RAJNISH  KUMAR

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 My research interests include Mechanism design, Cost sharing, Game theory, Social choice theory and Microeconomic theory.

 

Job market paper

“Secure Implementation in Production Economies” (pdf)

Abstract:  One thing that has been assumed for a long time is that whenever there is dominant strategy equilibrium in the game form of any mechanism and the outcome corresponding to that strategy profile is socially optimal, people will play that particular equilibrium strategy profile. The theory has been silent on why they will play that particular strategy profile when there are other (Nash) equilibria. The Nash/Bayes’ Nash implementation being a possible solution to this problem suffers from the drawback of either the requirement of the designer knowing the (common) prior (in case of Bayes’ Nash implementation) or the requirement of the players predicting the actions of other players and collaborate without pre-talk (in case of Nash implementation with absence of dominant strategy or unique Nash).

Secure implementation [Saijo et al. (2007)] is a relatively new concept in the theory of mechanism design and implementation. This requires double implementation in Dominant Strategy Equilibrium and Nash Equilibrium by the same Mechanism. This concept has worked well in some particular environments and has been tested on data [Cason et al. (2006)]. Unsurprisingly, being stronger than both the two above said concepts of implementation, there are many impossibility results in specific environments with richer domains. We look for secure implementability in production economies with divisible goods. We find that a very broad generalization of "Serial" Social Choice Function (SCF) [Moulin and Shenker (92)] as defined in [Shenker (92)] is securely implementable. We call such functions as Generalized Serial SCF (GSS). We also find that under certain conditions the Fixed Path SCFs are special cases of GSS and thus they are also securely Implementable.  We conjecture that these are the only securely implementable SCFs in our environment if we add few desirable axioms.

 

Working paper

“Implementing Efficient Graphs in Connection Networks” (pdf) co-authored with Ruben Juarez

Abstract: We consider the problem of sharing the cost of a network which meets the connection demands of a set of agents. The agents simultaneously choose a path in the network connecting the demand nodes of the agents, and a mechanism splits the total cost of the network formed among the participants.

The recent literature has converged to the Shapley mechanism (Sh) which splits the cost of edges equally among its users. Two reasons motivate us to look at alternatives mechanisms. First, Sh is inefficient, asymmetric and discontinuous at equilibrium. Second, Sh requires an amount of information which may not be practical in many settings.

We characterize a class of mechanisms in a setting of minimal information requirement, specifically when the inputs of a mechanism are the total cost of the network formed and the cost of the paths demanded by the agents. The Average Cost mechanism (AC) and other asymmetric mechanisms implement the efficient connection. These mechanisms are characterized under three alternative robust    properties of efficient implementation.

We also show that efficiency and individual rationality are mutually incompatible. The Egalitarian mechanism (EG), a variation of AC that meets individual rationality, is an optimal mechanism (under the price of stability measure) across all individually rational mechanisms. EG outperforms Sh on the grounds of information requirements, stability and symmetry at equilibrium. Moreover, EG is no more inefficient than Sh.

 

Publications:

Book:

SMALL AREA ESTIMATES OF SELECTED WELFARE INDICATORS: RESULTS FOR UTTARANCHAL. November 2005, United Nations World Food Programme. Co-authored with Shubhashis Gangopadhayay, PAN Network, Maithili Ramachandran, T.O.Sridevi, Brinda Viswanathan and Wilima Wadhwa.