An Introduction to Dynamo: Diagrams for Evolutionary Game Dynamics

Dynamo: Diagrams for Evolutionary Game Dynamics is free, open-source software used to create phase diagrams and other images related to dynamical systems from evolutionary game theory. We describe how to use the software’s default settings to generate phase diagrams quickly and easily. We then explain how to take advantage of the software’s intermediate and advanced features to create diagrams that highlight the key properties of the dynamical system under study. Sample code and output are provided to help demonstrate the software’s capabilities.

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

[2]  David E. Miller,et al.  Equation of state for hadronic matter , 1978 .

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

[4]  Mark Perlman,et al.  The Rational Foundations of Economic Behaviour , 1996 .

[5]  K. G. Troitzsch,et al.  Economic evolution and demographic change : formal models in social sciences , 1992 .

[6]  J M Smith,et al.  Evolution and the theory of games , 1976 .

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

[8]  A. Nagurney,et al.  Projected Dynamical Systems and Variational Inequalities with Applications , 1995 .

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

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

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

[12]  J. Weibull,et al.  Evolutionary Selection against dominated strategies , 1996 .

[13]  William H. Sandholm,et al.  The projection dynamic and the geometry of population games , 2008, Games Econ. Behav..

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

[15]  Brian Skyrms,et al.  The Dynamics Of Rational Deliberation , 1990 .

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

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

[18]  Robert A. Meyers,et al.  Encyclopedia of Complexity and Systems Science , 2009 .

[19]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[20]  BRIAN SKYRMS,et al.  Chaos in game dynamics , 1992, J. Log. Lang. Inf..

[21]  William H. Sandholm,et al.  ON THE GLOBAL CONVERGENCE OF STOCHASTIC FICTITIOUS PLAY , 2002 .

[22]  William H. Sandholm,et al.  Evolutionary Implementation and Congestion Pricing , 2002 .

[23]  William H. Sandholm,et al.  Local stability under evolutionary game dynamics , 2010 .

[24]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and an Introduction to Chaos , 2003 .

[25]  William H. Sandholm,et al.  The projection dynamic and the replicator dynamic , 2008, Games Econ. Behav..

[26]  Akihiko Matsui,et al.  Best response dynamics and socially stable strategies , 1992 .

[27]  Alain Arneodo,et al.  OCCURRENCE OF STRANGE ATTRACTORS IN 3 DIMENSIONAL VOLTERRA-EQUATIONS , 1980 .

[28]  J. Hofbauer From Nash and Brown to Maynard Smith: Equilibria, Dynamics and ESS , 2001 .

[29]  G. Brown SOME NOTES ON COMPUTATION OF GAMES SOLUTIONS , 1949 .

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

[31]  Cedric A. B. Smith,et al.  The Geometry of Population Genetics , 1980 .

[32]  J. Neumann,et al.  SOLUTIONS OF GAMES BY DIFFERENTIAL EQUATIONS , 1950 .

[33]  Jeroen M. Swinkels Adjustment Dynamics and Rational Play in Games , 1993 .

[34]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

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

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

[37]  J. Robinson AN ITERATIVE METHOD OF SOLVING A GAME , 1951, Classics in Game Theory.

[38]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[39]  William H. Sandholm,et al.  Negative Externalities and Evolutionary Implementation , 2005 .

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

[41]  J. Jordan Three Problems in Learning Mixed-Strategy Nash Equilibria , 1993 .

[42]  Alain Arneodo,et al.  Occurence of strange attractors in three-dimensional Volterra equations , 1980 .

[43]  Ross Cressman,et al.  Local stability of smooth selection dynamics for normal form games , 1997 .

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

[45]  O. H. Brownlee,et al.  ACTIVITY ANALYSIS OF PRODUCTION AND ALLOCATION , 1952 .

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