David P. Kraines

David P. Kraines
  • Associate Professor Emeritus of Mathematics
External address: 233 Physics Bldg, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2849

Research Areas and Keywords

Biological Modeling

Prisoner's dilemma, sequestering CO2


cohomology operations

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.

Education & Training
  • Ph.D., University of California at Berkeley 1965

  • M.A., University of California at Berkeley 1963

  • B.A., Oberlin College 1961

Selected Grants

VIGRE awarded by National Science Foundation (Co-Principal Investigator). 2000 to 2003

Kraines, D., and V. Kraines. “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, Jan. 2015, pp. 219–31.

Kraines, D. P., and V. Y. Kraines. “Natural selection of memory-one strategies for the iterated prisoner's dilemma.Journal of Theoretical Biology, vol. 203, no. 4, Apr. 2000, pp. 335–55. Epmc, doi:10.1006/jtbi.2000.1089. Full Text

Kraines, D., and V. Kraines. “Evolution of Learning among Pavlov Strategies in a Competitive Environment with Noise.” Journal of Conflict Resolution, vol. 39, no. 3, Jan. 1995, pp. 439–66. Scopus, doi:10.1177/0022002795039003003. Full Text

Kraines, D., and V. Kraines. “Learning to cooperate with Pavlov an adaptive strategy for the iterated Prisoner's Dilemma with noise.” Theory and Decision, vol. 35, no. 2, Sept. 1993, pp. 107–50. Scopus, doi:10.1007/BF01074955. Full Text

Kraines, D., and V. Kraines. “Pavlov and the prisoner's dilemma.” Theory and Decision, vol. 26, no. 1, Jan. 1989, pp. 47–79. Scopus, doi:10.1007/BF00134056. Full Text


Kraines, D. “The Kernel of the loop suspension map.” Illinois Journal of Mathematics, vol. 21, no. 1, Jan. 1977, pp. 91–108.

Kraines, D. “The A(p) cohomology of some k stage Postnikov systems.” Commentarii Mathematici Helvetici, vol. 48, no. 1, 1973, pp. 56–71. Manual, doi:10.1007/BF02566111. Full Text

Kraines, D., and C. Schochet. “Differentials in the Eilenberg-Moore spectral sequence.” Journal of Pure and Applied Algebra, vol. 2, no. 2, Jan. 1972, pp. 131–48. Scopus, doi:10.1016/0022-4049(72)90018-7. Full Text

Kraines, D. “A duality between transpotence elements and Massey products.” Pacific Journal of Mathematics, vol. 39, no. 1, Jan. 1971, pp. 119–23.


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