-as-bid mechanisms

Enterprises are facing a challenging dilemma. In order to be able to accommodate peak loads on their IT systems, they must maintain large computing clusters, which lie idle most of the time. At the same time, IT departments are under constant pressure to cut down on hardand software expenses. Grid technology offers a promising way out of this dilemma by allowing the dynamic sharing both within enterprises as well as across organizational boundaries. This sharing approach, however, requires proper economic incentives. This paper is concerned with the determination of dynamic market-based prices. Due to their simplicity, so-called pay-as-bid mechanisms have become popular. This paper is novel as we provide an in-depth analysis of two such pay-as-bid mechanisms – Proportional Share and a discriminatory pay-as-bid mechanism – for the case of three users, thus extending previous work by Sanghavi and Hajek (2004) and Stößer et al. (2008). This analysis is important as we show that the nice results for two users cannot be retained once three or more users are present. Even worse, we show that these results can even be reversed if we move to games with more than two players.