Mean‐Variance Payoff Applied to Stackelberg Games

We analyse a Stackelberg duopoly in which the leader faces uncertainty about the intercept demand, while the follower observes the realised demand and decides whether to enter the market after the uncertainty is resolved. The leader evaluates the uncertainty by maximising a mean‐variance utility function that captures its risk aversion. We show that the leader's best‐response problem admits a unique equilibrium. Our main result establishes the existence of a no‐entry threshold for risk aversion: when the leader's risk aversion exceeds this threshold, entry is not optimal. This threshold is shown to be equal to the ratio of the expected value of the intercept demand to its standard deviation. Conditional on entry and on the realisation of the lowest demand outcome, three scenarios may arise for the leader: competition; monopoly without dumping, yielding zero profit; and monopoly with dumping, generating negative profit. We fully characterise the ex‐ante expected profits of both firms, and also the corresponding ex‐ante isoprofit curve in the model's parameter space.