David P. Kraines, Associate Professor Emeritus
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.  Contact Info:
Teaching (Fall 2021):
 MATH 283S.01, ADVANCED PROBLEM SOLVING
Synopsis
 Physics 119, Tu 07:00 PM08:15 PM
 Office Hours:
 send message to dkrain@math.duke.edu
 Education:
Ph.D.  University of California  Berkeley  1965 
M.A.  University of California  Berkeley  1963 
B.A.  Oberlin College  1961 
 Research Interests: Algebraic Topology and Game Theory
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.
 Keywords:
Animals • Cooperative Behavior • Game Theory • Humans • Mathematics • Memory • Models, Genetic • Population Dynamics • Selection, Genetic
 Curriculum Vitae
 Undergraduate Research Supervised
 Theodore Freylinghuysen (2010  2012)
 Hans Kist (2009  2011)
 Recent Publications
(More Publications)
 Kraines, D; 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), vol. 1193
(January, 2015),
pp. 219231, ISSN 03029743 [abs]
 Kraines, DP; Kraines, VY, Natural selection of memoryone strategies for the iterated prisoner's dilemma.,
Journal of Theoretical Biology, vol. 203 no. 4
(April, 2000),
pp. 335355, ISSN 00225193 [10736212], [doi] [abs]
 Kraines, D; Kraines, V, Evolution of Learning among Pavlov Strategies in a Competitive Environment with Noise,
Journal of Conflict Resolution, vol. 39 no. 3
(January, 1995),
pp. 439466, SAGE Publications [doi] [abs]
 Kraines, D; Kraines, V, Learning to cooperate with Pavlov an adaptive strategy for the iterated Prisoner's Dilemma with noise,
Theory and Decision, vol. 35 no. 2
(September, 1993),
pp. 107150, Springer Nature, ISSN 00405833 [doi] [abs]
 Kraines, D; Kraines, V, Pavlov and the prisoner's dilemma,
Theory and Decision, vol. 26 no. 1
(January, 1989),
pp. 4779, Springer Nature, ISSN 00405833 [doi] [abs]
