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, 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 (September 1993): 107-150. Full Text
Kraines, D, and Fink, P. "NATURAL LANGUAGE COMPUTING IN A LINEAR ALGEBRA COURSE." (December 1, 1982): 203-208.
"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 (July 1972): 131-148. Full Text
Registration for the 2018 Duke Math Meet is now CLOSED. The Duke Math Meet (DMM) is a regional mathematics competition for high school students held at Duke University each year. The contest is organized by the members of the Duke University... read more »
On a cool, cloudy Saturday in early November, 45 teams of high school students from Virginia, the Carolinas, and even three from China came to the Duke Campus to participate in the annual Duke Math Meet. After a light breakfast, each team was led to... 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 »