Karl Sigmund | Academic Influence

Karl Sigmund's AcademicInfluence.com Rankings

Karl Sigmund

Mathematics

#678

World Rank

#1243

Historical Rank

Measure Theory

#542

World Rank

#757

Historical Rank

mathematics Degrees

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Mathematics

Karl Sigmund's Degrees

PhD Mathematics University of Vienna

Why Is Karl Sigmund Influential?

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According to Wikipedia, Karl Sigmund is a Professor of Mathematics at the University of Vienna and one of the pioneers of evolutionary game theory. Career Sigmund was schooled in the Lycée Francais de Vienne. From 1963 to 1968 he studied at the Institute of Mathematics at the University of Vienna, and obtained his Ph.D. under the supervision of Leopold Schmetterer. He spent his postdoctorate years at Manchester , the Institut des hautes études scientifiques in Bures-sur-Yvette near Paris , the Hebrew University in Jerusalem , the University of Vienna and the Austrian Academy of Sciences . In 1972 he received habilitation.

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Karl Sigmund's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Evolutionary Games and Population Dynamics (1998) (4948)
Evolution of indirect reciprocity by image scoring (1998) (2449)
A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game (1993) (1613)
Evolution of indirect reciprocity (2005) (1333)
Evolutionary game dynamics (2011) (1077)
Evolutionary Dynamics of Biological Games (2004) (964)
Tit for tat in heterogeneous populations (1992) (904)
Ergodic Theory on Compact Spaces (1976) (845)
Volunteering as Red Queen Mechanism for Cooperation in Public Goods Games (2002) (844)
Fairness versus reason in the ultimatum game. (2000) (803)
Via Freedom to Coercion: The Emergence of Costly Punishment (2007) (663)
Reward and punishment (2001) (585)
Social learning promotes institutions for governing the commons (2010) (455)
The Calculus of Selfishness (2010) (377)
Antigenic oscillations and shifting immunodominance in HIV-1 infections (1995) (357)
Punishment and reputation in spatial public goods games (2003) (337)
The dynamics of indirect reciprocity. (1998) (327)
A note on evolutionary stable strategies and game dynamics. (1979) (307)
Replicator dynamics for optional public good games. (2002) (295)
Punish or perish? Retaliation and collaboration among humans. (2007) (294)
The evolution of stochastic strategies in the Prisoner's Dilemma (1990) (288)
Exploration dynamics in evolutionary games (2009) (256)
Evolution of extortion in Iterated Prisoner’s Dilemma games (2012) (245)
The theory of evolution and dynamic systems mathematical aspects of selection (1984) (233)
Inferring Cellular Networks Using Probabilistic Graphical Models (2004) (220)
Adaptive dynamics and evolutionary stability (1990) (200)
Evolutionary game theory (1995) (194)
Punishing and abstaining for public goods (2006) (190)
Games of Life: Explorations in Ecology, Evolution and Behaviour (1993) (178)
On dynamical systems with the specification property (1974) (177)
The Alternating Prisoner's Dilemma (1994) (167)
The arithmetics of mutual help. (1995) (165)
The logic of reprobation: assessment and action rules for indirect reciprocation. (2004) (162)
The spatial ultimatum game (2000) (161)
Incentives and opportunism: from the carrot to the stick (2010) (157)
Indirect reciprocity, image scoring, and moral hazard. (2005) (153)
Generic properties of invariant measures for AxiomA-diffeomorphisms (1970) (153)
Chaos and the evolution of cooperation. (1993) (133)
Dynamical systems under constant organiza-tion III: Cooperative and competitive behaviour of hypercy (1979) (128)
Oscillations in the evolution of reciprocity. (1989) (123)
Coyness, philandering and stable strategies (1981) (121)
The economics of fair play. (2002) (118)
The good, the bad and the discriminator--errors in direct and indirect reciprocity. (2006) (116)
Topological dynamics of transformations induced on the space of probability measures (1975) (113)
Partners or rivals? Strategies for the iterated prisoner's dilemma☆ (2015) (111)
The take-it-or-leave-it option allows small penalties to overcome social dilemmas (2012) (110)
Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity (1998) (107)
Games Of Life (1993) (103)
Genetic and Cultural Evolution of Cooperation (2003) (102)
The efficiency of adapting aspiration levels (1998) (98)
Automata, repeated games and noise (1995) (98)
Moral assessment in indirect reciprocity (2012) (87)
Kepler’s conjecture: How some of the greatest minds in history helped solve one of the oldest math problems in the world (2004) (81)
Polynucleotide evolution and branching processes. (1985) (77)
Public Goods With Punishment and Abstaining in Finite and Infinite Populations (2008) (75)
Dynamical Systems Under Constant Organization II: Homogeneous Growth Functions of Degree $p = 2$ (1980) (74)
The competition of assessment rules for indirect reciprocity. (2010) (74)
Games on Grids (1999) (73)
What is life? The next fifty years (1996) (70)
The evolution of sanctioning institutions: an experimental approach to the social contract (2013) (68)
Shaken not stirred: on permanence in ecological communities. (1998) (67)
On $\omega $-Limits for Competition Between Three Species (1979) (65)
Dynamical systems under constant organization I. Topological analysis of a family of non-linear differential equations--a model for catalytic hypercycles. (1978) (62)
Game-dynamical aspects of the prisoner's dilemma (1989) (60)
Shrewd Investments (2000) (59)
Equal Pay for All Prisoners (1997) (55)
Dynamics of Evolutionary Optimization (1985) (55)
Immune responses against multiple epitopes. (1995) (53)
On the Space of Invariant Measures for Hyperbolic Flows (1972) (50)
Group Report: The Cultural and genetic Evolution of Human Cooperation (2003) (48)
Phage-lift for game theory (1999) (48)
Cooperation versus Competition (2000) (47)
Competition and cooperation in catalytic selfreplication (1981) (45)
Games of corruption: how to suppress illegal logging. (2015) (44)
On the dynamics of asymmetric games (1991) (44)
Complex Adaptive Systems and the Evolution of Reciprocation (1998) (42)
On the stabilizing effect of predators and competitors on ecological communities (1989) (40)
Freedom, enforcement, and the social dilemma of strong altruism (2010) (39)
The dynamics of public goods (2004) (39)
Mass action kinetics of selfreplication in flow reactors (1980) (37)
Selfregulation of behaviour in animal societies (1981) (36)
The logic of contrition. (1997) (36)
Social Control and the Social Contract: The Emergence of Sanctioning Systems for Collective Action (2011) (34)
The role of Mendelian genetics in strategic models on animal behaviour. (1983) (34)
A Survey of Indirect Reciprocity (2007) (31)
Elementary step dynamics of catalytic hypercycles. (1980) (31)
Kolmogorov and population dynamics (2007) (29)
Dynamics of Macrosystems (1985) (29)
Biodiversity: Bacterial game dynamics (2002) (29)
Time averages for unpredictable orbits of deterministic systems (1992) (29)
A Survey of Replicator Equations (1986) (28)
Evolutionary Games (2010) (27)
Permanence for Replicator Equations (1987) (27)
Game dynamics, mixed strategies, and gradient systems (1987) (26)
Permanence and Uninvadability for Deterministic Population Models (1984) (26)
Social evolution leads to persistent corruption (2019) (26)
Invasion Dynamics of the Finitely Repeated Prisoner's Dilemma (1995) (24)
Sympathy and similarity: The evolutionary dynamics of cooperation (2009) (24)
How Populations Cohere: Five Rules for Cooperation (2007) (24)
Selfregulation of behaviour in animal societies (1981) (23)
Selfregulation of behaviour in animal societies (2004) (22)
On prisoners and cells (1992) (22)
Game dynamics in mendelian populations (1982) (22)
Exact Thinking in Demented Times: The Vienna Circle and the Epic Quest for the Foundations of Science (2017) (22)
On minimal centers of attraction and generic points. (1977) (21)
On mixing measures for axiom A diffeomorphisms (1972) (20)
On the connectedness of ergodic systems (1977) (19)
Super- and Coinfection: The Two Extremes (2002) (19)
Towards a dynamics of social behaviour: Strategic and genetic models for the evolution of animal conflicts (1985) (18)
The Maximum Principle for Replicator Equations (1984) (18)
Evolutionary Games and Population Dynamics: Asymmetric games (1998) (18)
A philosopher’s mathematician: hans hahn and the vienna circle (1995) (18)
Evolutionary game dynamics : American Mathematical Society Short Course, January 4-5, 2011, New Orleans, Louisiana (2011) (17)
A note on the evolution of sexual dimorphism. (1982) (17)
The Economics of Fairness (2002) (16)
Random selection — a simple model based on linear birth and death processes (1984) (16)
A maximum principle for frequency dependent selection (1987) (15)
Exact thought in a demented time: Karl menger and his viennese mathematical colloquium (2000) (14)
On the distribution of periodic points for β-shifts (1976) (14)
Dynamics of macrosystems : proceedings of a Workshop on the Dynamics of Macrosystems held at the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria, September 3-7, 1984 (1985) (13)
John Maynard Smith and evolutionary game theory. (2005) (13)
III. Games between Two Populations with Selfinteraction (1981) (13)
Cooperation in heterogeneous populations (1994) (13)
On the prevalence of zero entropy (1971) (12)
Darwin's "circles of complexity": Assembling ecological communities (1995) (11)
Random Selection and the Neutral Theory — Sources of Stochasticity in Replication (1984) (11)
The Population Dynamics of Conflict and Cooperation (1998) (11)
Dynamical systems under constant organization I. Topological analysis of a family of non-linear differential equations —A model for catalytic hypercycles (1978) (11)
A Tale of Two Selves (2000) (10)
Evolution of exploitation and defence in plant-herbivore-predator interactions. (2002) (10)
Evolutionary Games and Population Dynamics: Preface (1998) (9)
Equal Pay for all Prisoners / The Logic of Contrition (1997) (8)
Permanence and viability (1988) (8)
You Will Like Geometry (2003) (8)
Evolution and Control in Biological Systems (1989) (8)
Evolutionary Games and Population Dynamics: Other game dynamics (1998) (7)
Polynucleotide evolution and branching processes (1985) (7)
Adaptive Dynamics of Infectious Diseases: Epilogue (2002) (6)
Ergodic averages for axiom a diffeomorphisms (1971) (6)
Public Good Games with Incentives: The Role of Reputation (2009) (6)
How Virtue Was Born (2017) (6)
On the time evolution of statistical states for Anosov systems (1974) (6)
Evolutionary Games and Population Dynamics: Adaptive dynamics (1998) (6)
What two legs can learn from four legs (1998) (5)
Deciphering an enigma (1997) (5)
Security in the Age of Systemic Risk: Strategies, Tactics and Options for Dealing with Femtorisks and Beyond (2012) (5)
A Mathematical Model of the Hypercycle (1980) (5)
Gradients for the evolution of bimatrix games (1987) (5)
William D. Hamilton's work in evolutionary game theory. (2001) (5)
Evolutionary Games and Population Dynamics: Mutation and recombination (1998) (5)
Population dynamics in evolutionary ecology (2004) (4)
Evolutionary Games and Population Dynamics: Discrete dynamical systems in population genetics (1998) (4)
Game theory and evolutionary ecology Evolutionary Games & Population Dynamics (4)
Toward ecoevolutionary dynamics (2021) (4)
Leray in edelbach (2005) (4)
The Fibonacci Chimney (2000) (4)
Biomathematics: Merging lines and emerging levels (1998) (4)
The social life of automata (1998) (4)
The Emergence of Altruistic Punishment: Via Freedom to Enforcement (2007) (4)
Self-Organization of Macromolecules (1987) (4)
The variational principle for topological entropy (1976) (3)
Darwin and the Evolution of Human Cooperation (2011) (3)
The physicist and the dawn of the double helix (2019) (3)
Adaptive Dynamics of Infectious Diseases: List of Boxes (2002) (3)
Gödel’s Vienna (2006) (3)
Hans Hahn collected works (1995) (3)
Strictly ergodic embedding (Theorem of Jewett and Krieger) (1976) (3)
Echoes of chaos (1995) (3)
Failing phoenix: Tauber, helly, and viennese life insurance (2004) (3)
Hans Hahn and the Foundational Debate (1995) (3)
The natural history of mutual aid (1996) (2)
Evolutionary Games and Population Dynamics: Evolutionarily stable strategies (1998) (2)
“Was you ever bit by a dead bee?” – Evolutionary games and dominated strategies (2003) (2)
Karl Menger and Vienna’s Golden Autumn (2002) (2)
Menger’s Ergebnisse — a biographical introduction (1998) (2)
Evolutionary Games and Population Dynamics: Game dynamics for Mendelian populations (1998) (2)
Kepler in eferding (2001) (2)
Lotka–Volterra equations for predator–prey systems (1998) (2)
Evolutionary Games and Population Dynamics: Replicator dynamics (1998) (2)
The basis of morality: Richard Alexander on indirect reciprocity (2013) (2)
Adaptive Dynamics of Infectious Diseases: References (2002) (2)
Indirect Reciprocity (2021) (2)
Karl Sigmund. (2004) (2)
Evolutionary Games and Population Dynamics: Stability of n -species communities (1998) (2)
Evolutionary Games and Population Dynamics: Ecological equations for two species (1998) (2)
Invariant measures for continuous tranformations (1976) (2)
Evolutionary Games and Population Dynamics: Introduction for biologists (1998) (1)
Normal and quasiregular points for automorphisms of the torus (1974) (1)
Heteroclinic cycles: Poincare maps and characteristic matrices (1998) (1)
Selecta Mathematica II (2002) (1)
Playing for Keeps (2000) (1)
Measures on compact metric spaces (1976) (1)
The loitering presence of the rational actor (2009) (1)
Random selection—A simple model based on linear birth and death processes (1984) (1)
Selecta Mathematica : Volume 2 (2003) (1)
Virtually A-Life. (Book Reviews: The Garden in the Machine. The Emerging Science of Artificial Life.) (1994) (1)
Oscillations in Optional Public Good Games (2001) (1)
Kurt Gödel—Das Album, The Album (2008) (1)
Fixation probabilities for advantageous mutants: a note on multiplication and sampling. (1989) (1)
Gradients for replicator systems (1987) (1)
Adaptive Dynamics of Infectious Diseases: Notational Standards (2002) (1)
Games Evolution Plays (1996) (1)
Have book, will travel (1993) (1)
A short tale of two cities: Otto schreier and the Hamburg— Vienna connection (2008) (1)
Primer: altruism. (2002) (1)
Emergence of the Social Contract (2012) (1)
Book Reviews (2002) (0)
The specification property (1976) (0)
Comments on Hans Hahn’s work in complex analysis Ludger Kaup (1997) (0)
The bounds of reason and the joys of virtue (2009) (0)
Evolutionary Games and Population Dynamics: Fertility selection (1998) (0)
Automata and Inner States for Repeated Games (1998) (0)
Introduction to Part D (2000) (0)
Chapter Two. Game Dynamics and Social Learning (2010) (0)
The Lotka–Volterra equations for two competing species (1998) (0)
Preparations for generator theorems (1976) (0)
CHAPTER 2 How populations cohere : five rules for cooperation (2006) (0)
Mixing and transitivity (1976) (0)
Specification and expansiveness (1976) (0)
Dynamical systems : proceedings of an IIASA (International Institute for Applied Systems Analysis) Workshop on Mathematics of Dynamic Processes held at Sopron, Hungary, September 9-13, 1985 (1987) (0)
Evolutionary Games and Population Dynamics: Catalytic hypercycles (1998) (0)
Continuous selection dynamics (1998) (0)
Measures on the shift space (1976) (0)
A SURVET OF REPLICATOR EQUATIONS (2006) (0)
The man of the crowd (2005) (0)
IR-98-102 / December The Population Dynamics of Conflict and Cooperation (1999) (0)
Subshifts of finite type (1976) (0)
Entropy for Bernoulli and Markov shifts (1976) (0)
Game Dynamics and Replicator Equations (1998) (0)
Finite generators for aperiodic transformations (1976) (0)
The Santa Fe telegraph (1995) (0)
Introduction: Social Traps and Simple Games (2016) (0)
Evolution and Control in Biological Systems: Proceedings of the IIASA Workshop, Laxenburg, Austria, 30 November - 4 December 1987 (2011) (0)
Adaptive Dynamics of Infectious Diseases: International Institute for Applied Systems Analysis (2002) (0)
Interim Report IR-12-070 Moral assessment and moral hazard in indirect reciprocity (2016) (0)
Embedding theorems for aperiodic transformations (1976) (0)
Book Reviews (2000) (0)
Introduction to the Sixth American Edition, 1960 (2003) (0)
Dynamical Systems; Proceedings of an IIASA Workshop, Sopron, Hungary, September 9-13, 1985 (1987) (0)
Evolutionary Games and Population Dynamics: Lotka–Volterra equations for more than two populations (1998) (0)
Moral assessment moral hazard in indirect reciprocity (2012) (0)
Part A Setting the Stage R 0 (2005) (0)
Special issue on mathematical biology: Introduction (1989) (0)
Adaptive dynamics of infectious diseases: Introduction (2002) (0)
Automorphisms of the torus (1976) (0)
Introduction to Part F (2002) (0)
Chapter Six. Public Goods and Joint Efforts: Between Freedom and Enforcement (2010) (0)
About this book (1998) (0)
Chapter Four. Indirect Reciprocity: The Role of Reputation (2010) (0)
Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984 (1985) (0)
Combinatorial construction of minimal sets (1976) (0)
Darwins Dynamik (1998) (0)
Play it again, John (2004) (0)
Evolutionary Games and Population Dynamics: Criteria for permanence (1998) (0)
How localized information affects the evolution of indirect reciprocity (2012) (0)
Introduction to Part E (2002) (0)
Adaptive Dynamics of Infectious Diseases: Introduction to Part B (2002) (0)
The computation of entropy (1976) (0)
Introduction to Part G (2002) (0)
Emergence of sanctioning systems through social learning (2012) (0)
Nestor of mathematicians: Leopold vietoris turns 105 (1996) (0)
Kurt Gödel and the Foundations of Mathematics: “Dozent Gödel Will Not Lecture” (2011) (0)
Introduction for game theorists (1998) (0)
Monomorphic and polymorphic populations (1994) (0)
Evolutionof indirect reciprocity by imagescoring (1998) (0)
Evolution and social science. A tale of two selves. (2000) (0)
John Forbes Nash Jr. 1928–2015 (2015) (0)
Deviating from the line (1999) (0)
Game Theory (2019) (0)
Faculty Opinions recommendation of Hamilton's rule in multi-level selection models. (2012) (0)
Finite generators for ergodic transformations (theorem of Krieger) (1976) (0)
Darwin's Dynamik (1998) (0)
Chapter Three. Direct Reciprocity: The Role of Repetition (2010) (0)
Game-Dpamicai Aspects of the Prisoner ’ s Dilemma (2001) (0)
Information and entropy (1976) (0)
Behavioral experiments reveal how risk perception and worldviews impact common-good governance (2017) (0)
Measures with maximal entropy—Intrinsically ergodic systems (1976) (0)
Let's keep the debate focused (2010) (0)
Buchbesprechung/Book Reviews (1991) (0)
Chapter Seven. Cooperation in Structured Populations (2010) (0)
Evolutionary Games and Population Dynamics: Logistic growth (1998) (0)
Institutions as Tools for Overcoming Social Dilemmas (2015) (0)
Some low-dimensional ecological systems (1998) (0)
Proceedings of an International Institute of Applied Systems Analysis workshop on Dynamical systems (1987) (0)
Shifts and subshifts (1976) (0)
Virtually a-life. (1994) (0)
Entropy—Expansive homeomorphisms (1976) (0)
Evolution theory system theory game theory Biocentric Modeling (2007) (0)
Partitions and generators (1976) (0)
Chapter Five. Fairness and Trust: The Power of Incentives (2010) (0)
Calculus — A Modern Approach (2003) (0)
Three's company when seeking unanimity (2004) (0)
Punishment Via Freedom to Coercion : The Emergence of Costly (2007) (0)
Introduction to Part B (2000) (0)
Measure-theoretic dynamical systems (1976) (0)
More on subshifts of finite type (1976) (0)
Automata and inner states for repeated games yearbook of the Institute Vienna circle: game theory, experience, rationality. Foundations of social sciences, economics and ethics. (1998) (0)
Nachlese zu den 'Gödel-lectures' (2003) (0)
Supporting Text : Exploration Dynamics in Evolutionary Games (2009) (0)
IR-98-099 / December The Social Life of Automata (1998) (0)
Basic sets for axiom A (1976) (0)
The evolution of sanctioning institutions: an experimental approach to the social contract (2013) (0)
More on bimatrix games (1998) (0)
Chapter One. Introduction: Social Traps and Simple Games (2010) (0)
Commentary on Menger’s ‘Austrian Marginalism and Mathematical Economics’ (2003) (0)
Introduction to Part C (2000) (0)
ORBITS OF DETERMINISTICTIME AVERAGES FOR UNPREDICTABLE SYSTEMS (2008) (0)
Evolutionary dynamics on multi-dimensional fitness landscapes (2011) (0)
Automata for Repeated Games (2001) (0)

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