- Tytuł:
- Modeling shortest path games with Petri nets: A Lyapunov based theory
- Autorzy:
- Clempner, J.
- Powiązania:
- https://bibliotekanauki.pl/articles/908393.pdf
- Data publikacji:
- 2006
- Wydawca:
- Uniwersytet Zielonogórski. Oficyna Wydawnicza
- Tematy:
-
Nash equilibrium point
shortest path game
game theory
Lyapunov equilibrium point
Bellman’s equation
Lyapunov-like fuction
stability
teoria gier
funkcja Lapunowa
równanie Bellmana
stabilność - Opis:
- In this paper we introduce a new modeling paradigm for shortest path games representation with Petri nets. Whereas previous works have restricted attention to tracking the net using Bellman’s equation as a utility function, this work uses a Lyapunov-like function. In this sense, we change the traditional cost function by a trajectory-tracking function which is also an optimal cost-to-target function. This makes a significant difference in the conceptualization of the problem domain, allowing the replacement of the Nash equilibrium point by the Lyapunov equilibrium point in game theory. We show that the Lyapunov equilibrium point coincides with the Nash equilibrium point. As a consequence, all properties of equilibrium and stability are preserved in game theory. This is the most important contribution of this work. The potential of this approach remains in its formal proof simplicity for the existence of an equilibrium point.
- Źródło:
-
International Journal of Applied Mathematics and Computer Science; 2006, 16, 3; 387-397
1641-876X
2083-8492 - Pojawia się w:
- International Journal of Applied Mathematics and Computer Science
- Dostawca treści:
- Biblioteka Nauki
Artykuł