Hostname: page-component-5d84bcc8dc-g8mt7 Total loading time: 0 Render date: 2026-08-10T13:26:46.084Z Has data issue: false hasContentIssue false
  • English
  • Français

Adversarial scheduling in discrete models of social dynamics†

Published online by Cambridge University Press:  06 September 2012

GABRIEL ISTRATE ,
MADHAV V. MARATHE  and
S. S. RAVI
GABRIEL ISTRATE
Affiliation:
Center for the Study of Complexity, Babeş-Bolyai University, Str. Fântânele 30, cam. A-14, Cluj-Napoca, RO-400294, Romania and e-Austria Research Institute, C. Coposu 4, cam 045B, Timişoara, RO-300223, Romania Email: gabrielistrate@acm.org
MADHAV V. MARATHE
Affiliation:
Network Dynamics and Simulation Science Laboratory, Virginia Bio-Informatics Institute, 1880 Pratt Drive Building XV, Blacksburg, VA 24061, U.S.A. Email: mmarathe@vbi.vt.edu
S. S. RAVI
Affiliation:
Computer Science Dept., S.U.N.Y. Albany, Albany, NY 12222, U.S.A. Email: ravi@cs.albany.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we advocate the study of discrete models of social dynamics under adversarial scheduling. The approach we propose forms part of a foundational basis for a generative approach to social science (Epstein 2007). We highlight the feasibility of the adversarial scheduling approach by using it to study the Prisoners's Dilemma Game with Pavlov update, a dynamics that has already been investigated under random update in Kittock (1994), Dyer et al. (2002), Mossel and Roch (2006) and Dyer and Velumailum (2011). The model is specified by letting players at the nodes of an underlying graph G repeatedly play the Prisoner's Dilemma against their neighbours. The players adapt their strategies based on the past behaviour of their opponents by applying the so-called win–stay lose–shift strategy. With random scheduling, starting from any initial configuration, the system reaches the fixed point in which all players cooperate with high probability. On the other hand, under adversarial scheduling the following results hold:

  • — A scheduler that can select both game participants can preclude the system from reaching the unique fixed point on most graph topologies.

  • — A non-adaptive scheduler that is only allowed to choose one of the participants is no more powerful than a random scheduler. With this restriction, even an adaptive scheduler is not significantly more powerful than the random scheduler, provided it is ‘reasonably fair’.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 22 , Special Issue 5: Computability of the Physical , October 2012 , pp. 788 - 815
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Aspnes, J. and Ruppert, E. (2007) An introduction to population protocols. Bulletin of the European Association for Theoretical Computer Science 93 98–117.Google Scholar
Axelrod, R. (1984) The Evolution of Cooperation, Basic Books.Google Scholar
Axelrod, R. (1997) The Complexity of Cooperation. Agent-Based Models of Competition and Cooperation, Princeton Studies in Complexity, Princeton University Press.Google Scholar
Axtell, R. and Epstein, J. (1996) Growing Artificial Societies: Social Science from the Bottom Up, The MIT Press.Google Scholar
Ballot, J. and Weisbuch, G. (2000) Introduction: Why simulation in the social sciences. Advances in Complex Systems 3 (1-4)9–16.Google Scholar
Barrett, C., Eubank, S. and Marathe, M. (2005) Modeling and simulation of large biological, information and socio-technical systems: An interaction based approach. In: Goldin, D., Smolka, S. and Wegner, P. (eds.) Interactive Computation: The New Paradigm, Springer Verlag 353–394.Google Scholar
Barrett, C., Hunt, H., Marathe, M. V., Ravi, S. S., Rosenkrantz, D. and Stearns, R. (2003) Reachability problems for sequential dynamical systems with threshold functions. Theoretical Computer Science 295 (1-3)41–64.CrossRefGoogle Scholar
Boudon, R. (1998) Social mechanisms without black boxes. In: Hedström, P. and Swedberg, R. (eds.) Social mechanisms: An analytical approach to social theory, Cambridge University Press.Google Scholar
Bournez, O., Chalopin, J., Cohen, J. and Koegler, X. (2009) Population protocols that correspond to symmetric games. (Preprint available at arXiv:0907.3126v1 [cs.GT].)CrossRefGoogle Scholar
Bunge, M. (1997) Mechanism and explanation. Philosophy of the Social Sciences 27 (4)410.CrossRefGoogle Scholar
Castellano, C., Fortunato, S. and Loreto, V. (2009) Statistical physics of social dynamics. Reviews of modern physics 81 (2)591–646.CrossRefGoogle Scholar
Coleman, A., Colman, A. and Thomas, R. M. (1991) Cooperation without awareness: A multiperson generalization of the minimal social situation. Behavioral Science 35 115–121.CrossRefGoogle Scholar
Colman, A. (2005) Cooperation in multi-player minimal social situations: An experimental investigation. British Academy Larger Research Grants Scheme Grant No. LRG-37265, 2004–2005.Google Scholar
Craver, C. F. (2006) When mechanistic models explain. Synthese 153 (3)355–376.CrossRefGoogle Scholar
Dolev, S., Israeli, A. and Moran, S. (1995) Analyzing expected time by scheduler-luck games. I.E.E.E. Transactions on Software Engineering 21 (5)429–439.Google Scholar
Dolev, S. (2000) Self-stabilization, M.I.T. Press.CrossRefGoogle Scholar
Durrett, R. (2006) Random Graph Dynamics, Cambridge University Press.CrossRefGoogle Scholar
Dyer, M., Greenhill, C., Goldberg, L., Istrate, G. and Jerrum, M. (2002) The Convergence of Iterated Prisoner's Dilemma Game. Combinatorics, Probability and Computing 11 135–147.CrossRefGoogle Scholar
Dyer, M. and Velumailum, M. (2011) The Iterated Prisoner's Dilemma on a cycle. (Available at arXiv:1102.3822v1 [cs.GT].)Google Scholar
Elster, J. (1998) A plea for mechanisms. In: Hedström, P. and Swedberg, R. (eds.) Social Mechanisms: An Analytical Approach to Social Theory, Cambridge University Press.Google Scholar
Epstein, J. M., Cummings, D., Chakravarty, S., Singa, R. and Burke, D. (2004) Toward a Containment Strategy for Smallpox Bioterror. An Individual-Based Computational Approach, Brookings Institution Press.Google Scholar
Epstein, J. (1999) Agent-based computational models and generative social science. Complexity 4 (5)41–60.3.0.CO;2-F>CrossRefGoogle Scholar
Epstein, J. (2007) Generative Social Science: Studies in Agent-based Computational Modeling, Princeton University Press.Google Scholar
Eubank, S., Guclu, H., Kumar, V. S. A., Marathe, M. V., Srinivasan, A., Toroczkai, Z. and Wang, N. (2004) Monitoring and mitigating smallpox epidemics: Strategies drawn from a census data instantiated virtual city. Nature 429 (6988)180–184.CrossRefGoogle Scholar
Fribourg, L. and Messika, S. (2005) Brief Announcement: Coupling for Markov Decision Processes – Application to Self-Stabilization with Arbitrary Schedulers. In: Proceedings of the Twenty-Fourth Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC'05) 322.CrossRefGoogle Scholar
Fribourg, L., Messika, S. and Picaronny, C. (2006) Coupling and self-stabilization. Distributed Computing 18 (3)221–232.CrossRefGoogle Scholar
Gilbert, N. and Troizch, K. (2005) Simulation for social scientists (second edition), Open University Press.Google Scholar
Glennan, S. S. (1996) Mechanisms and the nature of causation. Erkenntnis 44 (1)49–71.CrossRefGoogle Scholar
Hedström, P. (2005) Dissecting the social: on the principles of analytical sociology, Cambridge University Press.CrossRefGoogle Scholar
Hedström, P. and Bearman, P. (2009) The Oxford handbook of analytical sociology, Oxford University Press.Google Scholar
Hedström, P. and Swedberg, R. (eds.) (2006) Social Mechanisms: An Analytical Approach to Social Theory, Cambridge University Press.Google Scholar
Hegselmann, R. and Flache, A. (1998) Understanding complex social dynamics: A plea for cellular automata based modelling. Journal of Artificial Societies and Social Simulation 1 (3)1.Google Scholar
Jaggard, A., Schapira, M. and Wright, R. (2000) Distributed Computing with Adaptive Heuristics. Proceedings of the Innovations in Computer Science Conference (ICS 2011), Tsinghua University Press 417–443.Google Scholar
Janson, S., Luczak, T. and Ruczinski, A. (2000) Random Graphs, Wiley.CrossRefGoogle Scholar
Kittock, J. (1994) Emergent conventions and the structure of multi-agent systems. In: Nadel, L. and Stein, D. (eds.) 1993 Lecture Notes in Complex Systems: the proceedings of the 1993 Complex Systems Summer School Santa Fe Institute Studies in the Sciences of Complexity, Volume VI, Addison Wesley Publishing Co.Google Scholar
Krapivsky, P. L., Redner, S. and Ben-Naim, E. (2010) A kinetic view of statistical physics, Cambridge University Press.CrossRefGoogle Scholar
Lazer, D. (2009) Life in the network: the coming age of computational social science. Science 323 (5915)721.CrossRefGoogle Scholar
Machamer, P., Darden, L. and Craver, C. F. (2000) Thinking about mechanisms. Philosophy of Science 67 (1)1–25.CrossRefGoogle Scholar
Mirowski, P. (2002) Machine dreams: Economics becomes a cyborg science, Cambridge University Press.Google Scholar
Morris, S. (2000) Contagion. The Review of Economic Studies 67 (1)57–78.CrossRefGoogle Scholar
Mossel, E. and Roch, S. (2006) Slow emergence of cooperation for win–stay lose–shift on trees. Machine Learning 7 (1-2)7–22.Google Scholar
Mortveit, H. and Reidys, C. (2007) An Introduction to Sequential Dynamical Systems, Springer Verlag.Google Scholar
Newman, M., Barabási, A. L. and Watts, D. (eds.) The Structure and Dynamics of Networks, Princeton University Press.CrossRefGoogle Scholar
Nowak, M. and Sigmund, K. (1993) A strategy of win–stay, lose–shift that outperforms tit-for-tat in the prisoner's dilemma game. Nature 364 56–68.CrossRefGoogle ScholarPubMed
Pastor-Santorras, R. and Vespigniani, A. (2007) Evolution and Structure of the Internet: A Statistical Physics approach, Cambridge University Press.Google Scholar
Posch, M. (1997) Win stay–lose shift: An elementary learning rule for normal form games. Technical Report 97-06-056, the Santa Fe Institute.Google Scholar
Radloff, R., Kelley, H., Thibaut, J. and Mundy, D. (1962) The development of cooperation in the minimal social situation. Psychological Monographs 76.Google Scholar
Shoham, Y. and Tennenholtz, M. (1997) On the emergence of social conventions: modelling, analysis and simulations. Artificial Intelligence 94 (1-2)139–166.CrossRefGoogle Scholar
Sidowski, J. (1957) Reward and punishment in the minimal social situation. Journal of Experimental Psychology 54 318–326.CrossRefGoogle ScholarPubMed
Tesfatsion, L. and Judd, K. L. (eds.) (2006) Handbook of Computational Economics. Volume 2: Agent-based computational economics, North Holland.Google Scholar
Thibaut, J. and Kelley, H. (1959) The social Psychology of Groups, Wiley.Google Scholar
Velupillai, K. (2000) Computable economics: the Arne Ryde memorial lectures, Oxford University Press.CrossRefGoogle Scholar
Vriend, N. (2006) ACE models of endogenous interaction. In: Tesfatsion, L. and Judd, K. L. (eds.) Handbook of Computational Economics. Volume 2: Agent-based computational economics, North Holland.Google Scholar
Wilhite, A. (2006) Economic activity on fixed networks. In: Tesfatsion, L. and Judd, K. L. (eds.) Handbook of Computational Economics. Volume 2: Agent-based computational economics, North Holland.Google Scholar
Young, H. P. (1998) Individual Strategy and Social Structure: an Evolutionary Theory of Institutions, Princeton University Press.CrossRefGoogle Scholar