  We consider a market impact game for $n$ risk-averse agents that are
competing in a market model with linear transient price impact and additional
transaction costs. For both finite and infinite time horizons, the agents aim
to minimize a mean-variance functional of their costs or to maximize the
expected exponential utility of their revenues. We give explicit
representations for corresponding Nash equilibria and prove uniqueness in the
case of mean-variance optimization. A qualitative analysis of these Nash
equilibria is conducted by means of numerical analysis.
