David P. Kraines
- Associate Professor Emeritus of Mathematics
Research Areas and Keywords
Dr. Kraines contributed to the theory of homology and cohomology operations, particularly to Massey products and loop operations. Among the applications of his work has been his construction of the counterexample to the transfer conjecture of Quillen. He has also studied the variational bicomplex of Vinogradov and introduced the cohomology of quantum electrodynamics. Dr. Kraines has applied game theoretical techniques to study the evolution of cooperation. With Dr. Vivian Kraines, he introduced a stochastic learning approach, dubbed the Pavlov strategy, for the iterated Prisoner's Dilemma. They show that, in a noisy environment, agents using the Pavlov strategy may achieve a higher level of cooperation than those using Tit for Tat type strategies. Using computer simulations, dynamic systems and Markov chains, they extend their analysis to the evolution of the rate of learning in a society of Pavlov type agents. Recently, they have explored the natural selection of stochastic strategies in the simultaneous and the alternating Prisoner's Dilemma and identified several evolutionarily stable strategies.
Kraines, D, and Kraines, V. "The threshold of cooperation among adaptive agents: Pavlov and the stag hunt." Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 1193 (January 1, 2015): 219-231.
Kraines, DP, and Kraines, VY. "Natural selection of memory-one strategies for the iterated prisoner's dilemma." J Theor Biol 203.4 (April 21, 2000): 335-355. Full Text
Kraines, D, and Kraines, V. "Evolution of Learning among Pavlov Strategies in a Competitive Environment with Noise." Journal of Conflict Resolution 39.3 (September 1995): 439-466. Full Text
Kraines, D, and Kraines, V. "Learning to cooperate with Pavlov an adaptive strategy for the iterated Prisoner's Dilemma with noise." Theory and Decision 35.2 (1993): 107-150. Full Text
Geist, R, Kraines, D, and Fink, P. "NATURAL LANGUAGE COMPUTING IN A LINEAR ALGEBRA COURSE." (1982): 203-208.
Kraines, D. "The Kernel of the loop suspension map." Illinois Journal of Mathematics 21.1 (January 1, 1977): 91-108.
Kraines, D. "The A(p) cohomology of some k stage Postnikov systems." Commentarii Mathematici Helvetici 48.1 (1973): 56-71. Full Text
Kraines, D, and Schochet, C. "Differentials in the Eilenberg-Moore spectral sequence." Journal of Pure and Applied Algebra 2.2 (1972): 131-148. Full Text
Students and faculty enjoyed a break before exams to share food and conversation at the annual math party on April 24, 2017. Those who competed in the MCM/ICM competition received Duke Math shirts and certificates. Officers of DUMU and research... read more »
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Steven J. Miller, Associate Professor of mathematics at Williams College, delivered the first Duke University Math Union (DUMU) guest lecture of the 2016-2017 year to an audience including nearly 50 undergraduates on Wednesday, September 7, 2016..... read more »
The Duke University Math Union (DUMU) is devoted to organizing and providing resources to students interested in mathematics. Throughout the year, we invite guest lecturers, organize social events, and host a high school contest in mathematics.... read more »