Adaptive agents on evolving networks

In this work we study the learning dynamics for agents playing games on networks. We propose a model of network formation in repeated games where players strategically adopt actions and connections simultaneously using a reinforcement learning scheme which is called Boltzmann-Q-learning. This adaptation scheme in the continuous time limit has a proven relation to the evolutionary game theory through replicator dynamics. We assume that the agents adapt to their environment through a simple reinforcement mechanism. Among different reinforcement schemes, here we focus on (stateless) Q-learning. Within this scheme, the agents’ strategies are parameterized through so called Q–functions that characterize relative utility of a particular strategy. After each round of game, the Q functions are updated according to the following rule: