An introduction to ABED: Agent-based simulation of evolutionary game dynamics

Abstract ABED is free and open-source software for simulating evolutionary game dynamics in finite populations. We explain how ABED can be used to simulate a wide range of dynamics considered in the literature and many novel dynamics. In doing so, we introduce a general model of revisions for dynamic evolutionary models, one that decomposes strategy updates into selection of candidate strategies, payoff determination, and choice among candidates. Using examples, we explore ways in which simulations can complement theory in increasing our understanding of strategic interactions in finite populations.

[1]  Josef Hofbauer,et al.  Competition and cooperation in catalytic selfreplication , 1981 .

[2]  G. Szabó,et al.  Evolutionary games on graphs , 2006, cond-mat/0607344.

[3]  Angel Sánchez,et al.  Altruism may arise from individual selection. , 2004, Journal of theoretical biology.

[4]  Long Wang,et al.  Universality of weak selection. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  William H. Sandholm,et al.  An Introduction to Dynamo: Diagrams for Evolutionary Game Dynamics , 2013 .

[6]  Josef Hofbauer,et al.  Stable games and their dynamics , 2009, J. Econ. Theory.

[7]  A. Rubinstein,et al.  Games with Procedurally Rational Players , 1997 .

[8]  William H. Sandholm,et al.  Stability for best experienced payoff dynamics , 2020, J. Econ. Theory.

[9]  D. W. Stroock,et al.  Multidimensional Diffusion Processes , 1979 .

[10]  L. Samuelson,et al.  Musical Chairs: Modeling Noisy Evolution , 1995 .

[11]  Winfried Kurth,et al.  RNETLOGO: an R package for running and exploring individual‐based models implemented in NETLOGO , 2012 .

[12]  H. Young,et al.  The Evolution of Conventions , 1993 .

[13]  William H. Sandholm,et al.  Agent-Based Evolutionary Game Dynamics , 2019 .

[14]  P. Taylor,et al.  Evolutionarily Stable Strategies and Game Dynamics , 1978 .

[15]  Matjaž Perc,et al.  Stability of subsystem solutions in agent-based models , 2017, bioRxiv.

[16]  Segismundo S. Izquierdo,et al.  Stochastic Approximation to Understand Simple Simulation Models , 2012, Journal of Statistical Physics.

[17]  C. Cannings,et al.  Evolutionary Game Theory , 2010 .

[18]  Michael J. Smith,et al.  The Stability of a Dynamic Model of Traffic Assignment - An Application of a Method of Lyapunov , 1984, Transp. Sci..

[19]  J. Hofbauer,et al.  Fictitious Play, Shapley Polygons and the Replicator Equation , 1995 .

[20]  William H. Sandholm,et al.  Almost global convergence to p-dominant equilibrium , 2001, Int. J. Game Theory.

[21]  William H. Sandholm,et al.  Potential Games with Continuous Player Sets , 2001, J. Econ. Theory.

[22]  R. Rob,et al.  Learning, Mutation, and Long Run Equilibria in Games , 1993 .

[23]  Attila Szolnoki,et al.  Cyclic dominance in evolutionary games: a review , 2014, Journal of The Royal Society Interface.

[24]  Attila Szolnoki,et al.  Evolutionary dynamics of group interactions on structured populations: a review , 2013, Journal of The Royal Society Interface.

[25]  K Sigmund,et al.  A note on evolutionary stable strategies and game dynamics. , 1979, Journal of theoretical biology.

[26]  José Manuel Galán,et al.  Combining Mathematical and Simulation Approaches to Understand the Dynamics of Computer Models , 2017, Simulating Social Complexity.

[27]  Attila Szolnoki,et al.  Coevolutionary Games - A Mini Review , 2009, Biosyst..

[28]  William H. Sandholm,et al.  Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium , 2009, Games.

[29]  Michihiro Kandori,et al.  Evolution of Equilibria in the Long Run: A General Theory and Applications , 1995 .

[30]  Rajiv Sethi,et al.  Stable Sampling Equilibrium in Common Pool Resource Games , 2015, Games.

[31]  Drew Fudenberg,et al.  Evolutionary game dynamics in finite populations with strong selection and weak mutation. , 2006, Theoretical population biology.

[32]  Josef Hofbauer,et al.  The theory of evolution and dynamical systems , 1988 .

[33]  Rajiv Sethi,et al.  Stability of Equilibria in Games with Procedurally Rational Players , 1998, Games Econ. Behav..

[34]  Moreno Marzolla,et al.  Netlogo , 2019, Economics for a Fairer Society.

[35]  L. Shapley,et al.  Potential Games , 1994 .

[36]  Arend Hintze,et al.  The Reasonable Effectiveness of Agent-Based Simulations in Evolutionary Game Theory , 2016, Physics of life reviews.

[37]  Jason A. Papin,et al.  Novel Multiscale Modeling Tool Applied to Pseudomonas aeruginosa Biofilm Formation , 2013, PloS one.

[38]  Glenn Ellison.  Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution , 2000 .

[39]  M. Eigen,et al.  The Hypercycle: A principle of natural self-organization , 2009 .

[40]  H. Young.  Individual Strategy and Social Structure , 2020 .

[41]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[42]  George Loginov,et al.  Ordinal imitative dynamics , 2019, Int. J. Game Theory.

[43]  Karl H. Schlag,et al.  Evolutionarily stable sets , 2000, Int. J. Game Theory.

[44]  Rick Durrett,et al.  Extrapolating weak selection in evolutionary games , 2018, bioRxiv.

[45]  L. Blume,et al.  POPULATION GAMES , 1995 .

[46]  F. Vega-Redondo,et al.  Efficient Equilibrium Selection in Evolutionary Games with Random Matching , 1996 .

[47]  Julián García,et al.  In and out of equilibrium I: Evolution of strategies in repeated games with discounting , 2007, J. Econ. Theory.

[48]  Winfried Kurth,et al.  Agent-Based Modelling: Tools for Linking NetLogo And R , 2012, J. Artif. Soc. Soc. Simul..

[49]  M. Nowak.  Evolutionary Dynamics: Exploring the Equations of Life , 2006 .

[50]  E. Seneta,et al.  On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains , 1965, Journal of Applied Probability.

[51]  M. Nowak,et al.  Evolutionary game dynamics in a Wright-Fisher process , 2006, Journal of mathematical biology.

[52]  J. Weibull,et al.  Nash Equilibrium and Evolution by Imitation , 1994 .

[53]  H. Peyton Young,et al.  Fast convergence in evolutionary equilibrium selection , 2013, Games Econ. Behav..

[54]  E. C. Zeeman,et al.  Population dynamics from game theory , 1980 .

[55]  P. Schuster,et al.  Dynamical systems under constant organization I. Topological analysis of a family of non-linear differential equations —A model for catalytic hypercycles , 1978 .

[56]  Benjamin Allen,et al.  The limits of weak selection and large population size in evolutionary game theory , 2016, Journal of Mathematical Biology.

[57]  Corina E Tarnita,et al.  Mathematical approaches or agent-based methods?: Comment on "Evolutionary game theory using agent-based methods" by Christoph Adami et al. , 2016, Physics of life reviews.

[58]  K Sigmund,et al.  Dynamical systems under constant organization I. Topological analysis of a family of non-linear differential equations--a model for catalytic hypercycles. , 1978, Bulletin of mathematical biology.

[59]  William H. Sandholm,et al.  EvoDyn-3s: A Mathematica computable document to analyze evolutionary dynamics in 3-strategy games , 2018, SoftwareX.

[60]  Peter Schuster,et al.  Models of evolution and evolutionary game theory: A comment on "Evolutionary game theory using agent based models" by Christoph Adami, Jory Schossau, Arend Hintze. , 2016, Physics of life reviews.

[61]  Josef Hofbauer,et al.  Evolution in games with randomly disturbed payoffs , 2007, J. Econ. Theory.

[62]  M. Benaïm,et al.  Deterministic Approximation of Stochastic Evolution in Games , 2003 .

[63]  William H. Sandholm,et al.  Stochastic Approximations with Constant Step Size and Differential Inclusions , 2013, SIAM J. Control. Optim..

[64]  R. Durrett.  Stochastic Calculus: A Practical Introduction , 1996 .

[65]  Drew Fudenberg,et al.  Evolutionary game dynamics in finite populations , 2004, Bulletin of mathematical biology.

[66]  A. W. F. Edwards,et al.  The statistical processes of evolutionary theory , 1963 .

[67]  Jonathan Newton.  Evolutionary Game Theory: A Renaissance , 2018 .

[68]  Matthijs van Veelen,et al.  Robustness against indirect invasions , 2012, Games Econ. Behav..

[69]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[70]  Arne Traulsen,et al.  Coevolution of strategy and structure in complex networks with dynamical linking. , 2006, Physical review letters.

[71]  William H. Sandholm,et al.  Evolution and equilibrium under inexact information , 2003, Games Econ. Behav..

[72]  K. Schlag.  Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits , 1998 .

[73]  Nicola Bellomo,et al.  Space dynamics and stochastic features of evolutionary game dynamics: Comment on: "Evolutionary game theory using agent-based methods" by Christoph Adami, Jory Schossau and Arend Hintze. , 2016, Physics of life reviews.

[74]  D. Fudenberg,et al.  Evolutionary cycles of cooperation and defection. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[75]  Ángel Sánchez,et al.  Effect of spatial structure on the evolution of cooperation , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[76]  Drew Fudenberg,et al.  Monotone Imitation Dynamics in Large Populations , 2007, J. Econ. Theory.

[77]  F. Vega-Redondo.  The evolution of Walrasian behavior , 1997 .

[78]  Arne Traulsen,et al.  Stochastic payoff evaluation increases the temperature of selection. , 2007, Journal of theoretical biology.

[79]  Drew Fudenberg,et al.  Imitation Processes with Small Mutations , 2004, J. Econ. Theory.

[80]  M. Eigen.  The origin of genetic information , 1994, Origins of life and evolution of the biosphere.

[81]  William H. Sandholm,et al.  Population Games And Evolutionary Dynamics , 2010, Economic learning and social evolution.

[82]  Mark Voorneveld,et al.  A myopic adjustment process leading to best-reply matching , 2002, Games Econ. Behav..

[83]  Arne Traulsen,et al.  Only the combination of mathematics and agent-based simulations can leverage the full potential of evolutionary modeling: Comment on "Evolutionary game theory using agent-based methods" by C. Adami, J. Schossau and A. Hintze. , 2016, Physics of life reviews.

[84]  H. Peyton Young,et al.  Stochastic Evolutionary Game Dynamics , 1990 .

[85]  J. Sobel,et al.  AN EVOLUTIONARY APPROACH TO PRE-PLAY COMMUNICATION , 1995 .

[86]  William H. Sandholm,et al.  Sampling Best Response Dynamics and Deterministic Equilibrium Selection , 2014 .

[87]  Jan C. Thiele.  R Marries NetLogo: Introduction to the RNetLogo Package , 2014 .

[88]  Arend Hintze,et al.  Evolutionary game theory using agent-based methods. , 2014, Physics of life reviews.

[89]  J. Cuesta,et al.  Time scales in evolutionary dynamics. , 2006, Physical review letters.

[90]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[91]  Karl H. Schlag,et al.  Which One Should I Imitate , 1999 .

[92]  William H. Sandholm,et al.  Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics , 2015, Math. Oper. Res..

[93]  D. E. Matthews.  Evolution and the Theory of Games , 1977 .

[94]  D. Fudenberg,et al.  Emergence of cooperation and evolutionary stability in finite populations , 2004, Nature.

[95]  Rajiv Sethi,et al.  Efficiency and Stability of Sampling Equilibrium in Public Goods Games , 2018, Journal of Public Economic Theory.

[96]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[97]  P. A. P. Moran,et al.  Random processes in genetics , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[98]  William H. Sandholm,et al.  Population Games and Deterministic Evolutionary Dynamics , 2015 .

[99]  R. Rosenthal.  Games of perfect information, predatory pricing and the chain-store paradox , 1981 .

[100]  Arne Traulsen,et al.  Stochastic sampling of interaction partners versus deterministic payoff assignment. , 2009, Journal of theoretical biology.

[101]  D. Helbing.  A Mathematical Model for Behavioral Changes by Pair Interactions , 1998, cond-mat/9805102.

[102]  Ángel Sánchez,et al.  Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics , 2009, Physics of life reviews.

[103]  I. Gilboa,et al.  Social Stability and Equilibrium , 1991 .

[104]  Peter Norton,et al.  Python , 2019, login Usenix Mag..

[105]  Volker Grimm,et al.  NetLogo meets R: Linking agent-based models with a toolbox for their analysis , 2010, Environ. Model. Softw..

[106]  S. H..  Best experienced payoff dynamics and cooperation in the centipede game , 2019 .

[107]  Ken Binmore,et al.  Muddling Through: Noisy Equilibrium Selection☆ , 1997 .

[108]  Jan H. Kwakkel,et al.  PyNetLogo: Linking NetLogo with Python , 2018, J. Artif. Soc. Soc. Simul..

[109]  J. Hofbauer,et al.  Stable periodic solutions for the hypercycle system , 1991 .

[110]  Glenn Ellison,et al.  Basins of Attraction, Long-Run Equilibria, and the Speed of Step-by-Step Evolution , 1995 .

[111]  Daniel Friedman,et al.  Evolutionary Games in Natural, Social, and Virtual Worlds , 2016 .

[112]  W. Sandholm,et al.  Large deviations and stochastic stability in the small noise double limit , 2016 .

[113]  Peter C. Jurs,et al.  Mathematica , 2019, J. Chem. Inf. Comput. Sci..

[114]  Julián García,et al.  No Strategy Can Win in the Repeated Prisoner's Dilemma: Linking Game Theory and Computer Simulations , 2018, Front. Robot. AI.

[115]  Winfried Kurth,et al.  Facilitating Parameter Estimation and Sensitivity Analysis of Agent-Based Models: A Cookbook Using NetLogo and 'R' , 2014, J. Artif. Soc. Soc. Simul..