The potential game assumption, which posits that the utility functions are concave and lead to unique equilibria, may impose limitations in scenarios where player interactions are more complex or where the utility functions exhibit non-concave characteristics. In such cases, the existence of multiple equilibria or unstable dynamics can arise, complicating the analysis and interpretation of results.
To adapt the models to handle more general game structures, one approach is to relax the potential game assumption and allow for non-concave utility functions. This can be achieved by employing generalized Nash equilibrium concepts, where players' strategies are interdependent and can lead to multiple equilibria. Additionally, incorporating stochastic elements into the models can help capture the uncertainty and variability in player behavior, allowing for a more robust analysis of dynamic interactions.
Another adaptation could involve the use of evolutionary stable strategies (ESS) or replicator dynamics, which can provide insights into the stability of strategies in more complex games. By integrating these concepts into the GLD and MFG frameworks, the models can better accommodate a wider range of strategic interactions and provide a more comprehensive understanding of player behavior in various contexts.