David Kraines, Associate Professor

Contact Info:

Office Location:	211 Physics Bldg
Office Phone:	(919) 660-2849
Email Address:
Web Page:	http://www.math.duke.edu/~dkrain

Teaching (Fall 2008):

• MATH 103.01, INTERMEDIATE CALCULUS Synopsis

  LSRC A155, MWF 11:55 AM-12:45 PM

• MATH 149S.01, PROBLEM SOLVING SEMINAR Synopsis

  Physics 119, M 07:30 PM-08:45 PM

• MATH 151S.01, ADVANCED PROBLEM SOLVING Synopsis

  Physics 119, W 06:00 PM-08:00 PM

• MATH 181.01, COMPLEX ANALYSIS Synopsis

  Physics 235, MWF 01:30 PM-02:20 PM

Office Hours:

Tuesday and Thursday 9:00-10:00
& by appointment

Education:

A.B., Oberlin College, magna cum laude, 1961
M.A., University of California, Berkeley, 1963
Ph.D., University of California, Berkeley, 1965

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.

Curriculum Vitae

Recent Publications   (More Publications)

1. David P. Kraines & Vivian Y. Kraines, Protocols for Cooperation; Cultural Diversity of Strategies for the Alternating Prisoner's Dilemma (Submitted, 0) [pdf]
2. David Kraines & Vivian Kraines, Natural selection of memory-one strategies for the iterated prisoner's dilemma, Journal of Theoretical Biology 203 (2000) 335-355
3. David Kraines, Vivian Kraines, The Threshold of Cooperation among Adaptive Agents: Pavlov and the Stag Hunt, Lecture Notes in Artificial Intelligence, Springer Verlag, 1193 (1997), 219-231.
4. David Kraines, Vivian Kraines, Evolution of learning among Pavlov strategies, J. Conflict Resolution 39 (1995), 439-466.
5. David Kraines, Vivian Kraines, Learning to Cooperate with Pavlov: An adaptive strategy for the iterated Prisoner's Dilemma with noise, Theory and Decision 35 (1993), 107-150.