Changing risks and optimal effort

•Agents either face a 1st risk (more favorable) or a 2nd one (less favorable).•An effort can be made to increase the probability of being exposed to the 1st risk.•Effort changes resulting from Nth-order improvements in both risks are analyzed.•Improvements in the 1st risk raise the effort made by mixed risk averse agents.•Mixed risk lovers’ effort rises (falls) when the 2nd risk improves if N is even (odd).

Consider a decision maker who can engage in effort to increase the probability of facing a better risky situation. Intuition suggests that effort should increase when there is a greater difference between the best risky situation and the worse one. We show that this intuition is not necessarily valid and we consider the cases of risk averters and risk lovers.