Existing work on auctions assumes that bidders are symmetric in their types – they have the same risk attitude and their valuations are drawn from the same distribution. This is unrealistic in many real-world applications, where highly heterogeneous bidders with different risk attitudes and widely varying valuation distributions commonly compete with each other. Using computational service auctions that are emerging in cloud and grid settings as a motivating example, we examine how an intelligent agent should bid in such multi-unit auctions with asymmetric bidders. Specifically, we describe the equilibrium bidding strategies in three different settings that are distinguished by the levels of uncertainty about the types of other agents. First, we consider a setting with full knowledge about all agents? types, then we consider the case where the types are uncertain, but the number of bidders is known. Finally, we consider the case where both the number of bidders and their types are uncertain. Our experiments show that using the equilibrium strategies derived from our full analysis leads to increased utility (typically 20?25%) for the participants compared to previous state-of-the-art strategies