This paper studies a Nash game arising in portfolio optimization. We introduce a new general multi-portfolio model and state sufficient conditions for the monotonicity of the underlying Nash game. This property allows us to treat the problem numerically and, for the case of nonunique equilibria, to solve hierarchical problems of equilibrium selection. We also give sufficient conditions for the Nash game formulation to be a potential game. Our computational experience shows that the multi-portfolio model is solvable for relevant problem sizes and substantiates the significance of the equilibrium selection.
European Journal of Operational Research (2021), DOI: 10.1016/j.ejor.2021.02.033