My research emphasizes the theory of evolutionary games and its applications to models in biology and economics. These models can be used to predict the behaviour of individuals in biological populations under the influence of selection as well as the behaviour of humans in conflict situations that can be expressed as noncooperative games. Currently, I am investigating how evolutionary dynamics can be applied to extensive form games [1,21]; to coevolutionary models in biology [2,3,6,7,8,18,19]; to games with a continuous strategy space [5,6,9,17,24,W1]; to models of habitat selection [4,10,12,14,27]; to games with mutation and/or stochastic effects [11,15,16,19,21,26] and to marketing games . I have also recently completed a survey article on ESS , co-authored an article on bargaining , and conducted game experiments on the effects of costly punishment [22,23]. More information on these can be found in the PDF files linked to these references and through a list of my publications at Recent Research Publications and/or Research Publications.
- R.Cressman, Evolutionary Dynamics and Extensive Form Games, MIT Press, 2003.
- R.Cressman and J. Garay, Evolutionary Stability in Lotka-Volterra Systems, J. of Theoretical Biology, 222, 233-245, 2003.
- R. Cressman and J. Garay, Stability in N-Species Coevolutionary Systems, Theoretical Population Biology, 64, 519-533, 2003.
- R. Cressman, V. Krivan and J. Garay, Ideal Free Distributions, Evolutionary Games, and Population Dynamics in Multiple-Species Environments, The American Naturalist, 164, 473-489, 2004.
- R. Cressman, Stability of the Replicator Equation with Continuous Strategy Space, Mathematical Social Sciences, 50, 127-147, 2005.
- R. Cressman and J. Hofbauer, Measure Dynamics on a One-Dimensional Continuous Trait Space: Theoretical Foundations for Adaptive Dynamics, Theoretical Population Biology, 67, 47-59, 2005.
- R. Cressman, Uninvadability in N-Species Frequency Models with Discrete or Continuous Time, Theoretical Population Biology, 69, 253-262, 2006.
- R. Cressman and J. Garay, A Game-Theoretic Model for Punctuated Equilibrium: Species Invasion and Stasis through Coevolution, Biosystems, 84, 1-14, 2006.
- R. Cressman, J. Hofbauer and F. Riedel, Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Trait Space, J. of Theoretical Biology, 239, 273-288, 2006.
- R. Cressman and V. Krivan, Migration Dynamics for the Ideal Free Distribution, The American Naturalist 168, 384-397, 2006.
- Yi Tao and R. Cressman. Stochastic Fluctuations through Intrinsic Noise in Evolutionary Game Dynamics, Bull. of Mathematical Biology, 69, 1377-1399, 2007.
- P.A. Abrams, R. Cressman and V. Krivan, The Role of Behavioral Dynamics in Determining the Patch Distributions of Interacting Species, The American Naturalist, 169, 505-518, 2007.
- R. Cressman, Learing and Evolution in Games: ESS, The New Palgrave Dictionary of Economics, Second Edition (eds: S. Durlauf and L. Blume), Volume 5, 65-69, Palgrave Macmillan, London, 2008.
- V. Krivan, R. Cressman and C. Schneider. The Ideal Free Distribution: A Review and Synthesis of the Game Theoretic Perspective, Theoretical Population Biology, 73, 403-425, 2008.
- Yi Tao, R. Cressman, B. Zhang and X. Zhang. Stochastic Fluctuations in Frequency-Dependent Selection: A One-Locus, Two-Allele and Two-Phenotype Model, Theoretical Population Biology, 74, 263-272, 2008.
- S. Wang, B. Zhang, Z. Li, R. Cressman and Y. Tao. Evolutionary Game Dynamics with Impulsive Effects, J. of Theoretical Biology, 254, 384-389, 2008.
- R. Cressman, Continuously Stable Strategies, Neighborhood Superiority and Two-Player Games with Continuous Strategy Space, International Journal of Game Theory, 38, 221-247, 2009.
- R. Cressman and J. Garay. A Predator-Prey Refuge System: Evolutionary Stability in Ecological Systems, Theoretical Population Biology, 76, 248-257, 2009.
- V. Krivan and R. Cressman. On Evolutionary Stability in Prey-Predator Models with Fast Behavioral Dynamics, Evolutionary Ecology Research, 11, 227-251, 2009.
- R. Cressman and M. Gallego. On the Ranking of Bilateral Bargaining Opponents, Mathematical Social Sciences, 58, 64-83, 2009.
- H. Gintis, R. Cressman and T. Ruijgrok, Subgame Perfection in Evolutionary Dynamics with Recurrent Perturbations, in Handbook of Research on Complexity (ed. J. Barkley Rosser), 353-368, Edward Elgar Publishing, Northampton, MA, 2009.
- J-J. Wu, B-Y. Zhang, Z-X. Zhou, Q-Q. He, X-D. Zhang, R. Cressman and Y. Tao. Costly Punishment does not always increase Cooperation, Proceedings of the National Academy of Science USA, 106, 17448-17451, 2009.
- Y. Tao, C. Li., J-J. Wu and R. Cressman. The Efficiency Ratio of Costly Punishment, Proceedings of the National Academy of Science USA, 106, E136, 2009.
- R. Cressman. CSS, NIS and Dynamic Stability for Two-Species Behavioral Models with Continuous Trait Spaces, J. of Theoretical Biology, 262, 80-89, 2010.
- Z. Varga, A. Scarelli, R. Cressman and J. Garay. Evolutionary Game Model for a Marketing Cooperative with Penalty for Unfaithfulness, Nonlinear Analysis: Real World Applications, 11, 742-749, 2010.
- B. Zhang, R. Cressman and Y. Tao. Cooperation and Stability through Periodic Impulses, PLoS One 5, e9882.
- R. Cressman and V. Krivan. The Ideal Free Distribution as an Evolutionarily Stable State in Density-Dependent Populations Games, OIKOS, forthcoming, 2010.
- W1. R. Cressman, Coevolution, Adaptive Dynamics, and the Replicator Equation for a Single Species with a Continuous Strategy Space, mimeo, 2004.