Optimal decision-making under uncertainties

We consider stochastic games wherein players are striving to make optimal decisions but their decisions are subject to mistakes or random shocks. We assume that the players make decisions in the direction of higher payoffs and yet they are in a uncertain environment. The dynamics of this kind of evolutionary games can be described by stochastic differential equations, which are solved and the payoffs are calculated using a Monte Carlo simulation. Then, sensitivities are evaluated so as to assess the impact of changes in decisions. Numerical results have shown that noisy environments can lead to important payoff variations and higher payoff sensitivities with respect to a player's decisions. We also discussed equilibrium concepts that may result from the players' abilities to learn from mistakes and adopt successful strategies.