Abhimanyu Khan
webpage: http://researchers-sbe.unimaas.nl/AbhimanyuKhan
Contact Information
Maastricht University
Tongersestraat 53, P.O Box 6200 MD
Maastricht, Netherlands
Education
Email : [email protected]
Nationality: Indian
Ph.D., Economics, Maastricht University (expected : 2014)
Advisor: Jean-Jacques Herings, Ronald Peeters
Research Fields: Applied Evolutionary Game Theory, Networks,
Industrial Organisation
M.S. Economics, University of Illinois at Urbana Champaign, 2009
M.S. Quantitative Economics, Indian Statistical Institute, 2006
B.A. Economics (Honors), St. Stephen’s College, Delhi University, 2004
Papers
Coordination under global random interaction and local imitation [Accepted
at International Journal of Game Theory]
Abstract: Individuals are randomly matched to play a 2 × 2 coordination game where
the Pareto efficient and risk dominant equilibria differ. Players choose strategies by
imitating the strategy of the most successful individual they observe. So, while individuals interact globally, their observation and hence imitation, as determined by their
social network, may be local. When all individuals observe each other, the most successful individual in the entire population is imitated; here, in the stochastically stable
state, the population coordinates on the Pareto-efficient outcome. While this outcome
is always stochastically stable even when observability is incomplete, the state where
everyone plays the action of the risk-dominant equilibrium may be stochastically stable as well. Reasonably tight sufficient conditions for unique stochastic stability of the
state where all coordinate on the Pareto-efficient equilibrium strategy include each individual observing at least four other individuals or when each individual observes the
same number of other individuals. These properties are readily generaliseable to larger
m × m coordination games where the coordination outcomes can be Pareto-ranked.
Cognitive hierarchies in adaptive play (with Ronald Peeters) [Accepted, International Journal of Game Theory]
Abstract: Inspired by the behavior in repeated guessing game experiments, we study
adaptive play by populations containing individuals that reason with different levels of
cognition. Individuals play a higher order best response to samples from the empirical
data on the history of play, where the order of best response is determined by their exogenously given level of cognition. As in Young’s model of adaptive play, (unperturbed)
play still converges to a minimal curb set. Random perturbations of the best response
dynamic identifies the stochastically stable states. In Young’s model of adaptive play
with simple best-responses, the set of stochastically stable states are sensitive to the
sample size that individuals from a population can draw. In generic games with higher
order best-responders in both populations, the sample size is rendered irrelevant in
determination of the stochastically stable set. Perhaps counter-intuitively, higher cognition may actually be bad for both the individual with higher cognition and his parent
population.
Imitation by price and quantity setting firms in a differentiated market (with
Ronald Peeters) [Revise and re-submit, Journal of Economic Dynamics and Control]
Abstract: We study the evolution of imitation behaviour in a differentiated market
where firms are located equidistantly on a (Salop) circle. Firms choose price and quantity simultaneously, leaving open the possibility for non-market clearing outcomes. The
strategy of the most successful firm is imitated. Behaviour in the stochastically stable
outcome depends on the level of market differentiation and corresponds exactly with
the Nash equilibrium of the underlying game. For high level of differentiation, firms
end up at the monopoly outcome. For intermediate level of differentiation, they gravitate to a “mutually non-aggressive” outcome where price is higher than the monopoly
price. For low level of differentiation, firms price at a mark-up above the marginal cost.
Market clearing always results endogenously.
Evolution of behavior when duopolists choose prices and quantities (with
Ronald Peeters)
Abstract: We study duopolistic competition in a differentiated market with firms
setting prices and quantities, without explicitly imposing market clearing. Unlike the
commonly adopted assumption of profit maximizing firms, we assume firm behavior
to be shaped by a Darwinian dynamic: the less fitter firm imitates the fitter firm and
occasionally firms may experiment with a random price and/or quantity. Our two main
findings are that: (i) a market clearing outcome always belongs to the set of feasible
long run outcomes, but may co-exist with non-market clearing outcomes with as well
excess supply as excess demand being possible; and (ii) there exist parameter configurations for which the only feasible outcomes imply prices above monopoly level.
Referee
Activity
International Journal of Game Theory
Mathematical Social Sciences
Presentation at
Conferences
NAKE Day, Utrecht, 2011
Society for Advancement of Economic Theory (SAET) 2011
GAMES 2012 (4th World Congress of the Game Theory Society)
11th Workshop on Networks in Economics and Sociology, Utrecht University, 2013
Teaching
Experience
University of Illinois at Urbana Champaign: Teaching Assistant for Principles of
Macroeconomics (Fall 2007-Spring 2009)
Maastricht University: Teaching Assistant for Information, Markets and Organisation
(2010, 2011), Introduction to Business and Economics (2010, 2011, 2012), Microeconomics (2011, 2012), Intermediate Microeconomics (2012), Reflections on Academic
Discourse (2013), Economists Point of View (2013), Micro-Macro (2013)
Professional
Experience
Risk Analyst, Genpact (previously G.E. Capital International Services), 2006 - 2007
References
Jean-Jacques Herings
Maastricht University
[email protected]
William H. Sandholm
University of Wisconsin (Madison)
[email protected]
Ronald Peeters
Maastricht University
[email protected]