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

Author:

Góngora Pedro A.1,Rosenblueth David A.1

Affiliation:

1. Institute for Research in Applied Mathematics and Systems National Autonomous University of Mexico, A.P. 20-126, C.P. 01000, Mexico D.F.

Abstract

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

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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1. A robust algorithm to solve the signal setting problem considering different traffic assignment approaches;International Journal of Applied Mathematics and Computer Science;2017-12-20

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