Bounded Rationality in a Cournot Duopoly Game

Abstract

This paper analyzes choices and welfare in a Cournot duopoly setting with linear demand using four models of bounded rationality. The models studied in this paper are Level-k, Cognitive Hierarchy, Asymmetric Quantal Response and Noisy Introspection. It is found that in the Level-k model choices, profits and welfare alternate around the Nash Equilibrium levels depending on whether the level is odd or even. In the Cognitive Hierarchy model the choices of the first two types (L-0 and L-1) coincide with the choices in the Level-k model, a L-2 produces a smaller quantity while the quantity of a L-3 is higher or lower depending on the value of a particular parameter in the model. Both in the Asymmetric Quantal Response and Noisy Introspection models, we find that choices are spread around the Nash Equilibrium level for all parameter values and thus welfare is below the Nash Equilibrium benchmark. We also use parameter estimates from other well-known experiments to obtain an approximation to empirically plausible welfare levels.

Keywords

• Cournot Game
• Bounded Rationality
• Level-k Model
• Asymmetric Quantal Response Equilibrium
• Noisy Introspection
• Cognitive Hierarchy