Equilibrium selection for multi-portfolio optimization

We analyze a Nash equilibrium problem arising when trades from different accounts are pooled for execution. We introduce a new general multi-portfolio model and state sufficient conditions for the monotonicity of the underlying Nash equilibrium problem. Monotonicity makes it possible 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 equilibrium problem formulation to be a potential game. Our computational experience confirms the theoretical insights and substantiates the significance of the equilibrium selection.