[Assess students' ability to apply game-theoretic models (Cournot, Bertrand, Stackelberg, and mixed strategies) to determine optimal pricing and capacity decisions in duopoly markets with stochastic demand. Tasks include deriving Nash equilibria under demand uncertainty, solving for expected-profit-maximizing price and capacity choices subject to capacity or cost constraints, conducting comparative statics with respect to demand variance and marginal costs, and interpreting implications for market outcomes and firm strategy. Require mathematical derivations and concise economic interpretation.]