Essays in electronic commerce: Game theoretic analysis and optimization

This dissertation studies three problems motivated by electronic commerce applications.; The first problem deals with the design of revenue maximizing procurement auctions with divisible quantities in a setting where both the marginal cost and the production capacity are private information of the suppliers. We provide a closed-form solution for the revenue maximizing direct mechanism when the prior distribution of the marginal cost and the production capacity satisfies a particular regularity condition. We also present a sealed low bid implementation of the optimal direct mechanism for the special case of identical suppliers, i.e. the symmetric environment. Our results extend to other principle-agent mechanism design problems where the agents have a privately known upper bound on allocation. Examples of problems of this nature include monopoly pricing with adverse selection, forward auctions and scheduling with privately known deadlines and values.; The second problem deals with the design of the optimal sponsored search auctions used by the internet search service providers such as Google and Yahoo!. We begin with a general problem formulation which allows the privately known valuation per click to be a function of both the identity of the advertiser and the slot. We present a compact characterization of the set of all deterministic dominant strategy incentive compatible direct mechanisms for this model. This new characterization allows us to conclude that there are incentive compatible mechanisms for such an auction in a multi-dimensional type-space that are not affine maximizers. Next, we discuss two interesting special cases: slot independent valuation and slot independent valuation up to a privately known slot and zero thereafter. For both of these special cases, we characterize revenue maximizing and efficiency maximizing mechanisms and show that these mechanisms can be computed with a worst case computational complexity O(n2m2) and O(n2m3) respectively, where n is number of bidders and m is number of slots. Next, we characterize optimal rank based allocation rules and propose a new mechanism that we call the customized rank based allocation. We report the results of a numerical study that compare the revenue and efficiency of the proposed mechanisms. The results from this study suggest that customized rank based allocation rule is significantly superior to the rank-based allocation rules.; The third problem studied in this dissertation is the design and analysis of a simple online exchange for matching impatient demand with patient supply. Our proposed exchange mechanism is motivated by the limit order book mechanism used in stock markets. In this model, both buyers and sellers are elastic in the price-quantity space; however, only the sellers are assumed to be patient, i.e. only the sellers have a price-time elasticity, while the buyers are assumed to be impatient. We define and establish the existence of the equilibrium in this model and show how to numerically compute this equilibrium. We derive a closed form for the equilibrium distribution when the demand is price independent. At this equilibrium the selling (limit order) price distribution is power tailed as is empirically observed in order driven financial markets. We extend this model to multiple competing exchanges indexed by quality.