6 Conclusion
The energy markets are characterized by many agents simultaneously solving decision problems. A deterministic equilibrium model captures this complex structure by specifying the solution of the (deterministic) decision problems, along with relations taking interrelationships between actors and markets into account. How should this approach be extended to handle uncertainty? The standard approach to analyze uncertainty is Monte Carlo simulations, that is, to run a deterministic equilibrium model for different parameter values. As argued in the present article, this is not an adequate way to assess behavioral uncertainty; one should rather rely on some type of stochastic modelling. It is, however, not necessary to start the stochastic modelling from scratch. Rather, one could transform the existing deterministic model into a stochastic model by following our guide: For each decision variable determined under uncertainty, one should introduce one (probability adjusted) shadow price in the first-order condition, and a corresponding equation stating that the expected value of this shadow price is zero. All decision variables, as well as (probability adjusted) shadow prices, should be indexed by the scenario.
