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2015 | 25 | 3 | 577-596
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
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
Rocznik
Tom
25
Numer
3
Strony
577-596
Opis fizyczny
Daty
wydano
2015
otrzymano
2013-12-20
poprawiono
2014-07-30
poprawiono
2014-12-06
Twórcy
  • Institute for Research in Applied Mathematics and Systems, National Autonomous University of Mexico, A.P. 20-126, C.P. 01000, Mexico D.F., Mexico
  • Institute for Research in Applied Mathematics and Systems, National Autonomous University of Mexico, A.P. 20-126, C.P. 01000, Mexico D.F., Mexico
Bibliografia
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Typ dokumentu
Bibliografia
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