Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 340, Issue -, Pages 101-112Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2018.08.032
Keywords
Polymatrix game; Link uncertainty; Zero-sum game; Dempster-Shafer theory; Belief function
Categories
Funding
- National Natural Science Foundation of China [61703338, 61671384]
- Natural Science Basic Research Plan in Shaanxi Province of China [2018JQ6085]
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Polymatrix games belong to a class of multi-player games, in which players interact pair-wisely and the underlying pairwise interactions are defined by a simple undirected graph where all the edges are completely deterministic. But the link uncertainty between players is not taken into consideration in a standard polymatrix game. In this paper, we put our attention to a special class of polymatrix games - zero-sum polymatrix games, and aim to investigate zero-sum polymatrix games with uncertain links. By considering the diversity of uncertainty, we utilize Dempster-Shafer evidence theory to express the link uncertainty in the games. Then, based on a generalized minmax theorem, we develop a new linear programming model with two groups of constraints to calculate the equilibrium payoffs of players and find the equilibria of the zero-sum plymatrix games with belief links. In terms of these, we also establish a Dempster-Shafer theory solution to zero-sum polymatrix games with link uncertainty. Finally, a numerical example is given to illustrate the potential applications of the proposed model. (C) 2018 Elsevier Inc. All rights reserved.
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