Skip to main content
    • Aa
    • Aa

Adversarial scheduling in discrete models of social dynamics

  • GABRIEL ISTRATE (a1), MADHAV V. MARATHE (a2) and S. S. RAVI (a3)

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’.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

C. Barrett , H. Hunt , M. V. Marathe , S. S. Ravi , D. Rosenkrantz and R. Stearns (2003) Reachability problems for sequential dynamical systems with threshold functions. Theoretical Computer Science 295 (1-3) 4164.

R. Boudon (1998) Social mechanisms without black boxes. In: P. Hedström and R. Swedberg (eds.) Social mechanisms: An analytical approach to social theory, Cambridge University Press.

M. Bunge (1997) Mechanism and explanation. Philosophy of the Social Sciences 27 (4) 410.

C. Castellano , S. Fortunato and V. Loreto (2009) Statistical physics of social dynamics. Reviews of modern physics 81 (2) 591646.

A. Coleman , A. Colman and R. M. Thomas (1991) Cooperation without awareness: A multiperson generalization of the minimal social situation. Behavioral Science 35 115121.

C. F. Craver (2006) When mechanistic models explain. Synthese 153 (3) 355376.

S. Dolev , A. Israeli and S. Moran (1995) Analyzing expected time by scheduler-luck games. I.E.E.E. Transactions on Software Engineering 21 (5) 429439.

J. Elster (1998) A plea for mechanisms. In: P. Hedström and R. Swedberg (eds.) Social Mechanisms: An Analytical Approach to Social Theory, Cambridge University Press.

J. Epstein (1999) Agent-based computational models and generative social science. Complexity 4 (5) 4160.

S. Eubank , H. Guclu , V. S. A. Kumar , M. V. Marathe , A. Srinivasan , Z. Toroczkai and N. Wang (2004) Monitoring and mitigating smallpox epidemics: Strategies drawn from a census data instantiated virtual city. Nature 429 (6988) 180184.

L. Fribourg , S. Messika and C. Picaronny (2006) Coupling and self-stabilization. Distributed Computing 18 (3) 221232.

S. S. Glennan (1996) Mechanisms and the nature of causation. Erkenntnis 44 (1) 4971.

S. Janson , T. Luczak and A. Ruczinski (2000) Random Graphs, Wiley.

D. Lazer (2009) Life in the network: the coming age of computational social science. Science 323 (5915) 721.

P. Machamer , L. Darden and C. F. Craver (2000) Thinking about mechanisms. Philosophy of Science 67 (1) 125.

S. Morris (2000) Contagion. The Review of Economic Studies 67 (1) 5778.

M. Nowak and K. Sigmund (1993) A strategy of win–stay, lose–shift that outperforms tit-for-tat in the prisoner's dilemma game. Nature 364 5668.

Y. Shoham and M. Tennenholtz (1997) On the emergence of social conventions: modelling, analysis and simulations. Artificial Intelligence 94 (1-2) 139166.

J. Sidowski (1957) Reward and punishment in the minimal social situation. Journal of Experimental Psychology 54 318326.

L. Tesfatsion and K. L. Judd (eds.) (2006) Handbook of Computational Economics. Volume 2: Agent-based computational economics, North Holland.

K. Velupillai (2000) Computable economics: the Arne Ryde memorial lectures, Oxford University Press.

N. Vriend (2006) ACE models of endogenous interaction. In: L. Tesfatsion and K. L. Judd (eds.) Handbook of Computational Economics. Volume 2: Agent-based computational economics, North Holland.

A. Wilhite (2006) Economic activity on fixed networks. In: L. Tesfatsion and K. L. Judd (eds.) Handbook of Computational Economics. Volume 2: Agent-based computational economics, North Holland.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 62 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st July 2017. This data will be updated every 24 hours.