Uniqueness of DP-Nash Subgraphs and D-sets in Weighted Graphs of Netflix Games

Abstract

Gerke et al. (2019) introduced Netflix Games and proved that every such game has a pure strategy Nash equilibrium. In this paper, we explore the uniqueness of pure strategy Nash equilibria in Netflix Games. Let be a graph and a function, and call the pair a weighted graph. A spanning subgraph H of is called a DP-Nash subgraph if H is bipartite with partite sets D, P called the D-set and P-set of H, respectively, such that no vertex of P is isolated and for every We prove that whether has a unique DP-Nash subgraph can be decided in polynomial time. We also show that when for every, the problem of deciding whether has a unique D-set is polynomial time solvable for and 1, and co-NP-complete for.