## Doctoral Theses

### Essays on Strategy-Proofness and Implementation.

4-28-2015

4-28-2016

#### Institute Name (Publisher)

Indian Statistical Institute

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

Mathematics

#### Department

Economics and Planning Unit (EPU-Delhi)

#### Supervisor

Sen, Arunava (EPU-Delhi; ISI)

#### Abstract (Summary of the Work)

This thesis comprises of three chapters relating to strategy-proofness and implementation. We provide a brief description of each chapter below.1.1 A Hurwicz Type Result in a Model with Public Good Production We consider a two-good model with an arbitrary number of agents. One of the goods is a public good and the other is a private good. Each agent has an endowment of the private good and the private good can be converted into the public good using a well-behaved production function. A Social Choice Function (SCF) associates an allocation with each admissible preference profile. We impose the following requirements on the SCF. Strategy-proofness: Agent preferences are assumed to be private information and must be elicited. The SCF therefore must be designed to provide agents with dominant strategy incentives to reveal their private information truthfully. Pareto-efficiency: The SCF specifies a Pareto-efficient allocation at every preference profile. If this condition is violated, agents will have incentives to re-trade their received allocations ex-post. Individual Rationality: Agents must be at least as well-off as they would had they consumed their private good endowment. This is a minimal requirement for agents to participate voluntarily in the mechanism.We show that these requirements are incompatible with a minimal continuity requirement on the SCF defined over a small preference domain.For our result, we consider a domain D that consists of all preferences defined by utility functions of the formU(xi , y; Î¸i) = Î¸i âˆš xi + y, Î¸i > 0.where xi and y refer to the levels of the private good and the public good respectively.The domain D is a restricted domain - it is a single-crossing domain (see Goswami (2013) and Saporiti (2009)). We consider SCF’s that satisfy Pareto-efficiency, individual rationality and continuity (defined with respect to the Î¸i parameters) over D. However, the SCFs are strategy-proof over a larger domain. This domain consists of D and preferences that are common concavifications 1 of those in D at every consumption bundle. The entire classical domain satisfies this requirement but significantly smaller domains are sufficient. The public good is produced according to a general cost function c(y) that is strictly increasing and weakly convex. According to our result, there does not exist a SCF satisfying strategy-proofness over the extended domain and Pareto-efficiency, individual rationality and continuity over D.

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:28843052

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