In this chapter, the connection between efficient auctions for multiple, indivisible items and the duality theory of linear programming is investigated. Vickrey auctions are the focus of this investigation as they are efficient auctions well known for their incentive properties. The chapter begins with a description of the basic results for the assignment model that concerns allocations with indivisibilities and defines the combinatorial auction model and pricing equilibria, which is an extension of Walrasian equilibrium. It further discusses an equivalence between the sealed-bid Vickrey auction and pricing equilibrium. The chapter emphasizes that various combinatorial ascending price auctions are incentive compatible if an MP pricing equilibrium is implemented by them. It also discusses the implementation of dual algorithms, the subgradient algorithm, and the primal dual algorithm for solving linear programming problems.