Josef Hofbauer's Publications
A short proof of the Lagrange-Good formula. Discrete Math. 25 (1979) 135-139.
(with P. Schuster and Karl Sigmund)
A note on evolutionarily stable strategies and
game dynamics. J. theor. Biol. 81 (1979), 609-612.
(with Peter Schuster, Karl Sigmund and Robert Wolff)
Dynamical systems under constant organisation. Part 2: Homogeneous growth functions of degree 2. SIAM J. Appl. Math. 38 (1980), 282-304.
(with Peter Schuster and Karl Sigmund) Competition and cooperation in catalytic selfreplication. J. Math. Biol. 11 (1981), 155-168.
On the occurrence of limit cycles in the Volterra-Lotka equation. Nonlinear Analysis 5 (1981) 1003-1007.
A general cooperation theorem for hypercycles.
Monatshefte Math. 91 (1981) 233-240.
(with Peter Schuster, Karl Sigmund and Robert Wolff) Selfregulation of behaviour in animal societies. Part 1: Symmetric contests.
Biol. Cybern. 40 (1981), 1-8.
(with Peter Schuster, Karl Sigmund and Robert Wolff) Selfregulation of behaviour in animal societies. Part 2: Games between two populations without selfinteraction.
Biol. Cybern. 40 (1981), 9-15.
(with Peter Schuster, Karl Sigmund, R. Gottlieb and P. Merz)
Selfregulation of behaviour in
animal societies. Part 3: Games between two populations with
selfinteraction. Biol. Cybern. 40 (1981), 16-25.
Lagrange Inversion. Actes du Seminaire Lotharingien de Combinatoire 6 (1982).
(with Ethan Akin) Recurrence of the unfit. Math. Biosciences 61 (1982) 51-63.
(with Peter Schuster and Karl Sigmund) Game dynamics for Mendelian populations. Biol. Cybern. 43 (1982), 51-57.
(with Karl Sigmund) Evolutionstheorie und dynamische Systeme. Parey, Hamburg-Berlin (1984). 200 pp.
A q-analog of the Lagrange expansion. Archiv Math. 42 (1984) 536-544.
(with Peter Schuster) Dynamics of linear and nonlinear autocatalysis and
competition. In: Stochastic Phenomena and Chaotic Behaviour in Complex
Systems (Proc. Conf. Flattnitz 1983). Ed. P. Schuster. Springer Series in
Synergetics 21, pp. 159-171. 1984.
(with Gerard Iooss)
A Hopf bifurcation theorem for difference equations approximating a differential equation. Monatshefte Math. 98 (1984) 99-113.
A difference equation model for the hypercycle.
SIAM J. Appl. Math. 44 (1984) 762-772.
(with Erwin Amann) Permanence in Lotka-Volterra and replicator equations.
In: Lotka-Volterra Approach to Cooperation and Competition (Proc. Wartburg
1984). Ed. W. Ebeling and M. Peschel. pp. 23-34. Akademie-Verlag
Berlin 1985.
(with J. Fürlinger) q-Catalan numbers.
J. Combinatorial Theory A40 (1985) 248-264.
Gradients versus cycling in genetic selection models. In: Dynamics of
Macrosystems (Proc. Laxenburg 1984). Ed. J. P. Aubin, D. Saari and
K. Sigmund. pp. 90-101. Springer Lecture Notes in Economics and
Mathematical Systems 257. 1985.
The selection mutation equation. J. Math. Biol. 23 (1985) 41-53.
(with K. Sigmund) Permanence for replicator equations.
In: Dynamical Systems. A. Kurzhansky and K. Sigmund (eds.). Springer Lecture Notes Econ. Math. Syst. 287 (1987), pp.70-91.
(with John Maynard Smith) The `battle of the sexes': A genetic model with limit cycle behavior. Theor. Population Biology 32 (1987) 1-14.
(with Vivian Hutson und Wolfgang Jansen) Coexistence for systems governed by difference equations of Lotka-Volterra type. J. Math. Biol. 25 (1987) 553-570.
Heteroclinic cycles on the simplex. Proc. Int. Conf. Nonlinear
Oscillations. Ed. M. Farkas, V. Kertesz, G.Stepan.
Budapest: Janos Bolyai Math. Society. 1987.
(with
Karl Sigmund ): The Theory of Evolution and Dynamical Systems.
Cambridge University Press 1988.
Saturated equilibria, permanence and stability for ecological systems.
In: Mathematical Ecology (Proc. Conf. Trieste 1986).
Eds. L. J. Gross, T. G. Hallam and S. A. Levin.
Singapore-Hong Kong: World Scientific. 1988.
A unified approach to persistence. Acta
Applicandae Math. 14 (1989) 11 - 22.
(with Karl Sigmund): On the stabilizing effect of predators and competitors on ecological communities. J. Math. Biology 27 (1989) 537 - 548.
(with J. W.-H. So )
Uniform persistence and repellors for maps.
Proc. Amer. Math. Soc. 107 (1989) 1137-1142.
An index theorem for dissipative semiflows.
Rocky Mountains J. Math. 20 (1990) 1017-1031.
(with J. W.-H.
So)
Multiple limit cycles for predator-prey models.
Math. Biosciences 99 (1990) 71-75.
(mit Karl
Sigmund )
Adaptive dynamics and evolutionary stability.
Appl. Math. Letters 3 (1990) 75-79.
(with J. Mallet-Paret and
Hal Smith )
Stable periodic solutions for the hypercycle system.
J. Dynamics and Diff. Equs. 3 (1991) 423-436.
(with
Andrea
Gaunersdorfer
and Karl Sigmund
)
On the dynamics of asymmetric games.
Theor. Pop. Biol. 39 (1991) 345-357.
Heteroclinic cycles in ecological differential
equations.
Tatra Mount. Math. Publ.
4 (1994), 105-116.
(with J. W.-H.
So)
Competition in the gradostat: the global stability problem.
Nonlinear Analysis 22 (1994), 1017-1031.
(with R.
Bürger) Mutation load and mutation-selection balance in quantitative genetic traits. J. Math. Biol. 32 (1994) 193-218.
(with J. W.-H. So ) Multiple limit cycles in three dimensional Lotka--Volterra equations. Appl. Math. Letters 7 (1994) 65-70.
(with
A. Gaunersdorfer ) Fictitious play, Shapley polygons, and the
replicator equation . Games and Economic Behaviour
11 (1995) 279-303.
Rational versus Evolutionary Dynamics for Games.
In: Dynamic Evolutionary Game Theory in Biology and Economics.
August 1995. Waterloo and Guelph. Conference Report, ed.: R. Cressman.
(with Eva Jablonka, B. Oborny, I. Molnar, Éva Kisdi , T.
Czárán)
The adaptive advantage of phenotypic memory in changing environments.
Phil. Trans. Royal Soc. London
B 350 (1995) 133-141.
(with
J. W.-H. So and Yasuhiro Takeuchi)
Global stability of competition in a spatially heterogenous environment.
Differential Equations Dynamical Systems
4 (1996) 213-223.
Evolutionary dynamics for bimatrix games: A Hamiltonian system? J. Math. Biol. 34 (1996), 675-688.
Springer Link.
(with Ross Cressman, W.G.S. Hines) Evolutionary stability in strategic models of single-locus frequency-dependent viability selection. J. Math. Biol. 34 (1996), 707-733.
Springer Link.
(with Jörgen W. Weibull
) Evolutionary selection against dominated strategies. J. Economic Theory 71 (1996), 558-573.
(with Barnabas Garay) Chain recurrence and discretization. Bull. Austral. Math. Soc. 55, 63-71 (1997).
(with
Vivian Hutson ,
Glenn T. Vickers )
Travelling waves for games in economics and biology.
Nonlinear Analysis, Theory, Methods & Applications
30, 1235-1244 (1997).
Equilibrium selection via travelling waves.
In: Werner Leinfellner and Eckehart Köhler (eds.):
Vienna Circle Institute Yearbook 5/1997 :
Game Theory, Experience, Rationality.
Foundations of Social Sciences, Economics and Ethics.
In Honor of John C. Harsanyi. Dordrecht-Boston-London: Kluwer.
pp. 245-259.
(with Karl
Sigmund )
Evolutionary Games and Population Dynamics , Cambridge University Press 1998.
( contents)
(with Thomas Nagylaki and Pavol Brunovský)
Convergence of multilocus systems under weak epistasis or weak selection. J. Math. Biology 38 (1999) 103-133.
(with
Gerhard Sorger)
Perfect foresight and equilibrium selection in symmetric
potential games. J. Economic Theory 85, 1-23
(1999).
The spatially dominant equilibrium of a game.
Annals of Operations Research 89
(1999) 233-251.
Leopold Gegenbauer (1849-1903) zum 150. Geburtstag.
Jahresbericht des Piaristengymnasiums Krems an der Donau 1999, pp.
39-41.
(with Joseph Wai-Hung
So)
Diagonal dominance and harmless off-diagonal delays.
Proc. Amer. Math. Soc. 128 (2000), 2675-2682.
(with
Karl Schlag):
Sophisticated imitation in cyclic games.
J. Evolutionary Economics 10 (2000), 523-543.
From Nash and Brown to Maynard Smith: Equilibria, dynamics
and ESS.
Selection 1
(2000), 81-88.
(with Ross
Cressman and Garay József):
Evolutionary stability concepts for N-species
frequency-dependent interactions.
J. theor. Biol. 211 (2001) 1-10.
(with P. L. Simon):
An existence
theorem for parabolic equations on $\R^n$ with discontinuous nonlinearity.
Electronic Journal of
Qualitative Theory of Differential Equations (2001) No. 8, pp. 1-9.
Competitive exclusion of disjoint hypercycles.
Z. Phys. Chemie 216 (2002) 35-39.
A simple proof of 1 + 1/22 + 1/32 +
... = PI2/6 and related identities.
American Math. Monthly 109 (Feb 2002) 196-200.
(with Gerhard Sorger): A differential game approach to evolutionary equilibrium selection. Int. Game Theory Review 4 (March 2002) 17-31.
(with Christoph
Hauert , Silvia DeMonte, Karl Sigmund ):
Volunteering as Red Queen Mechanism for Cooperation in Public Goods Game.
Science 296 (May 2002) 1129-1132.
(with Christoph
Hauert , Silvia DeMonte, Karl Sigmund ):
Replicator dynamics for optional public good games.
J. Theor. Biol. 218 (Sept 2002), 187-194.
(with Bill Sandholm )
On the global convergence of stochastic fictitious play.
Econometrica 70 (Nov 2002) 2265-2294.
(with Barnabas Garay):
Robust permanence for ecological differential equations, minimax, and
discretizations. SIAM J. Math. Anal. 34 (2003) 1007-1039.
(with K. Sigmund): Evolutionary Game Dynamics.
Bull. Amer. Math. Soc. 40 (2003), 479-519.
Some thoughts on sustainable/learnable equilibria.
(Plenary lecture, published in the) Conference Book of the XV IMGTA
(Italian meeting on Game Theory and Applications), Urbino, July 9-12, 2003.
(with Y. Saito and R. Kon): Qualitative V-L stability and qualitative permanence for Lotka-Volterra equations.
Functional equations in mathematical models (in Japanese).
Surikaisekikenkyusho Kokyuroku 1309 (2003), 140--145.
%MR1998272
(with R. Kon): Structure of n-dimensional Lotka-Volterra systems for qualitative permanence.
Functional equations in mathematical models (in Japanese).
Surikaisekikenkyusho Kokyuroku 1309 (2003), 146--153.
%MR1998273
(with Franz Hofbauer, P. Raith, T. Steinberger):
Intermingled basins in a two species system. J. Math. Biology 49 (Sept 2004), 293-309.
SpringerLink
(with S.J. Schreiber): To persist or not to persist. Nonlinearity 17 (2004), 1393-1406.
(with Ross Cressman): Measure dynamics on a one-dimensional continuous trait space: Theoretical foundations for adaptive dynamics. Theor. Pop. Biol. 67 (Feb 2005), 47-59.
(with Ed Hopkins)
Learning in perturbed asymmetric games. Games and Economic Behavior 52 (July 2005), 133-152.
(with M. Benaim and S. Sorin):
Stochastic approximation and differential inclusions.
SIAM J. Control and Optimization 44 (1) (August 2005), 328-348.
(with Sylvain Sorin ):
Best response dynamics for continuous zero-sum games. Discrete and Continuous Dynamical Systems B6 (Jan 2006), 215-224.
(with Ross Cressman and Frank Riedel):
Stability of the replicator equation for a single-species with a multi-dimensional continuous trait space. J. Theor. Biol. 239 (March 2006), 273-288.
(with Ulrich Berger):
Irrational behavior in the Brown-von Neumann-Nash dynamics. Games and Economic Behavior 56 (July 2006), 1-6.
(with M. Benaim and S. Sorin):
Stochastic approximation and differential inclusions II: Applications. Math. Operations Research 31 (Nov 2006), 649-672.
(with St. Müller, L. Endler, Ch. Flamm, P. Schuster)
A generalized model of the repressilator.
J. Math. Biology 53 (Dec 2006), 905-937.
(with W.H. Sandholm )
Evolution in games with randomly perturbed payoffs .
J. Economic Theory 132 (Jan 2007), 47-69.
To persist or not to persist: Differential equations in ecology.
In: Trends in Dynamical Systems, F. Dumortier, D. Roose, A. Vanderbauwhede (eds.), Koninklijke Vlaamse Academie van Belgie voor Wetenschappen en Kunsten (pp. 19-32). 2007.
(with Simon Huttegger):
Selection-Mutation Dynamics of Signaling Games With Two Signals. ,
In: Proceedings of the
ESSLLI 2007 Workshop on Language, Games, and Evolution , pp. 25-32.
(with W. H. Sandholm): Stable Games.
Proceedings of the 46th IEEE Conference on Decision and Control (New Orleans, LA, USA, Dec. 12-14, 2007), pp. 3416-3421.
(with M. Benaim and W. H. Sandholm):
Robust permanence and impermanence for stochastic replicator dynamics. J. Biological Dynamics 2 (April 2008), 180 - 195.
(with D. Oyama, S. Takahashi):
Monotone methods for equilibrium selection under perfect foresight dynamics.
Theor. Economics 3 (June 2008), 155 - 192.
(with Simon Huttegger):
Feasibility of communication in binary signaling games. J. Theor. Biol. 254 (Oct 2008), 843-849.
(with R. Kon and Y. Saito):
Qualitative permanence of Lotka-Volterra equations.
J. Math. Biology 57 (Dec 2008), 863-881.
(with Joerg Oechssler and Frank Riedel):
Brown-von Neumann-Nash dynamics: The continuous strategy case. Games and Econ. Behav. 65 (March 2009), 406-429.
(with Sylvain Sorin and Yannick Viossat):
Time average replicator and best reply dynamics.
Math. Operations Research 34 (May 2009) 263-269.
(with W.H. Sandholm )
Stable games and their dynamics. J. Economic Theory 144 (July 2009) 1665-1693.
(with M. Benaim and Ed Hopkins):
Learning in games with unstable equilibria. J. Economic Theory 144 (July 2009) 1694-1709.
(with Lorens Imhof ):
Time averages, recurrence and transience in the stochastic replicator dynamics. Annals of Applied Probability 19 (Aug 2009), 1347-1368.
(with S. J. Schreiber):
Robust permanence for structured populations. J. Diff. Equs. 248 (April 2010), 1955-1971.
(with Daisuke Oyama and Satoru Takahashi):
Perfect foresight dynamics in binary supermodular games
International Journal of Economic Theory 7 (Sep 2011) 251-267.
(with W.H. Sandholm )
Survival of Dominated Strategies under Evolutionary Dynamics, Theor. Economics 6 (2011) 341-377.
Deterministic evolutionary game dynamics. In:
Evolutionary Game Dynamics. Edited by: Karl Sigmund.
Proceedings of Symposia in Applied Mathematics,
vol. 69, Amer. Math. Soc., Providence, RI, 2011, pp. 61-79.
(with M. Benaim and S. Sorin): Perturbations of set-valued dynamical systems, with applications to game theory. Dynamic Games and Applications 2 (2012) 195-205.
(with D. Balkenborg and C. Kuzmics): Refined best-response correspondence and dynamics.
Theor. Economics 8 (2013) 165-192.
(with Simon Huttegger): Selection-mutation dynamics in signaling games.
Games 6 (2015), 2-31.
(with D. Balkenborg and C. Kuzmics):
The refined best-response correspondence in normal form games.
International Journal of Game Theory 44 (Feb 2015), 165-193.
(with Boyu Zhang):
Equilibrium selection via replicator dynamics in 2x2 coordination games.
International Journal of Game Theory 44 (May 2015), 433-448.
(with Linlin Su ):
Global stability in diallelic migration-selection models. J. Math. Anal. Appl. 428 (2015), 677-695.
(with Stefan Müller):
Genetic recombination as a chemical reaction network.
Mathematical Modelling of Natural Phenomena (special issue on Dynamics of Chemical Reaction Networks)
10 (5) (2015), 84-99. Link
(with Linlin Su ):
Global stability of spatially homogeneous equilibria in migration-selection models.
SIAM J Appl Math 76 (March 2016) 578-597.
(with Boyu Zhang):
Quantal response methods for equilibrium selection in 2 x 2 coordination games .
Games Econ. Behav. 97 (May 2016) 19-31.
(with Peter Bednarik):
Discretized Best-Response Dynamics for the Rock-Paper-Scissors Game.
J. Dynamics and Games 4 (Jan 2017) 75-86.
(with Balázs Boros , Stefan Müller):
On global stability of the Lotka reactions with generalized mass-action kinetics. Acta Appl Math 151 (Oct 2017) 53-80
(with Martin Pontz and Reinhard Bürger):
Evolutionary dynamics in the two-locus two-allele model with weak selection.
J. Math. Biol. 76 (Jan 2018) 151-203.
(with Balázs Boros , Stefan Müller, Georg Regensburger):
The center problem for the Lotka reactions with generalized mass-action kinetics.
Qualitative Theory of Dynamical Systems, 17(2), 403-410 (2018).
( arXiv,
reprint)
Minmax via replicator dynamics.
Dynamic Games and Applications
(Sept 2018) 8 (3), 637-640.
(with D. Balkenborg and C. Kuzmics):
The refined best-response correspondence and backward induction.
German Economic Review
20 (Feb 2019) 52-66.
(with Balázs Boros , Stefan Müller, Georg Regensburger):
Planar S-systems: Stability and the center problem. ( arXiv)
Discrete and Continuous Dynamical Systems-A 39 (Feb 2019) 707-727.
(mit Balázs Boros ):
Planar S-systems: Permanence.
J. Diff. Equations 266 (Feb 2019) 3787-3817. ( arXiv, reprint)
(mit Balázs Boros ):
Permanence of Weakly Reversible Mass-Action Systems with a Single Linkage Class.
SIAM J. Applied Dynamical Systems 19 (Jan 2020), 352-365.
( arXiv)
(mit Balázs Boros ):
Oscillations in planar deficiency-one mass-action systems.
J. Dynamics Diff. Equations (2021)
(mit Murad Banaji und Balázs Boros ):
Adding species to chemical reaction networks: preserving rank preserves nondegenerate behaviours.
Appl. Math. Comput. 426 (2022), 127109.
(arXiv)
(mit Carlos Alós-Ferrer):
Excess Payoff Dynamics in Games.
J. Econ. Theory 204 (2022) 105464.
(mit Balázs Boros ):
Limit cycles in mass-conserving deficiency-one mass-action systems.
Electronic J. Qual. Th. Diff. Equ. (2022) 42, 1-18.
(arXiv)
(mit Sebastian Schreiber):
Permanence via invasion graphs: Incorporating community assembly into Modern Coexistence Theory.
J. Math. Biol. (2022) 85:54
(arXiv)
(mit Balázs Boros ):
Some minimal bimolecular mass-action systems with limit cycles.
Nonlinear Analysis: Real World Applications 72 (Aug 2023), 103839.
arXiv
(with Murad Banaji , Balázs Boros )
The smallest bimolecular mass-action system with a vertical Andronov--Hopf bifurcation.
Applied Math Letters 143 (Sept 2023), 108671.
arXiv
(with Murad Banaji , Balázs Boros ):
Oscillations in three-reaction quadratic mass-action systems.
Studies in Applied Mathematics (2023)
arXiv
(mit Christina Pawlowitsch):
The evolutionary dynamics of costly signaling