@misc{Góngora_Pedro_A._A,
 author={Góngora, Pedro A. and Rosenblueth, David A.},
 howpublished={online},
 publisher={Zielona Góra: Uniwersytet Zielonogórski},
 language={eng},
 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.},
 abstract={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).},
 abstract={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.},
 type={artykuł},
 title={A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria},
 keywords={shortest path, Bellman-Ford, Nash equilibrium, BDD, model checking},
}