Algorithmic Risk-Aware Optimization in Stochastic Duopoly: Nash Equilibrium with Pareto Payoffs

This chapter develops a framework for risk-aware optimization in stochastic Cournot duopoly games. We investigate how firms can strategically adjust from risk-neutral to risk-averse or risk-seeking behavior by tuning a risk parameter that governs sensitivity to variance. Analytical results establish closed-form expressions for the Nash equilibrium and Pareto frontier under full information, providing a benchmark for optimal decision-making. To bridge theory and practice, we introduce distributed and adaptive algorithms that require only limited information exchange, enabling firms to converge to Nash equilibria whose payoffs are enhanced to match Pareto-optimal outcomes. Numerical examples demonstrate how risk preferences shift equilibrium production and profits and show that efficient coordination and fairness can emerge even under uncertainty and partial information.