Abstract
Concurrent game structures model multi-player games played on finite graphs where the players simultaneously choose their moves and collectively determine the next state of the game. We extend this model with prices on transitions for each player. We study pure Nash equilibria in this framework where each player’s payoff is the accumulated price of all transitions until reaching their goal state. We provide a construction of a Büchi automaton accepting all Nash equilibria outcomes and show how this construction can be used to solve a variety of related problems, such as finding pareto-optimal equilibria. Furthermore, we prove the problem of deciding the existence of equilibria to be NP-complete.
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
Preview
Unable to display preview. Download preview PDF.
References
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49, 672–713 (2002)
Bouyer, P., Brenguier, R., Markey, N.: Nash Equilibria for Reachability Objectives in Multi-player Timed Games. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 192–206. Springer, Heidelberg (2010)
Brihaye, T., Bruyère, V., De Pril, J.: Equilibria in Quantitative Reachability Games. In: Ablayev, F., Mayr, E.W. (eds.) CSR 2010. LNCS, vol. 6072, pp. 72–83. Springer, Heidelberg (2010)
Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to algorithms, vol. 7, pp. 1162–1171. MIT Press and McGraw-Hill Book Company (1976)
Felegyhazi, M., Hubaux, J., Buttyan, L.: Nash equilibria of packet forwarding strategies in wireless ad hoc networks. IEEE Transactions on Mobile Computing, 463–476 (2006)
Nash, J.: Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America 36(1), 48–49 (1950)
Ummels, M., Wojtczak, D.: The Complexity of Nash Equilibria in Limit-Average Games. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 482–496. Springer, Heidelberg (2011)
Valk, R., Jantzen, M.: The residue of vector sets with applications to decidability problems in Petri nets. In: Application and Theory of Petri Nets, pp. 234–258 (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Klimoš, M., Larsen, K.G., Štefaňák, F., Thaarup, J. (2012). Nash Equilibria in Concurrent Priced Games. In: Dediu, AH., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2012. Lecture Notes in Computer Science, vol 7183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28332-1_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-28332-1_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28331-4
Online ISBN: 978-3-642-28332-1
eBook Packages: Computer ScienceComputer Science (R0)