Creator:
Góngora, Pedro A. ; Rosenblueth, David A.
Contributor:
Byrski, Aleksander - ed. ; Kisiel-Dorohinicki, Marek - ed. ; Dobrowolski, Grzegorz - ed.
Title:
A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria
Subtitle:
Group publication title:
Subject and Keywords:
shortest path ; Bellman-Ford ; Nash equilibrium ; BDD ; model checking
Abstract:
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.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Resource Type:
DOI:
Pages:
Source:
AMCS, volume 25, number 3 (2015) ; click here to follow the link