Analysis of Pure and Mixed Strategy Equilibria for Heterogeneous Players with Cobb–Douglas Utilities

We investigate the strategic behavior of a single type of heterogeneous players within a one-shot game framework, where each player’s preferences are modeled using Cobb–Douglas utility functions. The heterogeneity arises from variations in individual utility parameters, capturing taste and crowding influences in players’ sensitivity to strategic choices. We analytically derive the conditions for the existence and stability of both pure and mixed strategies that form Nash equilibria under this nonlinear utility structure. The study explores the stability of equilibria based on the heterogeneity parameters that influence equilibrium outcomes and players’ strategic diversity. Numerical simulations are provided to illustrate the transition between pure and mixed strategy domains, demonstrating the sensitivity of equilibrium configurations to the degree of heterogeneity. The results in this paper will contribute to understanding how Cobb–Douglas preferences shape (i) equilibrium selection among players, and (ii) stability in games with internally diverse yet structurally similar agents.