Essays in Mechanism Design/ Aditya Vikram

Thesis(Ph.D) - Indian Statistical Institute, 2021

Includes bibliography

Introduction -- Stability and double auction design -- Budget-balanced mechanisms for single-object allocation problems with interdependent values -- Probability-burning mechanisms in multiple-good allocation problems -- References

Guided by Prof. Arunava Sen

The first chapter investigates the stability of internet platform trading mechanisms using the notion of ex-ante stability. Standard double auction mechanisms in the literature as well as the revenue-maximizing mechanism of the platform may not be single-buyer-single-seller (SBSS) ex-ante stable. We characterize interim incentive-compatible, interim individually-rational and symmetric revenue-maximizing mechanisms that are SBSS ex-ante stable using methods in Myerson and Satterthwaite (1983). The second chapter concerns the allocation of a single object among a set of agents whose valuations are interdependent. We define signal-ranking and valuation-ranking mechanisms. We show that if the s-ranking allocation rule satisfies a combinatorial condition and the valuation functions are additively separable, there exist budget-balanced and ex-post incentive-compatible s-ranking mechanisms. A similar result holds for v-ranking mechanisms if valuation functions also satisfy single-crossing condition. We discuss the efficiency properties of these mechanisms. We also define a third class of mechanisms called probability-burning mechanisms and study its welfare properties. In the third chapter, we study a multi-unit allocation problem where all agents have private valuations. We consider budget-balanced, dominant strategy incentive-compatible and individually-rational probability-burning mechanisms which allocate the units of good with non-zero probability only to the topmost agents. We propose one such mechanism with a reserve price and show that it is welfare-improving over probability-burning mechanism without reserve price given by Mishra and Sharma (2018).