TY - CHAP

T1 - Numerical solution of the game of two cars with a neurosimulator and grid computing

AU - Breitner, Michael H.

AU - von Mettenheim, Hans Jörg

N1 - Publisher Copyright: © Birkhäuser Boston, a part of Springer Science + Business Media, LLC 2009. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2009

Y1 - 2009

N2 - The famous game of two cars is a pursuit-evasion dynamic game. In the extended version presented here, a correct driver (evader) on a freeway detects a wrong-way driver (pursuer in a worst case scenario), i.e., a car driving on the wrong lanes of the road or in the wrong direction. The correct driver must try to avoid collision against all possible maneuvers of the wrong-way driver. Additionally, he must try to stay on the freeway lanes. Analytically, the game is not fully solvable. The state-space is cut by various singular manifolds, e.g., barriers, universal, and dispersal manifolds. Here, discretized Stackelberg games are solved numerically for many positions in the state-space. The resulting trajectories and their adherent information are used to synthesize optimal strategies with artificial neural networks. These networks learn the optimal turn rates and optimal velocity change rates. The networks are trained with the high-end neurosimulator FAUN (Fast Approximation with Universal Neural Networks). A grid computing implementation is used which allows significantly shorter computing times. This implementation runs on low-budget, idle PC clusters and moreover power saving allows to wake up and shut down computers automatically. Parallelization on cheap hardware is one of the key benefits of the presented approach as it leads to fast but nonetheless good results. The computed artificial neural networks approximate the Stackelberg strategies accurately. The approach presented here is applicable to many other complex dynamic games which are not (fully) solvable analytically.

AB - The famous game of two cars is a pursuit-evasion dynamic game. In the extended version presented here, a correct driver (evader) on a freeway detects a wrong-way driver (pursuer in a worst case scenario), i.e., a car driving on the wrong lanes of the road or in the wrong direction. The correct driver must try to avoid collision against all possible maneuvers of the wrong-way driver. Additionally, he must try to stay on the freeway lanes. Analytically, the game is not fully solvable. The state-space is cut by various singular manifolds, e.g., barriers, universal, and dispersal manifolds. Here, discretized Stackelberg games are solved numerically for many positions in the state-space. The resulting trajectories and their adherent information are used to synthesize optimal strategies with artificial neural networks. These networks learn the optimal turn rates and optimal velocity change rates. The networks are trained with the high-end neurosimulator FAUN (Fast Approximation with Universal Neural Networks). A grid computing implementation is used which allows significantly shorter computing times. This implementation runs on low-budget, idle PC clusters and moreover power saving allows to wake up and shut down computers automatically. Parallelization on cheap hardware is one of the key benefits of the presented approach as it leads to fast but nonetheless good results. The computed artificial neural networks approximate the Stackelberg strategies accurately. The approach presented here is applicable to many other complex dynamic games which are not (fully) solvable analytically.

KW - Artificial neural networks

KW - Dynamic game

KW - Game of two cars

KW - Grid computing

KW - Parallel computation

KW - Stackelberg game

KW - Synthesis of optimal strategies

UR - http://www.scopus.com/inward/record.url?scp=84865202657&partnerID=8YFLogxK

U2 - 10.1007/978-0-8176-4834-3_12

DO - 10.1007/978-0-8176-4834-3_12

M3 - Contribution to book/anthology

AN - SCOPUS:84865202657

T3 - Annals of the International Society of Dynamic Games

SP - 207

EP - 230

BT - Annals of the International Society of Dynamic Games

PB - Birkhauser Boston

ER -