The project aims to study optimal combinatorial auctions, which are a challenging problem in economic theory. The study of optimal multi-object auctions is one of the most challenging problems due to the change in incentive constraints as we move from a single object to multiple objects. In the case of a government selling a single object to a set of buyers, the seller must design a mechanism that maximizes expected revenue/payment from selling the right to mine. The optimal solution of this optimization problem is "integral," meaning either no buyer is given the right to mine or one buyer is given the right to mine for the entire period (the price paid by such a buyer is a function of this allocation rule). This remarkable theoretical result explains many existing practices where such auctions are used to allocate a single object. The main objective of this project is to investigate how far this theoretical result extends if there are multiple objects. The significance of this result is twofold: (i) optimization over the set of deterministic mechanisms is easy (can be done in a computer), and (ii) deterministic mechanisms are widely used, providing a foundation for these mechanisms. The results of the project will serve as guideposts for the design of optimal combinatorial auctions, as they provide a foundation for optimizing over the set of deterministic mechanisms without loss of generality.
Indian Statistical Institute, West Bengal
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