- Tytuł:
- A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria
- Autorzy:
-
Góngora, P. A
Rosenblueth, D. A. - Powiązania:
- https://bibliotekanauki.pl/articles/329934.pdf
- Data publikacji:
- 2015
- Wydawca:
- Uniwersytet Zielonogórski. Oficyna Wydawnicza
- Tematy:
-
shortest path
Bellman–Ford algorithm
Nash equilibrium
BDD
model checking
najkrótsza ścieżka
równowaga Nasha
sprawdzanie modelu - Opis:
- 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.
- Źródło:
-
International Journal of Applied Mathematics and Computer Science; 2015, 25, 3; 577-596
1641-876X
2083-8492 - Pojawia się w:
- International Journal of Applied Mathematics and Computer Science
- Dostawca treści:
- Biblioteka Nauki
Artykuł