Automatica (Journal of IFAC)
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Solution concepts in hypergames
Applied Mathematics and Computation
Group-theoretic Algorithms for Matrix Multiplication
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A decision support system for interactive decision making-Part I: model formulation
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Preference uncertainty in the graph model for conflict resolution
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Policy Equilibrium and Generalized Metarationalities for Multiple Decision-Maker Conflicts
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
An algebraic approach to calculating stabilities in the graph model with strength of preference
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Matrix representation and extension of coalition analysis in group decision support
Computers & Mathematics with Applications
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A matrix method is developed to apply four solution concepts to a graph model for conflict resolution in order to model human behavior in a multiple-decision-maker (DM) strategic conflict. A graph model represents the interaction of two or more DMs and can be analyzed to identify possible equilibrium states according to each solution concept. Previously, solution concepts were defined logically, in terms of the underlying graphs. However, procedures to identify stable states based on these definitions are difficult to code because of the nature of the logical representations. In this paper, a graph model and four graph model solution concepts are formulated explicitly using matrices. More specifically, matrix expressions are given for relative preferences, joint unilateral movements, and joint unilateral improvements in a multiple-DM model. Then, it is shown how to calculate stability under each of the four solution concepts using the matrix representation. Compared with the existing approach, matrix representation is more effective and convenient for calculating stabilities and predicting equilibria of a graph model. In particular, the proposed method is easy to code and extend to other contexts.