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

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.