Forward-looking evolutionary game dynamics subject to exploration cost
This work addresses theoretical modeling in evolutionary game theory, offering an incremental extension to existing frameworks.
The authors tackled the problem of extending classical evolutionary game dynamics by incorporating forward-looking behavior and exploration costs, showing that this can be modeled as a mean field game with a unique solution under certain conditions.
We extend classical evolutionary game dynamics based on the momentary action choices of agents by accounting for two elements: forward-looking behavior and exploration cost. We focus on pairwise comparison protocols that cover major evolutionary game dynamics, such as replicator and logit models. In the proposed mathematical framework, agents update their actions by paying a cost so that a utility or its relative difference is maximized. We show that forward-looking behavior can be modeled as a coupling between the evolutionary game dynamic and static Hamilton-Jacobi-Bellman equation: a mean field game. The exploration cost and its constraint are naturally related to these equations as a function of the optimal Lagrangian multiplier serving as a relaxation parameter, and it is incorporated into the game as a constraint. We show that under certain conditions, our evolutionary game dynamic admits a unique solution. Finally, we computationally investigate one- and two-dimensional problems.