Model Checking Coalition Nash Equilibria in MAD Distributed Systems

  • Federico Mari
  • Igor Melatti
  • Ivano Salvo
  • Enrico Tronci
  • Lorenzo Alvisi
  • Allen Clement
  • Harry Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5873)


We present two OBDD based model checking algorithms for the verification of Nash equilibria in finite state mechanisms modeling Multiple Administrative Domains (MAD) distributed systems with possibly colluding agents (coalitions) and with possibly faulty or malicious nodes (Byzantine agents). Given a finite state mechanism, a proposed protocol for each agent and the maximum sizes f for Byzantine agents and q for agents collusions, our model checkers return Pass if the proposed protocol is an ε-f-q-Nash equilibrium, i.e. no coalition of size up to q may have an interest greater than ε in deviating from the proposed protocol when up to f Byzantine agents are present, Fail otherwise. We implemented our model checking algorithms within the NuSMV model checker: the first one explicitly checks equilibria for each coalition, while the second represents symbolically all coalitions. We present experimental results showing their effectiveness for moderate size mechanisms. For example, we can verify coalition Nash equilibria for mechanisms which corresponding normal form games would have more than 5 ×1021 entries. Moreover, we compare the two approaches, and the explicit algorithm turns out to outperform the symbolic one. To the best of our knowledge, no model checking algorithm for verification of Nash equilibria of mechanisms with coalitions has been previously published.


Nash Equilibrium Model Check Malicious Node Reward Function Congestion Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Federico Mari
    • 1
  • Igor Melatti
    • 1
  • Ivano Salvo
    • 1
  • Enrico Tronci
    • 1
  • Lorenzo Alvisi
    • 2
  • Allen Clement
    • 2
  • Harry Li
    • 2
  1. 1.Dep. of Computer ScienceUniversity of Rome “La Sapienza”RomaItaly
  2. 2.Dep. of Computer ScienceUniversity of Texas at AustinAustinUSA

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