Abstract
Reactive Modules is a high-level specification language for concurrent and multi-agent systems, used in a number of practical model checking tools. Reactive Modules Games is a game-theoretic extension of Reactive Modules, in which concurrent agents in the system are assumed to act strategically in an attempt to satisfy a temporal logic formula representing their individual goal. The basic analytical concept for Reactive Modules Games is Nash equilibrium. In this paper, we describe a tool through which we can automatically verify Nash equilibrium strategies for Reactive Modules Games. Our tool takes as input a system, specified in the Reactive Modules language, a representation of players’ goals (expressed as CTL formulae), and a representation of players strategies; it then checks whether these strategies form a Nash equilibrium of the Reactive Modules Game passed as input. The tool makes extensive use of conventional temporal logic satisfiability and model checking techniques. We first give an overview of the theory underpinning the tool, briefly describe its structure and implementation, and conclude by presenting a worked example analysed using the tool.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Goals can be given by any logic with a Kripke structure semantics. Although we will consider CTL goals here, due to generality, at this point all definitions will be made leaving this open. Indeed, one could extend our implementation to SRML games with CTL\(^*\) or \(\mu \)-calculus goals.
- 2.
\({\textsc {EAGLE}}\) is being improved and updated frequently. The implementation details in this paper constitute the main design decisions at the moment of submission to ICTAC (in June 2015).
References
Alur, R., Henzinger, T.A., Mang, F., Qadeer, S., Rajamani, S., Tasiran, S.: MOCHA: modularity in model checking. In: Hu, A.J., Vardi, M.Y. (eds.) CAV 1998. LNCS, vol. 1427, pp. 521–525. Springer, Heidelberg (1998)
Alur, R., Henzinger, T.A.: Reactive modules. Form. Meth. Syst. Des. 15(1), 7–48 (1999)
Berwanger, D., Chatterjee, K., De Wulf, M., Doyen, L., Henzinger, T.A.: Alpaga: a tool for solving parity games with imperfect information. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 58–61. Springer, Heidelberg (2009)
Brenguier, R.: PRALINE: a tool for computing nash equilibria in concurrent games. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 890–895. Springer, Heidelberg (2013)
Cermák, P., Lomuscio, A., Mogavero, F., Murano, A.: MCMAS-SLK: a model checker for the verification of strategy logic specifications. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 525–532. Springer, Heidelberg (2014)
David, A., Jensen, P.G., Larsen, K.G., Mikucionis, M., Taankvist, J.H.: Uppaal Stratego. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 206–211. Springer, Heidelberg (2015)
Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science Volume B: Formal Models and Semantics, pp. 996–1072. Elsevier, Amsterdam (1990)
Fisman, D., Kupferman, O., Lustig, Y.: Rational synthesis. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 190–204. Springer, Heidelberg (2010)
Friedmann, O., Lange, M.: Solving parity games in practice. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 182–196. Springer, Heidelberg (2009)
Gutierrez, J., Harrenstein, P., Wooldridge, M.: Iterated boolean games. In: IJCAI, IJCAI/AAAI (2013)
Gutierrez, J., Harrenstein, P., Wooldridge, M.: Verification of temporal equilibrium properties of games on Reactive Modules. Technical report, University of Oxford (2015)
Kupferman, O., Vardi, M., Wolper, P.: Module checking. Inf. Comput. 164(2), 322–344 (2001)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)
Lomuscio, A., Qu, H., Raimondi, F.: MCMAS: a model checker for the verification of multi-agent systems. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 682–688. Springer, Heidelberg (2009)
Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (1994)
Prezza, N.: CTLSAT (2015). https://github.com/nicolaprezza/CTLSAT
Reynaud, D., Mr. Waffles: (2015). http://mrwaffles.gforge.inria.fr
Toumi, A.: Equilibrium checking in Reactive Modules games. Technical report, Department of Computer Science, University of Oxford (2015)
van der Hoek, W., Lomuscio, A., Wooldridge, M.: On the complexity of practical ATL model checking. In: AAMAS, pp. 201–208. ACM (2006)
Acknowledgment
\({\textsc {EAGLE}}\) was implemented by Toumi as part of his final Computer Science project [18] at Oxford. Both \({\textsc {EAGLE}}\) and [18] can be obtained from him. (To obtain \({\textsc {EAGLE}}\) or [18], please, send an email to Alexis.Toumi at gmail.com). We also acknowledge the support of the ERC Research Grant 291528 (“RACE”) at Oxford.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Toumi, A., Gutierrez, J., Wooldridge, M. (2015). A Tool for the Automated Verification of Nash Equilibria in Concurrent Games. In: Leucker, M., Rueda, C., Valencia, F. (eds) Theoretical Aspects of Computing - ICTAC 2015. ICTAC 2015. Lecture Notes in Computer Science(), vol 9399. Springer, Cham. https://doi.org/10.1007/978-3-319-25150-9_34
Download citation
DOI: https://doi.org/10.1007/978-3-319-25150-9_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25149-3
Online ISBN: 978-3-319-25150-9
eBook Packages: Computer ScienceComputer Science (R0)