References
Abar, S., Theodoropoulos, G. K., Lemarinier, P., and O’Hare, G. M. (2017). Agent based modelling and simulation tools: A review of the state-of-art software. Computer Science Review, 24 (Supplement C):13–33. https://doi.org/10.1016/j.cosrev.2017.03.001
Adami, C., Schossau, J., and Hintze, A. (2016). Evolutionary game theory using agent-based methods. Physics of Life Reviews, 19:1–26. https://doi.org/10.1016/j.plrev.2016.08.015
Alexander, J. M. (2023). Evolutionary Game Theory. Elements in Decision Theory and Philosophy. Cambridge University Press. https://doi.org/10.1017/9781108582063
Antonioni, A. and Tomassini, M. (2012). Cooperation on social networks and its robustness. Advances in Complex Systems, 15(supp01):1250046. https://doi.org/10.1142/S0219525912500464
Aydinonat, N. E. (2007). Models, conjectures and exploration: an analysis of Schelling’s checkerboard model of residential segregation. Journal of Economic Methodology, 14(4):429–454. https://doi.org/10.1080/13501780701718680
Bakshy, E. and Wilensky, U. (2007). NetLogo-Mathematica link. Software. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. http://ccl.northwestern.edu/netlogo/mathematica.html
Barabási, A.-L. and Albert, R. (1999). Emergence of scaling in random networks. Science,
286(5439):509–512. https://doi.org/10.1126/science.286.5439.509
Benaïm, M. and Weibull, J.W. (2003). Deterministic approximation of stochastic evolution in games. Econometrica, 71:873–903. https://doi.org/10.1111/1468-0262.00429
Berto, F. and Tagliabue, J. (2023). Cellular Automata. In Zalta, E. N. and Nodelman, U., editors, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Winter 2023 edition. https://plato.stanford.edu/archives/win2023/entries/cellular-automata/
Bhattacharjee, K., Naskar, N., Roy, S., and Das, S. (2020). A survey of cellular automata: types, dynamics, non-uniformity and applications. Natural Computing, 19(2):433–461. https://doi.org/10.1007/s11047-018-9696-8
Biggs, M. B. and Papin, J. A. (2013). Novel multiscale modeling tool applied to pseudomonas aeruginosa biofilm formation. PLOS ONE, 8(10). https://doi.org/10.1371/journal.pone.0078011
Binmore, K. (2007). Playing for Real: A Text on Game Theory. Oxford University Press.
Binmore, K. (2011). Rational Decisions. Princeton University Press.
Binmore, K. (2013). Sexual drift. Biological Theory, 8(2):201–208. https://doi.org/10.1007/s13752-013-0103-5
Binmore, K. and Samuelson, L. (1994). An economist’s perspective on the evolution of norms. Journal of Institutional and Theoretical Economics, 150(1):45–63. http://www.jstor.org/stable/40753015
Binmore, K., Samuelson, L., and Vaughan, R. (1995). Musical chairs: Modeling noisy evolution. Games and Economic Behavior, 11:1–35. Erratum, 21 (1997), 325. https://doi.org/10.1006/game.1995.1039
Binmore, K. and Shaked, A. (2010). Experimental economics: Where next?. Journal of Economic Behavior and Organization, 73(1):87–100. https://doi.org/10.1016/j.jebo.2008.10.019
Björnerstedt, J. and Weibull, J.W. (1996). Nash equilibrium and evolution by imitation. In Arrow, K. J. et al., editors, The Rational Foundations of Economic Behavior, pages 155–181. St. Martin’s Press, New York.
Blume, L. E. (1997). Population games. In Arthur, W. B., Durlauf, S. N., and Lane, D. A., editors, The Economy as an Evolving Complex System II, pages 425–460. Addison-Wesley, Reading, MA. https://doi.org/10.1201/9780429496639
Boyd, R. and Richerson, P. J. (1985). Culture and the Evolutionary Process. University of Chicago Press.
Chung, K. L. (1960). Markov Chains with Stationary Transition Probabilities. Springer Berlin Heidelberg. http://dx.doi.org/10.1007/978-3-642-49686-8
Colman, A. M. (1995). Game Theory and its Applications in the Social and Biological Sciences. Routledge, 2nd edition.
Cook, M. (2004). Universality in elementary cellular automata. Complex Systems, 15(1):1–40. https://www.complex-systems.com/abstracts/v15_i01_a01/
Cornforth, D., Green, D. G., and Newth, D. (2005). Ordered asynchronous processes in multi-agent systems. Physica D: Nonlinear Phenomena, 204(1):70–82. https://doi.org/10.1016/j.physd.2005.04.005
Darwin, C. R. (1859). On the origin of species by means of natural selection, or the preservation of favoured races in the struggle for life. John Murray, London.
Dawes, R. M. (1980). Social dilemmas. Annual Review of Psychology, 31(1):169–193. https://doi.org/10.1146/annurev.ps.31.020180.001125
Dixit, A. K. and Nalebuff, B. J. (2008). The Art of Strategy: A Game Theorist’s Guide to Success in Business and Life. W. W. Norton & Company.
Edmonds, B. (2001). The use of models – making MABS more informative. In Moss, S. and Davidsson, P., editors, Multi-Agent-Based Simulation: Second International Workshop, MABS 2000 Boston, MA, USA, 15–32. Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-44561-7_2
Edmonds, B. and Hales, D. (2005). Computational simulation as theoretical experiment. The Journal of Mathematical Sociology, 29(3):209–232. https://doi.org/10.1080/00222500590921283
Ellison, G. (2000). Basins of attraction, long run equilibria, and the speed of step-by-step evolution. Review of Economic Studies, 67:17–45. https://doi.org/10.1111/1467-937X.00119
Epstein, J. M. and Axtell, R. (1996). Growing Artificial Societies. Brookings Institution Press/MIT Press, Washington/Cambridge.
Erdös, P. and Rényi, A. (1959). On random graphs I. Publicationes Mathematicae, 6(3–4):290–297. https://doi.org/10.5486%2FPMD.1959.6.3-4.12
Foster, D. P. and Young, H. P. (1990). Stochastic evolutionary game dynamics. Theoretical Population Biology, 38:219–232. Corrigendum, 51 (1997), 77-78. https://doi.org/10.1016/0040-5809(90)90011-J
Fu, F., Nowak, M. A., and Hauert, C. (2010). Invasion and expansion of cooperators in lattice populations: Prisoner’s dilemma vs. snowdrift games. Journal of Theoretical Biology, 266(3):358–366. https://doi.org/10.1016/j.jtbi.2010.06.042
Fudenberg, D. and Imhof, L. A. (2008). Monotone imitation dynamics in large populations. Journal of Economic Theory, 140:229–245. https://doi.org/10.1016/j.jet.2007.08.002
Fudenberg, D. and Levine, D. K. (1998). The Theory of Learning in Games. MIT Press, Cambridge.
Fudenberg, D. and Tirole, J. (1991). Game Theory. MIT Press, Cambridge.
Galán, J. M., Izquierdo, L. R., Izquierdo, S. S., Santos, J. I., del Olmo, R., López-Paredes,A., and Edmonds, B. (2009). Errors and artefacts in agent-based modelling. Journal of Artificial Societies and Social Simulation, 12(1):1. https://www.jasss.org/12/1/1.html
García, J. and van Veelen, M. (2016). In and out of equilibrium I: Evolution of strategies in repeated games with discounting. Journal of Economic Theory, 161:161–189. http://dx.doi.org/10.1016/j.jet.2015.11.007
García, J. and van Veelen, M. (2018). No strategy can win in the repeated prisoner’s dilemma: Linking game theory and computer simulations. Frontiers in Robotics and AI, 5:102. https://doi.org/10.3389/frobt.2018.00102
Gilbert, N. (2007). Agent-Based Models, volume 153 of Quantitative Applications in the Social Sciences. Sage Publications, London.
Gilbert, N. and Terna, P. (2000). How to build and use agent-based models in social science. Mind & Society, 1(1):57–72. https://doi.org/10.1007/BF02512229
Gilboa, I. and Matsui, A. (1991). Social stability and equilibrium. Econometrica, 59:859–867. https://doi.org/10.2307/2938230
Gintis, H. (2009). Game Theory Evolving Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction. Princeton University Press, 2nd edition.
Gintis, H. (2013). Markov models of social dynamics: Theory and applications. ACM Trans. Intell. Syst. Technol., 4(3), Article 53. http://dx.doi.org/10.1145/2483669.2483686
Gintis, H. (2014). The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences. Princeton University Press, revised edition.
Gómez-Gardeñes, J., Campillo, M., Floría, L. M., and Moreno, Y. (2007). Dynamical organization of cooperation in complex topologies. Phys. Rev. Lett., 98:108103. http://dx.doi.org/10.1103/PhysRevLett.98.108103
Gotts, N., Polhill, J., and Law, A. (2003). Agent-based simulation in the study of social dilemmas. Artificial Intelligence Review, 19(1):3–92. https://doi.org/10.1023/A:1022120928602
Hamill, L. and Gilbert, N. (2016). Agent-based Modelling in Economics. John Wiley & Sons, Ltd. http://dx.doi.org/10.1002/9781118945520
Hamilton, W. D. (1967). Extraordinary sex ratios. Science, 156:477–488. http://dx.doi.org/10.1126/science.156.3774.477
Harsanyi, J. C. (1967). Games with Incomplete Information Played by “Bayesian” Players. Part I. The Basic Model. Management Science, 14(3):159–182. https://doi.org/10.1287/mnsc.14.3.159
Harsanyi, J. C. (1968a). Games with Incomplete Information Played by “Bayesian” Players. Part II. Bayesian Equilibrium Points. Management Science, 14(5):320-334. https://doi.org/10.1287/mnsc.14.5.320
Harsanyi, J. C. (1968b). Games with Incomplete Information Played by “Bayesian” Players. Part III. The Basic Probability Distribution of the Game. Management Science, 14(7):486-502. https://doi.org/10.1287/mnsc.14.7.486
Hauert, C. (2002). Effects of space in 2×2 games. International Journal of Bifurcation and Chaos, 12(07):1531–1548. https://doi.org/10.1142/S0218127402005273
Hauert, C. (2006). Spatial effects in social dilemmas. Journal of Theoretical Biology, 240(4):627–636. https://doi.org/10.1016/j.jtbi.2005.10.024
Hauert, C. (2018). EvoLudo: Interactive tutorials in evolutionary games. https://wiki.evoludo.org/
Hauert, C. and Doebeli, M. (2004). Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature, 428:643–646. http://dx.doi.org/10.1038/nature02360
Hauert, C. and Miȩkisz, J. (2018). Effects of sampling interaction partners and competitors in evolutionary games. Phys. Rev. E, 98:052301. https://doi.org/10.1103/PhysRevE.98.052301
Hauert, C. and Szabó, G. (2005). Game theory and physics. American Journal of Physics, 73(5):405–414. https://doi.org/10.1119/1.1848514
Head, B. (2018). NetLogo Python extension. Software. https://github.com/NetLogo/Python-Extension.
Hegselmann, R. (2017). Thomas C. Schelling and James M. Sakoda: The intellectual, technical, and social history of a model. Journal of Artificial Societies and Social Simulation, 20(3):15. https://doi.org/10.18564/jasss.3511
Helbing, D. (1992). A mathematical model for behavioral changes by pair interactions. In Haag, G., Mueller, U., and Troitzsch, K. G., editors, Economic Evolution and Demographic Change: Formal Models in Social Sciences, pages 330–348. Springer, Berlin. https://doi.org/10.1007/978-3-642-48808-5_18
Hilbe, C. and Traulsen, A. (2016). 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. Physics of Life Reviews, 19:29–31. https://doi.org/10.1016/j.plrev.2016.10.004
Hindersin, L., Wu, B., Traulsen, A., and García, J. (2019). Computation and simulation of evolutionary game dynamics in finite populations. Scientific Reports, 9(1):6946. https://doi.org/10.1038/s41598-019-43102-z
Hofbauer, J. (1995a). Imitation dynamics for games. Unpublished manuscript, University of Vienna.
Hofbauer, J. (1995b). Stability for the best response dynamics. Unpublished manuscript, University of Vienna.
Hofbauer, J. and Sandholm, W. H. (2007). Evolution in games with randomly disturbed payoffs. Journal of Economic Theory, 132:47–69. https://doi.org/10.1016/j.jet.2005.05.011
Hofbauer, J. and Sigmund, K. (1998). Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9781139173179
Hofbauer, J. and Sigmund, K. (2003). Evolutionary game dynamics. Bulletin of the American Mathematical Society, 40(4):479–519. http://dx.doi.org/10.1090/S0273-0979-03-00988-1
Holt, C. A. and Roth, A. E. (2004). The Nash equilibrium: A perspective. Proceedings of the National Academy of Sciences, 101(12):3999–4002. http://dx.doi.org/10.1073/pnas.0308738101
Huberman, B. A. and Glance, N. S. (1993). Evolutionary games and computer simulations. Proceedings of the National Academy of Sciences, 90:7716–7718. https://doi.org/10.1073/pnas.90.16.7716
Isaac, A. G. (2008). Simulating evolutionary games: a python-based introduction. Journal of Artificial Societies and Social Simulation, 11(3):8. http://jasss.soc.surrey.ac.uk/11/3/8.html
Izquierdo, L. R., Izquierdo, S. S., Galán, J. M., and Santos, J. I. (2009). Techniques to understand computer simulations: Markov chain analysis. Journal of Artificial Societies and Social Simulation, 12(1):6. http://jasss.soc.surrey.ac.uk/12/1/6.html
Izquierdo, L. R., Izquierdo, S. S., Galán, J. M., and Santos, J. I. (2013). Combining mathematical and simulation approaches to understand the dynamics of computer models. In Edmonds, B. and Meyer, R., editors, Simulating Social Complexity: A Handbook, chapter 11, pages 235–271. Springer Berlin Heidelberg. http://doi.org/10.1007/978-3-540-93813-2_11. Second edition (2017) available at: https://doi.org/10.1007/978-3-319-66948-9_13
Izquierdo, L. R., Izquierdo, S. S., Galán, J. M., Santos, J. I., and Sandholm, W. H. (2022). Schelling-Sakoda model of spatial segregation. Software available at https://luis-r-izquierdo.github.io/schelling-sakoda-refuting-machine/. https://doi.org/10.5281/zenodo.7065864
Izquierdo, L. R., Izquierdo, S. S., and Hauert, C. (2024). Pair approximation for 2×2 symmetric games on regular networks. Software available at https://github.com/luis-r-izquierdo/pair-approximation. https://doi.org/10.5281/zenodo.10975163
Izquierdo, L. R., Izquierdo, S. S., and Rodríguez, J. (2022). Fast and scalable global convergence in single-optimum decentralized coordination problems. IEEE Transactions on Control of Network Systems, 9(4):1937–1948. https://doi.org/10.1109/TCNS.2022.3181545
Izquierdo, L. R., Izquierdo, S. S., and Sandholm, W. H. (2019). An introduction to ABED: Agent-based simulation of evolutionary game dynamics. Games and Economic Behavior, 118:434–462. https://doi.org/10.1016/j.geb.2019.09.014
Izquierdo, L. R., Izquierdo, S. S., and Vega-Redondo, F. (2012). Learning and evolutionary game theory. In Seel, N. M., editor, Encyclopedia of the Sciences of Learning, pages 1782–1788. Springer US, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_576
Izquierdo, L. R., Izquierdo, S. S., and Vega-Redondo, F. (2014). Leave and let leave: A sufficient condition to explain the evolutionary emergence of cooperation. Journal of Economic Dynamics and Control, 46:91–113. https://doi.org/10.1016/j.jedc.2014.06.007
Izquierdo, L. R. and Polhill, J. G. (2006). Is your model susceptible to floating-point errors? Journal of Artificial Societies and Social Simulation, 9(4):4. http://jasss.soc.surrey.ac.uk/9/4/4.html
Izquierdo, S. S. and Izquierdo, L. R. (2013). Stochastic approximation to understand simple simulation models. Journal of Statistical Physics, 151(1):254–276. http://dx.doi.org/10.1007/s10955-012-0654-z
Janssen, M.A. (2020). Introduction to Agent-Based Modeling: With applications to social, ecological and social-ecological systems. https://intro2abm.com
Janssen, J. and Manca, R. (2006). Applied semi-markov processes. Springer-Verlag, New York. http://dx.doi.org/10.1007/0-387-29548-8
Jaxa-Rozen, M. and Kwakkel, J. H. (2018). PyNetlogo: Linking NetLogo with Python. Journal of Artificial Societies and Social Simulation, 21(2):4. https://dx.doi.org/10.18564/jasss.3668
Kandori, M. and Rob, R. (1995). Evolution of equilibria in the long run: A general theory and applications. Journal of Economic Theory, 65:383–414. https://doi.org/10.1006/jeth.1995.1014
Karr, A. F. (1990). Markov processes. In Heyman, D. P. and Sobel, M. J. (eds.), Stochastic Models, volume 2 of Handbooks in Operations Research and Management Science, chapter 2, pages 95–123. Elsevier. https://doi.org/10.1016/S0927-0507(05)80166-5
Killingback, T. and Doebeli, M. (1996). Spatial evolutionary game theory: Hawks and doves revisited. Proceedings of the Royal Society of London. Series B: Biological Sciences, 263(1374):1135–1144. https://doi.org/10.1098/rspb.1996.0166
Kosfeld, M., Droste, E., and Voorneveld, M. (2002). A myopic adjustment process leading to best reply matching. Journal of Economic Theory, 40:270–298. https://doi.org/10.1016/S0899-8256(02)00007-6
Kravari, K. and Bassiliades, N. (2015). A survey of agent platforms. Journal of Artificial Societies and Social Simulation, 18(1):11. https://doi.org/10.18564/jasss.2661
Kulkarni, V. G. (1995). Modeling and Analysis of Stochastic Systems. Chapman & Hall, Ltd., London, UK.
Kulkarni, V. G. (1999). Modeling, Analysis, Design, and Control of Stochastic Systems. Springer New York, NY. https://doi.org/10.1007/978-1-4757-3098-2
Lahkar, R. and Sandholm, W. H. (2008). The projection dynamic and the geometry of population games. Games and Economic Behavior, 64(2):565–590. Special Issue in Honor of Michael B. Maschler. https://doi.org/10.1016/j.geb.2008.02.002
Lipowski, A. and Lipowska, D. (2012). Roulette-wheel selection via stochastic acceptance. Physica A: Statistical Mechanics and its Applications, 391(6):2193–2196. https://doi.org/10.1016/j.physa.2011.12.004
Loginov, G. (2022). Ordinal Imitative Dynamics. International Journal of Game Theory, 51:391–412. https://doi.org/10.1007/s00182-021-00797-7
Lytinen, S. L. and Railsback, S. F. (2012). The evolution of agent-based simulation platforms: A review of NetLogo 5.0 and ReLogo. In Proceedings of the fourth international symposium on agent-based modeling and simulation (21st European Meeting on Cybernetics and Systems Research).
Maciejewski,W., Fu, F., and Hauert, C. (2014). Evolutionary game dynamics in populations with heterogenous structures. PLOS Computational Biology, 10(4):1–16. https://doi.org/10.1371/journal.pcbi.1003567
Marden, J. R. and Shamma, J. S. (2015). Game theory and distributed control. In Young, H.P. and Zamir, S., editors, Handbook of Game Theory with Economic Applications, volume 4, chapter 16, pages 861–899. Elsevier, Amsterdam. https://doi.org/10.1016/B978-0-444-53766-9.00016-1
Masuda, N. (2007). Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation. Proceedings of the Royal Society B: Biological Sciences, 274(1620):1815–1821. https://doi.org/10.1098/rspb.2007.0294
Maynard Smith, J. (1982). Evolution and the Theory of Games. Cambridge University Press, Cambridge.
Maynard Smith, J. and Price, G. R. (1973). The logic of animal conflict. Nature, 246:15–18. https://doi.org/10.1038/246015a0
Mitchell, M. (1998). Computation in cellular automata: A selected review. In Gramß, T., Bornholdt, S., Groß, M., Mitchell, M., and Pellizzari, T., editors, Non-Standard Computation: Molecular Computation – Cellular Automata – Evolutionary Algorithms – Quantum Computers, chapter 4, pages 95–140. John Wiley & Sons, Ltd. https://doi.org/10.1002/3527602968.ch4
Morita, S. (2008). Extended Pair Approximation of Evolutionary Game on Complex Networks. Progress of Theoretical Physics, 119(1):29–38. https://doi.org/10.1143/PTP.119.29
Mukherji, A., Rajan, V., and Slagle, J. R. (1996). Robustness of cooperation. Nature, 379(6561):125–126. https://dx.doi.org/10.1038/379125b0
Myerson, R. B. (1997). Game theory: Analysis of Conflict. Harvard University Press.
Nakamaru, M., Matsuda, H., and Iwasa, Y. (1997). The evolution of cooperation in a lattice-structured population. Journal of Theoretical Biology, 184(1):65–81. https://doi.org/10.1006/jtbi.1996.0243
Nash, J. F. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36:48–49. https://doi.org/10.1073/pnas.36.1.48
Nelson, R. R. and Winter, S. G. (1982). An Evolutionary Theory of Economic Change. Harvard University Press.
Newth, D. and Cornforth, D. (2009). Asynchronous spatial evolutionary games. Biosystems, 95(2):120–129. https://doi.org/10.1016/j.biosystems.2008.09.003
Newton, J. (2018). Evolutionary game theory: A renaissance. Games, 9(2), 31. https://doi.org/10.3390/g9020031
Nikolai, C. and Madey, G. (2009). Tools of the trade: A survey of various agent based modeling platforms. Journal of Artificial Societies and Social Simulation, 12(2):2. http://jasss.soc.surrey.ac.uk/12/2/2.html
Norris, J. R. (1997). Markov Chains. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511810633
Nowak, M. A., Bonhoeffer, S., and May, R. M. (1994a). More spatial games. International Journal of Bifurcation and Chaos, 4:33–56. https://doi.org/10.1142/S0218127494000046
Nowak, M. A., Bonhoeffer, S., and May, R. M. (1994b). Spatial games and the maintenance of cooperation. Proceedings of the National Academy of Sciences, 91:4877–4881. https://doi.org/10.1073/pnas.91.11.4877
Nowak, M. A., Bonhoeffer, S., and May, R. M. (1996). Robustness of cooperation. Nature, 379(6561):126–126. https://doi.org/10.1038/379126a0
Nowak, M. A. and May, R. M. (1992). Evolutionary games and spatial chaos. Nature, 359:826–829. http://dx.doi.org/10.1038/359826a0
Nowak, M. A. and May, R. M. (1993). The spatial dilemmas of evolution. International Journal of Bifurcation and Chaos, 3:35–78. https://doi.org/10.1142/S0218127493000040
Ohtsuki, H., Nowak, M. A., and Pacheco, J. M. (2007a). Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. Phys. Rev. Lett., 98:108106. https://doi.org/10.1103/PhysRevLett.98.108106
Ohtsuki, H., Pacheco, J. M., and Nowak, M. A. (2007b). Evolutionary graph theory: Breaking the symmetry between interaction and replacement. Journal of Theoretical Biology, 246(4):681–694. https://doi.org/10.1016/j.jtbi.2007.01.024
Osborne, M. (2004). An Introduction to Game Theory. Oxford University Press, Oxford.
Osborne, M. J. and Rubinstein, A. (1998). Games with procedurally rational players. American Economic Review, 88:834–847. https://www.jstor.org/stable/117008
Oyama, D., Sandholm, W. H., and Tercieux, O. (2015). Sampling best response dynamics and deterministic equilibrium selection. Theoretical Economics, 10:243–281. https://doi.org/10.3982/TE1405
Perc, M. and Szolnoki, A. (2010). Coevolutionary games—a mini review. Biosystems, 99(2):109–125. https://doi.org/10.1016/j.biosystems.2009.10.003
Polhill, J. G., Izquierdo, L. R., and Gotts, N. M. (2006). What every agent-based modeller should know about floating point arithmetic. Environmental Modelling & Software, 21(3):283–309. https://doi.org/10.1016/j.envsoft.2004.10.011
Poncela, J., Gómez-Gardeñes, J., Floría, L. M., and Moreno, Y. (2007). Robustness of cooperation in the evolutionary prisoner’s dilemma on complex networks. New Journal of Physics, 9(6):184. https://doi.org/10.1088/1367-2630/9/6/184
Probst, D. (1999). Book review of “Evolutionary Game Theory” by Jörgen W. Weibull. Journal of Artificial Societies and Social Simulation, 2(1). http://jasss.soc.surrey.ac.uk/2/1/review3.html
Python Software Foundation (2019). Python. Software. http://www.python.org.
Quijano, N., Ocampo-Martinez, C., Barreiro-Gomez, J., Obando, G., Pantoja, A., and Mojica-Nava, E. (2017). The role of population games and evolutionary dynamics in distributed control systems: The advantages of evolutionary game theory. IEEE Control Systems Magazine, 37(1):70–97. https://doi.org/10.1109/MCS.2016.2621479
R Core Team (2019). R: A Language and Environment for Statistical Computing. Software. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org.
Railsback, S., Ayllón, D., Berger, U., Grimm, V., Lytinen, S., Sheppard, C., and Thiele, J. (2017). Improving execution speed of models implemented in netlogo. Journal of Artificial Societies and Social Simulation, 20(1):3. https://doi.org/10.18564/jasss.3282
Railsback, S. F. and Grimm, V. (2019). Agent-Based and Individual-Based Modeling: A Practical Introduction, Second edition. Princeton University Press, Princeton, NJ. http://www.railsback-grimm-abm-book.com. First edition (2011) at http://www.jstor.org/stable/j.ctt7sns7
Railsback, S. F., Lytinen, S. L., and Jackson, S. K. (2006). Agent-based simulation platforms: Review and development recommendations. Simulation, 82(9):609–623. https://doi.org/10.1177/0037549706073695
Rand, D. A. (1999). Correlation Equations and Pair Approximations for Spatial Ecologies. In Advanced Ecological Theory, J. McGlade (Ed.), chapter 4, pages 100–142. John Wiley & Sons, Ltd. https://doi.org/10.1002/9781444311501.ch4
Roca, C. P., Cuesta, J. A., and Sánchez, A. (2009a). Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics. Physics of Life Reviews, 6(4):208 – 249. https://doi.org/10.1016/j.plrev.2009.08.001
Roca, C. P., Cuesta, J. A., and Sánchez, A. (2009b). Effect of spatial structure on the evolution of cooperation. Phys. Rev. E, 80:046106. https://doi.org/10.1103/PhysRevE.80.046106
Roth, G. and Sandholm, W. H. (2013). Stochastic approximations with constant step size and differential inclusions. SIAM Journal on Control and Optimization, 51:525–555. https://doi.org/10.1137/110844192
Sakoda, J. M. (1949). Minidoka: An Analysis of Changing Patterns of Social Behavior. PhD thesis, University of California.
Sakoda, J. M. (1971). The checkerboard model of social interaction. The Journal of Mathematical Sociology, 1(1):119–132. https://doi.org/10.1080/0022250X.1971.9989791
Samuelson, L. (1997). Evolutionary Games and Equilibrium Selection. MIT Press, Cambridge.
Sandholm, W. H. (2001). Almost global convergence to p-dominant equilibrium. International Journal of Game Theory, 30:107–116. https://doi.org/10.1007/s001820100067
Sandholm, W. H. (2003). Evolution and equilibrium under inexact information. Games and Economic Behavior, 44:343–378. https://doi.org/10.1016/S0899-8256(03)00026-5
Sandholm, W. H. (2007). Simple formulas for stationary distributions and stochastically
stable states. Games and Economic Behavior, 59:154–162. https://doi.org/10.1016/j.geb.2006.07.001
Sandholm, W. H. (2009). Evolutionary game theory. In Meyers, R. A., editor, Encyclopedia of Complexity and Systems Science, pages 3176–3205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_188-3
Sandholm, W. H. (2010a). Population Games and Evolutionary Dynamics. MIT Press, Cambridge.
Sandholm, W. H. (2010b). Pairwise comparison dynamics and evolutionary foundations for Nash equilibrium. Games, 1:3–17. https://doi.org/10.3390/g1010003
Sandholm, W. H., Izquierdo, S. S., and Izquierdo, L. R. (2019). Best experienced payoff dynamics and cooperation in the Centipede game. Theoretical Economics, 14: 1347–1385. https://doi.org/10.3982/TE3565
Sandholm, W. H., Izquierdo, S. S., and Izquierdo, L. R. (2020). Stability for best experienced payoff dynamics. Journal of Economic Theory, 185:104957. https://doi.org/10.1016/j.jet.2019.104957
Sandholm, W. H. and Staudigl, M. (2018). Sample path large deviations for stochastic evolutionary game dynamics. Mathematics of Operations Research, 43(4):1348–1377. https://doi.org/10.1287/moor.2017.0908
Santos, F. C., Rodrigues, J. F., and Pacheco, J. M. (2006a). Graph topology plays a determinant role in the evolution of cooperation. Proceedings of the Royal Society B: Biological Sciences, 273(1582):51–55. https://doi.org/10.1098/rspb.2005.3272
Santos, F. C. and Pacheco, J. M. (2005). Scale-free networks provide a unifying framework for the emergence of cooperation. Phys. Rev. Lett., 95:098104. https://doi.org/10.1103/PhysRevLett.95.098104
Santos, F. C. and Pacheco, J. M. (2006). A new route to the evolution of cooperation. Journal of Evolutionary Biology, 19(3):726–733. https://doi.org/10.1111/j.1420-9101.2005.01063.x
Santos, F. C., Pacheco, J. M., and Lenaerts, T. (2006b). Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proceedings of the National Academy of Sciences, 103(9):3490–3494. https://doi.org/10.1073/pnas.0508201103
Sayama, H. (2015). Introduction to the Modeling and Analysis of Complex Systems. Milne Open Textbooks. https://milneopentextbooks.org/introduction-to-the-modeling-and-analysis-of-complex-systems/
Schelling, T. C. (1969). Models of segregation. The American Economic Review, 59(2):488–493. http://www.jstor.org/stable/1823701
Schelling, T. C. (1971). Dynamic models of segregation. The Journal of Mathematical Sociology, 1(2):143–186. https://doi.org/10.1080/0022250X.1971.9989794
Schelling, T. C. (1978). Micromotives and Macrobehavior. Norton, New York.
Schlag, K. H. (1998). Why imitate, and if so, how? A boundedly rational approach to multi-armed bandits. Journal of Economic Theory, 78:130–156. https://doi.org/10.1006/jeth.1997.2347
Schwarz, K. (2011). Darts, dice, and coins: Sampling from a discrete distribution. https://www.keithschwarz.com/darts-dice-coins/
Selten, R. (1965). Spieltheoretische Behandlung eines Oligopolmodells mit Nachfrageträgheit. Zeitschrift für die gesamte Staatswissenschaft / Journal of Institutional and Theoretical Economics, 121(2):301–324. http://www.jstor.org/stable/40748884
Selten, R. (1975). Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory, 4(1):25–55. https://doi.org/10.1007/BF01766400
Seri, R. (2016). Analytical approaches to agent-based models. In Secci, D. and Neumann, M., editors, Agent-Based Simulation of Organizational Behavior, chapter 13, pages 265–286. Springer International Publishing. https://doi.org/10.1007/978-3-319-18153-0_13
Sethi, R. (2000). Stability of equilibria in games with procedurally rational players. Games and Economic Behavior, 32:85–104. https://doi.org/10.1006/game.1999.0753
Sethi, R. (2021). Stable sampling in repeated games. Journal of Economic Theory, 197:105343. https://doi.org/10.1016/j.jet.2021.105343
Sigmund, K. (1983). Games of Life: Explorations in Ecology, Evolution, and Behaviour. Oxford University Press.
Sklar, E. (2007). NetLogo, a multi-agent simulation environment. Artificial Life, 13(3):303–311. https://doi.org/10.1162/artl.2007.13.3.303
Skyrms, B. (2001). The Stag Hunt. Proceedings and Addresses of the American Philosophical Association, 75(2):31–41. https://doi.org/10.2307/3218711
Smaldino, P. E. (2023). Modeling Social Behavior: Mathematical and Agent-Based Models of Social Dynamics and Cultural Evolution. Princeton University Press.
Smith, M. J. (1984). The stability of a dynamic model of traffic assignment —an application of a method of Lyapunov. Transportation Science, 18:245–252. https://doi.org/10.1287/trsc.18.3.245
Szabó, G. and Fáth, G. (2007). Evolutionary games on graphs. Physics Reports, 446:97–216. https://doi.org/10.1016/j.physrep.2007.04.004
Szabó, G. and Tőke, C. (1998). Evolutionary prisoner’s dilemma game on a square lattice. Phys. Rev. E, 58:69–73. https://doi.org/10.1103/PhysRevE.58.69
Szolnoki, A., Perc, M., and Danku, Z. (2008). Towards effective payoffs in the prisoner’s dilemma game on scale-free networks. Physica A: Statistical Mechanics and its Applications, 387(8):2075–2082. https://doi.org/10.1016/j.physa.2007.11.021
Taylor, P. D. and Jonker, L. (1978). Evolutionarily stable strategies and game dynamics. Mathematical Biosciences, 40:145–156. https://doi.org/10.1016/0025-5564(78)90077-9
The MathWorks, Inc. (2019). Matlab. Software. Natick, Massachusetts. https://mathworks.com
Thiele, J. C. (2014). R marries NetLogo: Introduction to the RNetLogo package. Journal of Statistical Software, 58(2):1–41. http://dx.doi.org/10.18637/jss.v058.i02
Thiele, J. C. and Grimm, V. (2010). NetLogo meets R: Linking agent-based models with a toolbox for their analysis. Environmental Modelling & Software, 25(8):972–974. https://doi.org/10.1016/j.envsoft.2010.02.008
Thiele, J. C., Kurth, W., and Grimm, V. (2012a). Agent-based modelling: Tools for linking Netlogo and R. Journal of Artificial Societies and Social Simulation, 15(3):8. http://dx.doi.org/10.18564/jasss.2018
Thiele, J. C., Kurth,W., and Grimm, V. (2012b). RNetLogo: An R package for running and exploring individual-based models implemented in NetLogo. Methods in Ecology and Evolution, 3(3):480–483. http://dx.doi.org/10.1111/j.2041-210X.2011.00180.x
Thiele, J. C., Kurth, W., and Grimm, V. (2014). Facilitating parameter estimation and sensitivity analysis of agent-based models: A cookbook using netlogo and R. Journal of Artificial Societies and Social Simulation, 17(3):11. http://dx.doi.org/10.18564/jasss.2503
Thomas, B. (1984). Evolutionary stability: States and strategies. Theoretical Population Biology, 26:49–67. https://doi.org/10.1016/0040-5809(84)90023-6
Tomassini, M., Pestelacci, E., and Luthi, L. (2007). Social dilemmas and cooperation in complex networks. International Journal of Modern Physics C, 18(07):1173–1185. https://doi.org/10.1142/S0129183107011212
Traulsen, A. and Hauert, C. (2009). Stochastic evolutionary game dynamics. In Schuster, H. G., editor, Reviews of Nonlinear Dynamics and Complexity, volume 2, pages 25–61. Wiley, New York. https://doi.org/10.1002/9783527628001.ch2
van Baalen, M. (2000). Pair Approximations for Different Spatial Geometries. In Dieckmann, U., Law, R., and Metz, J. A. J., editors, The Geometry of Ecological Interactions: Simplifying Spatial Complexity, pages 359–387. Cambridge Studies in Adaptive Dynamics. Cambridge University Press. https://doi.org/10.1017/CBO9780511525537.023
Vega-Redondo, F. (1997). The evolution of Walrasian behavior. Econometrica, 65:375–384. https://doi.org/10.2307/2171898
Vega-Redondo, F. (2003). Economics and the Theory of Games. Cambridge University Press, Cambridge, UK.
von Neumann, J. and Morgenstern, O. (1944). Theory of Games and Economic Behavior. Prentice-Hall, Princeton.
Vose, M. (1991). A linear algorithm for generating random numbers with a given distribution. IEEE Transactions on Software Engineering, 17(9):972–975. https://doi.org/10.1109/32.92917
Wallace, C. and Young, H. P. (2015). Stochastic evolutionary game dynamics. In Young, H.P. and Zamir, S., editors, Handbook of Game Theory with Economic Applications, volume 4, chapter 6, pages 327–380. Elsevier, Amsterdam. https://doi.org/10.1016/B978-0-444-53766-9.00006-9
Watts, D. J. and Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393(6684):440–442. https://doi.org/10.1038/30918
Weibull, J. W. (1995). Evolutionary Game Theory. MIT Press, Cambridge.
Wilensky, U. (1999). NetLogo. Software. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. http://ccl.northwestern.edu/netlogo/
Wilensky, U. (2023). The NetLogo User Manual. Version 6.4.0. https://ccl.northwestern.edu/netlogo/6.4.0/docs/
Wilensky, U. (2005a). NetLogo Preferential Attachment model. http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
Wilensky, U. (2005b). Mouse Drag One Example. http://ccl.northwestern.edu/netlogo/models/MouseDragOneExample. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
Wilensky, U. and Rand, W. (2015). An Introduction to Agent-Based Modeling: Modeling Natural, Social, and Engineered Complex Systems with NetLogo. The MIT Press. https://www.jstor.org/stable/j.ctt17kk851
Wilensky, U. and Shargel, B. (2002). Behaviorspace. Software. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. http://ccl.northwestern.edu/netlogo/behaviorspace.html
Wilensky, U. and Stroup, W. (1999). Hubnet. Software. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. http://ccl.northwestern.edu/netlogo/hubnet.html
Woelfing, B. and Traulsen, A. (2009). Stochastic sampling of interaction partners versus deterministic payoff assignment. Journal of Theoretical Biology, 257(4):689–695. https://doi.org/10.1016/j.jtbi.2008.12.025
Wolfram, S. (1983). Statistical mechanics of cellular automata. Reviews of modern physics, 55(3):601. https://doi.org/10.1103/RevModPhys.55.601
Wolfram, S. (2002). A new kind of science. Wolfram-Media. https://www.wolframscience.com/nks/
Wolfram Research, Inc. (2019). Mathematica. Software. Champaign, Illinois. https://www.wolfram.com
Wu, Z.-X., Guan, J.-Y., Xu, X.-J., and Wang, Y.-H. (2007). Evolutionary prisoner’s dilemma game on Barabási–Albert scale-free networks. Physica A: Statistical Mechanics and its Applications, 379(2):672–680. https://doi.org/10.1016/j.physa.2007.02.085
Wu, Z.-X., Xu, X.-J., and Wang, Y.-H. (2005). Does the scale-free topology favor the emergence of cooperation?. arXiv:physics/0508220 https://doi.org/10.48550/arXiv.physics/0508220
Young, H. P. (1998). Individual Strategy and Social Structure. Princeton University Press, Princeton.
Young, H. P. (2004). Strategic Learning and Its Limits. Oxford University Press, Oxford.
