Zero-sum polymatrix games with link uncertainty: A Dempster-Shafer theory solution

Xinyang Deng, Wen Jiang and Zhen Wang

Applied Mathematics and Computation, 2019, vol. 340, issue C, 101-112

Abstract: Polymatrix games belong to a class of multi-player games, in which players interact pairwisely 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.

Keywords: Polymatrix game; Link uncertainty; Zero-sum game; Dempster-Shafer theory; Belief function (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630031830746X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:340:y:2019:i:c:p:101-112

DOI: 10.1016/j.amc.2018.08.032

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().