  Entropic risk (ERisk) is an established risk measure in finance, quantifying
risk by an exponential re-weighting of rewards. We study ERisk for the first
time in the context of turn-based stochastic games with the total reward
objective. This gives rise to an objective function that demands the control of
systems in a risk-averse manner. We show that the resulting games are
determined and, in particular, admit optimal memoryless deterministic
strategies. This contrasts risk measures that previously have been considered
in the special case of Markov decision processes and that require randomization
and/or memory. We provide several results on the decidability and the
computational complexity of the threshold problem, i.e. whether the optimal
value of ERisk exceeds a given threshold. In the most general case, the problem
is decidable subject to Shanuel's conjecture. If all inputs are rational, the
resulting threshold problem can be solved using algebraic numbers, leading to
decidability via a polynomial-time reduction to the existential theory of the
reals. Further restrictions on the encoding of the input allow the solution of
the threshold problem in NP$\cap$coNP. Finally, an approximation algorithm for
the optimal value of ERisk is provided.
