CDMTCS Research Report Series

On Game-Theoretic Models of Networks

Hans L. Bodlaender Institute of Information and Computing Sciences, Utrecht University, Utrecht, the Netherlands

Michael J. Dinneen Bakhadyr Khoussainov Department of Computer Science, University of Auckland, Auckland, New Zealand

CDMTCS-151 April 2001

Centre for Discrete Mathematics and Theoretical Computer Science

On Game-Theoretic Models of Networks

Hans L. Bodlaender Institute of Information and Computing Sciences Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, the Netherlands

                       hansb@cs.uu.nl

Michael J. Dinneen and Bakhadyr Khoussainov Department of Computer Science The University of Auckland, Private Bag 92019 Auckland, New Zealand

                 {mjd,bmk}@cs.auckland.ac.nz

Abstract In this paper, we study the complexity of deciding which player has a winning strategy in certain types of McNaughton games. These graph games can be used as models for computational problems and processes of infinite duration. We consider the cases (1) where the first player wins when vertices in a specified set are visited infinitely often and vertices in another specified set are visited finitely often, (2) where the first player wins when exactly those vertices in one of a number of specified disjoint sets are visited infinitely often, and (3) a generalization of these first two cases. We give polynomial time algorithms to determine which player has a winning strategy in each of the games considered.

Keywords: graph and network algorithms, complexity, infinite graph games, McNaughton games.

In this paper, we study the complexity of deciding which player has a winning strategy in certain types of McNaughton games. These graph games can be used as models for computational problems and processes of infinite duration. We consider the cases (1) where the first player wins when vertices in a specified set are visited infinitely often and vertices in another specified set are visited finitely often, (2) where the first player wins when exactly those vertices in one of a number of specified disjoint sets are visited infinitely often, and (3) a generalization of these first two cases. We give polynomial time algorithms to determine which player has a winning strategy in each of the games considered.

In this paper, we study the complexity of deciding which player has a winning strategy in certain types of McNaughton games. These graph games can be used as models for computational problems and processes of infinite duration. We consider the cases (1) where the first player wins when vertices in a specified set are visited infinitely often and vertices in another specified set are visited finitely often, (2) where the first player wins when exactly those vertices in one of a number of specified disjoint sets are visited infinitely often, and (3) a generalization of these first two cases. We give polynomial time algorithms to determine which player has a winning strategy in each of the games considered.

In this paper, we study the complexity of deciding which player has a winning strategy in certain types of McNaughton games. These graph games can be used as models for computational problems and processes of infinite duration. We consider the cases (1) where the first player wins when vertices in a specified set are visited infinitely often and vertices in another specified set are visited finitely often, (2) where the first player wins when exactly those vertices in one of a number of specified disjoint sets are visited infinitely often, and (3) a generalization of these first two cases. We give polynomial time algorithms to determine which player has a winning strategy in each of the games considered.

In this paper, we study the complexity of deciding which player has a winning strategy in certain types of McNaughton games. These graph games can be used as models for computational problems and processes of infinite duration. We consider the cases (1) where the first player wins when vertices in a specified set are visited infinitely often and vertices in another specified set are visited finitely often, (2) where the first player wins when exactly those vertices in one of a number of specified disjoint sets are visited infinitely often, and (3) a generalization of these first two cases. We give polynomial time algorithms to determine which player has a winning strategy in each of the games considered.

In this paper, we study the complexity of deciding which player has a winning strategy in certain types of McNaughton games. These graph games can be used as models for computational problems and processes of infinite duration. We consider the cases (1) where the first player wins when vertices in a specified set are visited infinitely often and vertices in another specified set are visited finitely often, (2) where the first player wins when exactly those vertices in one of a number of specified disjoint sets are visited infinitely often, and (3) a generalization of these first two cases. We give polynomial time algorithms to determine which player has a winning strategy in each of the games considered.

In this paper, we study the complexity of deciding which player has a winning strategy in certain types of McNaughton games. These graph games can be used as models for computational problems and processes of infinite duration. We consider the cases (1) where the first player wins when vertices in a specified set are visited infinitely often and vertices in another specified set are visited finitely often, (2) where the first player wins when exactly those vertices in one of a number of specified disjoint sets are visited infinitely often, and (3) a generalization of these first two cases. We give polynomial time algorithms to determine which player has a winning strategy in each of the games considered.

In this paper, we study the complexity of deciding which player has a winning strategy in certain types of McNaughton games. These graph games can be used as models for computational problems and processes of infinite duration. We consider the cases (1) where the first player wins when vertices in a specified set are visited infinitely often and vertices in another specified set are visited finitely often, (2) where the first player wins when exactly those vertices in one of a number of specified disjoint sets are visited infinitely often, and (3) a generalization of these first two cases. We give polynomial time algorithms to determine which player has a winning strategy in each of the games considered.

In this paper, we study the complexity of deciding which player has a winning strategy in certain types of McNaughton games. These graph games can be used as models for computational problems and processes of infinite duration. We consider the cases (1) where the first player wins when vertices in a specified set are visited infinitely often and vertices in another specified set are visited finitely often, (2) where the first player wins when exactly those vertices in one of a number of specified disjoint sets are visited infinitely often, and (3) a generalization of these first two cases. We give polynomial time algorithms to determine which player has a winning strategy in each of the games considered.