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