The proposed Generalized Logit Dynamic (GLD) and Mean Field Game (MFG) models can be extended to incorporate more complex player interactions by introducing mechanisms that allow for strategic cooperation and competition among players. One approach is to modify the utility functions to include terms that account for the benefits of cooperation, such as shared resources or collective outcomes. This can be achieved by integrating cooperative game theory concepts, where players can form coalitions and share payoffs based on their joint strategies.
Additionally, the interaction structure can be enhanced by incorporating network effects, where players' decisions are influenced by their connections to others in a social network. This can be modeled using graph theory, where nodes represent players and edges represent potential cooperative or competitive relationships. By adjusting the transition rates in the GLD and the control costs in the MFG to reflect these interactions, the models can capture the dynamics of cooperation and competition more accurately.
Furthermore, the introduction of mixed strategies, where players randomize their actions based on the strategies of others, can also be integrated into the GLD and MFG frameworks. This would allow for a richer set of strategic interactions, enabling the models to reflect real-world scenarios where players may not always act in a purely competitive or cooperative manner.