  We consider the general problem of a set of agents trading a portfolio of
assets in the presence of transient price impact and additional quadratic
transaction costs and we study, with analytical and numerical methods, the
resulting Nash equilibria. Extending significantly the framework of Schied &
Zhang (2019) and Luo & Schied (2020), who considered the single asset case, we
prove the existence and uniqueness of the corresponding Nash equilibria for the
related mean-variance optimization problem. We then focus our attention on the
conditions on the model parameters making the trading profile of the agents at
equilibrium, and as a consequence the price trajectory, wildly oscillating and
the market unstable. While Schied & Zhang (2019) and Luo & Schied (2020)
highlighted the importance of the value of transaction cost in determining the
transition between a stable and an unstable phase, we show that also the
scaling of market impact with the number of agents J and the number of assets M
determines the asymptotic stability (in J and M ) of markets.
