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

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.

A robust algorithm to solve the signal setting problem considering different traffic assignment approaches

“…The performance of a traffic network can be influenced through several types of actions or decision variables. Some of these pertain to changing the load pattern on the network, through demand management actions, including attempts to route vehicles optimally through the network (Góngora and Rosenblueth, 2015;Klaučo et al, 2016); others are concerned with how the traffic flow is controlled through the network components, such as junction utilization through signal control. Although the potential of explicitly combining both types of actions, especially joint signal control and route assignment, long has been suggested, most of the research and virtually all the approaches used in practice have followed one of two schemes: (a) considering signal control to be fixed and using traffic assignment * Corresponding author as decision variables (traffic assignment models), and (b) considering traffic assignment (loading pattern) to be fixed and using signal control as decision variables (signal optimization models).…”

Multipath Routing Algorithm for Video Stream Transmission Based on Clustering Theory

“…Multipath routing ReInForM method ensures the reliability of data transmission through its more copies by sending multiple copies of the data packet. Multiple QoS guaranteed ASAR routing algorithm applies the weighted average network QoS parameters and sets up the corresponding weighting factor, makes use of the clustering theory to carry out the selection of the routing, however, it still adopts single path routing for each kind of multimedia services, and has no special safeguard for the video transmission (Góngora and Rosenblueth, 2015). ASAR algorithm simulation only makes use of 20 nodes； For the network with larger scale, the analysis on the feasibility has not been provided (Vesović, Smiljanić and Kostić, 2016).…”