A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria

Bahar, R., Frohm, E., Gaona, C., Hachtel, G., Macii, E., Pardo, A. and Somenzi, F. (1997). Algebraic decision diagrams and their applications, Formal Methods in System Design 10(2-3): 171-206.10.1023/A:1008699807402Search in Google Scholar

Baier, C. and Katoen, J.-P. (2008). Principles of Model Checking, MIT Press, New York, NY.Search in Google Scholar

Berghammer, R. and Bolus, S. (2012). On the use of binary decision diagrams for solving problems on simple games, European Journal of Operational Research 222(3): 529-541.10.1016/j.ejor.2012.04.015Search in Google Scholar

Bolus, S. (2011). Power indices of simple games and vector-weighted majority games by means of binary decision diagrams, European Journal of Operational Research 210(2): 258-272.10.1016/j.ejor.2010.09.020Search in Google Scholar

Bonanno, G. (2001). Branching time, perfect information games, and backward induction, Games and Economic Behavior 36(1): 57-73.10.1006/game.1999.0812Search in Google Scholar

Bryant, R.E. (1986). Graph-based algorithms for Boolean function manipulation, IEEE Transactions on Computers 35(8): 677-691.10.1109/TC.1986.1676819Search in Google Scholar

Burch, J., Clarke, E., McMillan, K., Dill, D. and Hwang, L. (1992). Symbolic model checking: 1020 states and beyond, Information and Computation 98(2): 142 - 170.10.1016/0890-5401(92)90017-ASearch in Google Scholar

Clarke, E. and Emerson, E. (1982). Design and synthesis of synchronization skeletons using branching time temporal logic, in D. Kozen (Ed.), Workshop on Logics of Programs, Lecture Notes in Computer Science, Vol. 131, Springer, Berlin/Heidelberg, pp. 52-71.10.1007/BFb0025774Search in Google Scholar

Clarke, E.M., Emerson, E.A. and Sistla, A.P. (1986). Automatic verification of finite-state concurrent systems using temporal logic specifications, ACM Transactions on Programming Languages and Systems 8(2): 244-263.10.1145/5397.5399Search in Google Scholar

Clarke, E.M., Grumberg, O. and Peled, D.A. (1999). Model Checking, MIT Press, London.Search in Google Scholar

Clarke, E., McMillan, K., Zhao, X., Fujita, M. and Yang, J. (1993). Spectral transforms for large Boolean functions with applications to technology mapping, 30th Conference on Design Automation, Dallas, TX, USA, pp. 54-60.Search in Google Scholar

Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C. (2009). Introduction to Algorithms, 3rd Edn., MIT Press, Cambridge, MA.Search in Google Scholar

Dasgupta, P., Chakrabarti, P.P., Deka, J.K. and Sankaranarayanan, S. (2001). Min-max computation tree logic, Artificial Intelligence 127(1): 137-162.10.1016/S0004-3702(01)00059-5Search in Google Scholar

Dsouza, A. and Bloom, B. (1995). Generating BDD models for process algebra terms, Proceedings of the 7th International Conference on Computer Aided Verification, Li`ege, Belgium, pp. 16-30.Search in Google Scholar

Enders, R., Filkorn, T. and Taubner, D. (1992). Generating BDDs for symbolic model checking in CCS, Proceedings of the 3rd International Workshop on Computer Aided Verification, CAV’91, London, UK, pp. 203-213.Search in Google Scholar

Fujita, M., McGeer, P.C. and Yang, J.C.-Y. (1997). Multi-terminal binary decision diagrams: An efficient data structure for matrix representation, Formal Methods in System Design 10(2-3): 149-169.10.1023/A:1008647823331Search in Google Scholar

Garroppo, R.G., Giordano, S. and Tavanti, L. (2010). A survey on multi-constrained optimal path computation: Exact and approximate algorithms, Computer Networks 54(17): 3081-3107.10.1016/j.comnet.2010.05.017Search in Google Scholar

Harrenstein, P., van der Hoek, W., Meyer, J.-J.C. and Witteveen, C. (2003). A modal characterization of Nash equilibrium, Fundamenta Informaticae 57(2-4): 281-321.Search in Google Scholar

Hermanns, H., Meyer-Kayser, J. and Siegle, M. (1999). Multi terminal binary decision diagrams to represent and analyse continuous time Markov chains, in B. Plateau, W.J.Search in Google Scholar

Stewart and M. Silva (Eds.), 3rd International Workshop on the Numerical Solution of Markov Chains, Zaragoza, Spain, Prensas Universitarias de Zaragoza, Zaragoza, pp. 188-207.Search in Google Scholar

Kelley, Jr, J.E. and Walker, M.R. (1959). Critical-path planning and scheduling, Eastern Joint IRE-AIEE-ACM Computer Conference, Boston, MA, USA, pp. 160-173.Search in Google Scholar

Lozovanu, D. and Pickl, S. (2009). Optimization and Multiobjective Control of Time-Discrete Systems, Springer, Berlin/Heidelberg.10.1007/978-3-540-85025-0_1Search in Google Scholar

McKelvey, R.D. and McLennan, A. (1996). Computation of equilibria in finite games, in H.M. Amman, D.A.Search in Google Scholar

Kendrick and J. Rust (Eds.), Handbook of Computational Economics, Vol. 1, Elsevier, North Holland, Chapter 2, pp. 87-142.Search in Google Scholar

McKelvey, R.D., McLennan, A.M. and Turocy, T.L. (2014). Gambit: Software tools for game theory, version 13.1.2, http://www.gambit-project.org .Search in Google Scholar

Meinel, C. and Theobald, T. (1998). Algorithms and Data Structures in VSLI Design: OBDD-Foundations and Applications, Springer-Verlag, Berlin.10.1007/978-3-642-58940-9Search in Google Scholar

MSDN (2013). Memory limits for windows releases, Microsoft Developer Network, http://msdn.microsoft.com/en-us/library/windows/desktop/aa366778(v=vs.85).aspx .Search in Google Scholar

Osborne, M.J. and Rubinstein, A. (1994). A Course in Game Theory, The MIT Press, Cambridge, MA.Search in Google Scholar

Raimondi, F. and Lomuscio, A. (2007). Automatic verification of multi-agent systems by model checking via ordered binary decision diagrams, Journal of Applied Logic 5(2): 235-251.10.1016/j.jal.2005.12.010Search in Google Scholar

Russell, S. and Norvig, P. (2003). Artificial Intelligence. A Modern Approach, Prentince Hall, Englewood Cliffs, NJ.Search in Google Scholar

Sawitzki, D. (2004). Experimental studies of symbolic shortest-path algorithms, in C.C. Ribeiro and S.L. Martins (Eds.), Experimental and Efficient Algorithms, Lecture Notes in Computer Science, Vol. 3059, Springer, Berlin/Heidelberg, pp. 482-497.10.1007/978-3-540-24838-5_36Search in Google Scholar

Tarapata, Z. (2007). Selected multicriteria shortest path problems: An analysis of complexity, models and adaptation of standard algorithms, International Journal of Applied Mathematics and Computer Science 17(2): 269-287, DOI: 10.2478/v10006-007-0023-2. 10.2478/v10006-007-0023-2Search in Google Scholar