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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
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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’.

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

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