#### Date of Submission

7-28-1998

#### Date of Award

7-28-1999

#### 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

Dutta, Bhaskar (EPU-Delhi; ISI)

#### Abstract (Summary of the Work)

The theory of implementation or mechanism design had its origins in the debates in the 1930s between Hayek, Lange and Lerner on the informational efficiency of the market economy. However, it was the work of Hurwicz in the 1950s and the 1960s which formalised the insights of Hayek, Lange and Lerner and paved the way for the body of work that followed his pioneering effort.In addition to the considerable theoretical literature on mechanism de- sign'. there also exists a body of literature which uses the mechanism design approach to address specific problems. Some examples of work in this vein include Laffont and Tirole (34) on the economies of regulation, Mirrlees (39] on oprimal income tax schemes and Moulin [12 on cost sharing. The thre essays in this thesis are also examples of such wurk. While two of the es- says are formally problems in mechanism design. the third essay is heavily influenced by this literature.In the rest of this chapter, we shall formaily introduce the problem of mechanism design and discuss some theoretical results in this area. We shall then provide an overview of the work contained in this thesis by discussing briefty cach of the essays, and the results contained in them.Formally, a non-cooperative game in strategic form is G= (N, {S.}heN (ui,)eN). where N is the (finite) set of players. Si, is the strategy set of player i and ,: len S,+ R is the payoff function of player i. Let S= IEN S, and S = IIJENJ) A generic element of S-i, shall be denoted s-i An equilib- rium concept e for the game G is a selection from S and is denoted e(G). We now define some specific equilibrium eoncepts.Definition 1.1.1 The atrategy is said to be a dominant strategy for player i if u,(si.8-i) 2 (si, s-1) for all si, E S, and all a-, e S-1 Definition 1.1.2 The atrategy profile s = (si),CN is a dominant strategy nqualibrium of the game G if for each player i e N, si; is a dominant strategy for i. The set of all dominant strategy equilibria of G will be denoted by DS(G).Obviously, a dominant strategy equilibrium need not exist for a given game G. The next equilibrium concept to which we turn to is Nash equilib- rium.Definition 1.1.3 The strategy profile s is a Nash equilibrium of the game G if ui(si,8-i ) 2 (si, 8-i) for all si, E Si. The set of all Nash equilibria of G will be denoted by NE(G).In contrast to the previous concepts which only considered individual incentives to deviate, the next two concepts will require that the equilib- rium situation be immune against coalitional attempts to deviate. Given a coalition TS N, the terms ay and s-t will refer to (s.)ier and (si,)Emr respectively.Definition 1.1.4 The strategy profile s is a Strong Nash equilibrium of the game G if there does not erist TCN, a strategy profile ay for T such that u,(st, r) > ui(s") for all i e T.

#### Control Number

ISILib-TH155

#### 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

Mutuswami, Suresh Dr., "Essays in Mechanism Design." (1999). *Doctoral Theses*. 249.

https://digitalcommons.isical.ac.in/doctoral-theses/249

## 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:28843027