#### Date of Submission

10-28-2014

#### Date of Award

10-28-2015

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Quantitative Economics

#### Department

Economics and Planning Unit (EPU-Delhi)

#### Supervisor

Mishra, Debasis (EPU-Delhi; ISI)

#### Abstract (Summary of the Work)

This thesis consists of three chapters that aim to characterize incentive compatible mechanisms in specific mechanism design settings. In these settings, the designer is allowed to use payments but the net utility of every agent is linear in payments. This particular assumption on net utility is called quasi-linearity. Each of the three chapters in the thesis identifies a class of mechanisms and characterizes them (in quasilinear private value environment) using dominant strategy incentive compatibility and some additional reasonable conditions.In quasi-linear environment, a mechanism can be decomposed into an allocation rule and a payment rule for every agent. If a mechanism is dominant strategy incentive compatible, then we say that the corresponding allocation rule is implementable. The classic Vickrey-Clarke-Groves (Vickrey, 1961; Clarke, 1971; Groves, 1973) mechanisms implement the efficient allocation rule by using Groves payments. Under reasonable conditions, these are the only payment rules that implement the efficient allocation rule (Holmstrom, 1979). This feature generalizes to any implementable allocation rule, and is known as the revenue equivalence principle. As a consequence of the revenue equivalence, the characterization of the class of incentive compatible mechanism can be done in two steps: (a) characterize the implementable allocation rules (b) for each implementable allocation rule, identify one payment rule that implements it. We follow this prescription in all three chapters. The characterization of implementable allocation rules will depend, among other things, on the type space considered in the problem. The type space that we consider in all these three chapters is one dimensional (a connected subset of R++). This makes the characterization harder since the type space is restricted. If the type space was unrestricted, then Roberts (1979) has shown that under mild additional condition only affine maximizer allocation rules are implementable. Affine maximizers are linear generalization of efficient allocation rule. In one dimensional type spaces that we consider, we identify a significantly larger class of implementable allocation rules and characterize them.The first chapter considers the standard single object auction model in private values setting. It identifies the class of allocation rules that is called strongly rationalizable allocation rules. These are the only rules that are implementable and satisfy a condition knownas non-bossiness (Satterthwaite and Sonnenschein, 1981). Non-bossiness requires that if an agent changes his type such that his own allocation does not change, then the allocation of other agents must not change. Under additional technical condition, this characterization can be sharpened. In particular, we identify a class of allocation rules called simple utility maximizers and show that each strongly rationalizable allocation rule is equivalent to a simple utility maximizer under a technical condition. The advantage of this characterization is that simple utility maximizer is easier to use and interpret than the strongly rationalizable allocation rule. They are also a natural extension of Robertsâ€™ affine maximizer rules.The second chapter considers an abstract model where the set of alternatives exhibits certain discrete structural properties. In particular, we assume that alternatives are bases of a matroid. Each agent owns an element of the ground set of the matroid. The advantage of this model is that it covers many practical models as special cases. We show that this model covers the single object auction problem, multi-unit auction model with unit demand, the heterogeneous good auction with dichotomous preferences and a connected graph model.

#### Control Number

ISILib-TH394

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

#### DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

#### Recommended Citation

Quadir, Abdul Dr., "Essays on Auctions and Mechanism Design." (2015). *Doctoral Theses*. 266.

https://digitalcommons.isical.ac.in/doctoral-theses/266

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843045