Skip to main content

David P. Kraines

Associate Professor Emeritus of Mathematics
Mathematics
Office hours send message to dkrain@math.duke.edu  

Selected Publications


The threshold of cooperation among adaptive agents: Pavlov and the stag hunt

Journal Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) · January 1, 2015 Why is it that in an animal society, persistent selfishness is quite rare yet in human society, even strict laws and severe punishment do not eliminate selfish action against the interests of the whole? Stochastic learning agents called Pavlov strategies a ... Cite

Natural selection of memory-one strategies for the iterated prisoner's dilemma.

Journal Article Journal of theoretical biology · April 2000 In the iterated Prisoner's Dilemma, mutually cooperative behavior can become established through Darwinian natural selection. In simulated interactions of stochastic memory-one strategies for the Iterated Prisoner's Dilemma, Nowak and Sigmund discovered th ... Full text Cite

Evolution of Learning among Pavlov Strategies in a Competitive Environment with Noise

Journal Article Journal of Conflict Resolution · January 1, 1995 Pavlov denotes a family of stochastic learning strategies that achieves the mutually cooperative outcome in the iterated prisoner's dilemma against a wide variety of strategies, although it can be exploited to some extent by some. When restricted to an env ... Full text Cite

Learning to cooperate with Pavlov an adaptive strategy for the iterated Prisoner's Dilemma with noise

Journal Article Theory and Decision · September 1, 1993 Conflict of interest may be modeled, heuristically, by the iterated Prisoner's Dilemma game. Although several researchers have shown that the Tit-For-Tat strategy can encourage the evolution of cooperation, this strategy can never outscore any opponent and ... Full text Cite

Pavlov and the prisoner's dilemma

Journal Article Theory and Decision · January 1, 1989 Our Pavlov learns by conditioned response, through rewards and punishments, to cooperate or defect. We analyze the behavior of an extended play Prisoner's Dilemma with Pavlov against various opponents and compute the time and cost to train Pavlov to cooper ... Full text Cite

The Kernel of the loop suspension map

Journal Article Illinois Journal of Mathematics · January 1, 1977 Full text Cite

The A(p) cohomology of some k stage Postnikov systems

Journal Article Commentarii Mathematici Helvetici · 1973 Full text Cite

Differentials in the Eilenberg-Moore spectral sequence

Journal Article Journal of Pure and Applied Algebra · January 1, 1972 Full text Cite

A duality between transpotence elements and Massey products

Journal Article Pacific Journal of Mathematics · January 1, 1971 The purpose of this note is to show that if v is an element whose suspension is nonzero, and if n is dual to v, then the transpotence φk(v) is defined and nonzero if and only if the K-Massey product k is defined and nonzero. © 1971, Pacific Journal of Math ... Full text Cite

On Excess in the Milnor Basis

Journal Article Bulletin of the London Mathematical Society · January 1, 1971 Full text Cite

Rational cohomology operations and massey products

Journal Article Proceedings of the American Mathematical Society · January 1, 1969 Full text Cite

Primitive chains and H*(ΩX)

Journal Article Topology · January 1, 1969 Full text Cite

Primitive chains and H*(ΩX)

Journal Article Topology · 1969 Cite

Higher products

Journal Article Bulletin of the American Mathematical Society · January 1, 1966 Full text Cite

Massey higher products

Journal Article Transactions of the American Mathematical Society · January 1, 1966 Full text Cite