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

• Autorzy: Góngora P. A , Rosenblueth D. A.

Identyfikatory

DOI

10.1515/amcs-2015-0043

• Języki publikacji: EN

Abstrakty

EN

Consider games where players wish to minimize the cost to reach some state. A subgame-perfect Nash equilibrium can be regarded as a collection of optimal paths on such games. Similarly, the well-known state-labeling algorithm used in model checking can be viewed as computing optimal paths on a Kripke structure, where each path has a minimum number of transitions. We exploit these similarities in a common generalization of extensive games and Kripke structures that we name “graph games”. By extending the Bellman–Ford algorithm for computing shortest paths, we obtain a model-checking algorithm for graph games with respect to formulas in an appropriate logic. Hence, when given a certain formula, our model-checking algorithm computes the subgame-perfect Nash equilibrium (as opposed to simply determining whether or not a given collection of paths is a Nash equilibrium). Next, we develop a symbolic version of our model checker allowing us to handle larger graph games. We illustrate our formalism on the critical-path method as well as games with perfect information. Finally, we report on the execution time of benchmarks of an implementation of our algorithms.

Słowa kluczowe

EN

shortest path; Bellman–Ford algorithm; Nash equilibrium; BDD; model checking

PL

najkrótsza ścieżka; równowaga Nasha; sprawdzanie modelu

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2015
• Tom: Vol. 25, no. 3
• Strony: 577--596
• Opis fizyczny: Bibliogr. 30 poz., rys., tab., wykr.

Twórcy

autor

Góngora P. A

• Institute for Research in Applied Mathematics and Systems, National Autonomous University of Mexico, A.P. 20-126, C.P. 01000, Mexico D.F., Mexico

autor

Rosenblueth D. A.

• Institute for Research in Applied Mathematics and Systems, National Autonomous University of Mexico, A.P. 20-126, C.P. 01000, Mexico D.F., Mexico

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