, Volume 156, Issue 1, pp 1–19 | Cite as

Social laws in alternating time: effectiveness, feasibility, and synthesis

  • Wiebe van der HoekEmail author
  • Mark Roberts
  • Michael Wooldridge
Original Paper


Since it was first proposed by Moses, Shoham, and Tennenholtz, the social laws paradigm has proved to be one of the most compelling approaches to the offline coordination of multiagent systems. In this paper, we make four key contributions to the theory and practice of social laws in multiagent systems. First, we show that the Alternating-time Temporal Logic (atl) of Alur, Henzinger, and Kupferman provides an elegant and powerful framework within which to express and understand social laws for multiagent systems. Second, we show that the effectiveness, feasibility, and synthesis problems for social laws may naturally be framed as atl model checking problems, and that as a consequence, existing atl model checkers may be applied to these problems. Third, we show that the complexity of the feasibility problem in our framework is no more complex in the general case than that of the corresponding problem in the Shoham–Tennenholtz framework (it is np-complete). Finally, we show how our basic framework can easily be extended to permit social laws in which constraints on the legality or otherwise of some action may be explicitly required. We illustrate the concepts and techniques developed by means of a running example.


Multi-Agent Systems Social Laws Coordination Alternating-time Temporal Logic Model checking 


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • Wiebe van der Hoek
    • 1
    Email author
  • Mark Roberts
    • 1
  • Michael Wooldridge
    • 1
  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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