Prof. Dr. Lorens Imhof

E-mail: limhof(at)
Phone: +49 228 73 9265
Institute: Department of Economics
Research Area: Research Area G
Date of birth: 04.Nov 1969
Mathscinet-Number: 360774

Academic Career


Diploma, RWTH Aachen


Dr. rer. nat., RWTH Aachen

1998 - 2004

Assistant Professor of Statistics, RWTH Aachen

1999 - 2000

Postdoc, Stanford University, CA, USA


Habilitation, RWTH Aachen

Since 2004

Associate Professor of Statistics, University of Bonn

Research Profile

I am interested in stochastic models and their applications to economic problems. The focus of my work has been on dynamic models for evolution and learning in games [1,2,3,4]. For example, in [2] we study the evolution of cooperation in a finite population subject to mutation and random migration between subpopulations. A second line of my research is concerned with the economic theory of incentives [5,6]. I have worked on principal-agent models that include various stochastic components. The goal is to develop contracts that provide strong incentives for the agents, when there is uncertainty about, for example, the tasks to be carried out and about the abilities of the agents. Another part of my recent research deals with some questions in information theory. In [7] we study the capacity and achievable data rate in some Gaussian fading channels.

Much of my research on evolutionary game dynamics has focused on the long-run behavior and on equilibrium analysis. In the future I intend to examine the time scales on which evolution takes place. It has been observed in several specific examples that the time needed to reach a state close to equilibrium behavior can be very sensitive to small changes of the underlying game. In [1] we used a Lyapunov approach to determine for some relatively simple models whether a certain target state is reached quickly. I would like to extend these initial investigations to more complex dynamics. For example, such an extension could lead to new insights into equilibrium selection under dynamics for games with iterated dominant equilibria, where a goal state may or may not be reached quickly through several intermediate stages. Another promising area for useful extensions are dynamics in fluctuating environments, which have received a lot of attention recently.

Contribution to Research Areas

Research Area G
My contribution to research area G consists in the development and analysis of stochastic models that help to understand evolution and learning in populations that play games. Essential ingredients are concepts and results from non-cooperative game theory and the theory of stochastic processes, in particular stochastic differential equations and Markov chains.

Selected Publications

[1] Glenn Ellison, Drew Fudenberg, Lorens A. Imhof
Fast convergence in evolutionary models: a Lyapunov approach
J. Econom. Theory , 161: : 1--36
DOI: 10.1016/j.jet.2015.10.008
[2] Christoph Hauert, Yu-Ting Chen, Lorens A. Imhof
Fixation times in deme structured, finite populations with rare migration
J. Stat. Phys. , 156: (4): 739--759
DOI: 10.1007/s10955-014-1022-y
[3] Josef Hofbauer, Lorens A. Imhof
Time averages, recurrence and transience in the stochastic replicator dynamics
Ann. Appl. Probab. , 19: (4): 1347--1368
DOI: 10.1214/08-AAP577
[4] Lorens A. Imhof
The long-run behavior of the stochastic replicator dynamics
Ann. Appl. Probab. , 15: (1B): 1019--1045
DOI: 10.1214/105051604000000837
[5] L. Imhof, M. Kräkel
Bonus pools and the informativeness principle
European Economic Review , 66: : 180--191
[6] L. Imhof, M. Kräkel
\em Ex post unbalanced tournaments
RAND Journal of Economics , 47: (1): 73--98
DOI: 10.1111/1756-2171.12119
[7] Meik Dörpinghaus, Norbert Gaffke, Lorens A. Imhof, Rudolf Mathar
A log-det inequality for random matrices
SIAM J. Matrix Anal. Appl. , 36: (3): 1164--1179
DOI: 10.1137/140954647
[8] Holger Dette, Lorens A. Imhof
Uniform approximation of eigenvalues in Laguerre and Hermite β-ensembles by roots of orthogonal polynomials
Trans. Amer. Math. Soc. , 359: (10): 4999--5018
DOI: 10.1090/S0002-9947-07-04191-8
[9] L. Imhof, S. Walcher
Exclusion and persistence in deterministic and stochastic chemostat models
J. Differential Equations , 217: (1): 26--53
DOI: 10.1016/j.jde.2005.06.017
[10] Lorens A. Imhof
Maximin designs for exponential growth models and heteroscedastic polynomial models
Ann. Statist. , 29: (2): 561--576
DOI: 10.1214/aos/1009210553

Publication List


• Journal of Dynamics and Games, American Institute of Mathematical Sciences (since 2014)

Selected Invited Lectures


Evolutionary Game Dynamics, Banff, AB, Canada


Workshop on Games, Madrid, Spain


Conference on Theoretical and Empirical Population Genetics, Max Planck Institute for Evolutionary Biology, Plön


Conference on Dynamics, Games and Science II, Lisbon, Portugal


Workshop on Persistence of Population Models in Temporally Fluctuating Environments, CIB, EPFL Lausanne, Switzerland

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